Note: Descriptions are shown in the official language in which they were submitted.
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QUANTUM COMPUTING INTEGRATED DEVELOPMENT
ENVIRONMENT
CROSS REFERENCE TO RELATED APPLICATIONS
This application is a continuation-in-part of U.S. Patent Application Serial
No. 10/028,891 filed on December 22, 2001, which is incorporated herein, by
reference, in its entirety.
1.0 FIELD OF THE INVENTION
The invention relates to quantum computers and to methods and apparatus
for simulating the operation of a quantum computer.
2.0 BACKGROUND
2.1 QUBITS
A quantum bit or qubit is the building block of a quantum computer in the
same way that a conventional binary bit is a building block of a classical
computer. The conventional binary bit always adopts the values 0 and 1. The
values 0 and 1 can be termed the basis states of a conventional bit. A qubit
is
similar to a conventional binary bit in the sense that it can adopt basis
states as
well. The basis states of a qubit are referred to as the ~0) basis state and
the ~1)
basis state. During quantum computation, the state of a qubit is defined as a
superposition of the ~0) basis state and the ~1) basis state. This means that
the
state of the qubit simultaneously has a nonzero probability of occupying the
~0)
basis state and a nonzero probability of occupying the ~1) basis state. The
ability
of a qubit to have a nonzero probability of occupying a first basis state
(~0)) and a
nonzero probability of occupying a second basis state (~1)) is different from
a
conventional bit, which always has a value of 0 or 1.~
Qualitatively, a superposition of basis states means that the qubit can be in
both basis states ~0) and (~1)) at the same time. Mathematically a
superposition of
basis states means that the overall state of the qubit, which is denoted
~~I'), has the
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form
~~') = a~0) + ~~1)
where a and (3 are probability amplitudes. The terms a and (3 each have real
and
imaginary components. Typically, when the state of a qubit is measured (e.g.,
read out), the quantum nature of the qubit is temporarily lost and the
superposition of basis states collapses to either the ~0) basis state or the
~1) basis
state, thus regaining its similarity to a conventional bit. The actual state
of the
qubit after it has collapsed depends on the probability amplitudes a and (3
immediately prior to the readout operation.
For discussion of qubit operations and control systems for performing
quantum computation, see United States Patent Application Serial No.
09/872,495, "Quantum processing system and method for a superconducting
phase qubit," filed June 1, 2001, which is hereby incorporated by reference in
its
entirety.
2.1.1 FLUX QUBITS
A number of physical implementations of qubits exist. One such proposal
is a superconducting flux qubit. See Mooij et al., 1999, Science 285, 1036,
which is hereby incorporated by reference in its entirety. The flux qubit
consists
of an internal superconducting loop that includes three or more Josephson
junctions, inductively coupled to an external dc-SQUID that includes two
Josephson junctions. The dc-SQUID has leads through which a bias current can
be driven. The bias current through the leads provides a basis for operating
on
the inner loop, which forms the qubit.
The Mooij qubit can be biased to adjust the energy-phase profile. This
DC bias or flux bias adjusts the relative values of a double well of the
energy
phase profile that describes the qubit. Coupling of flux qubits can be
accomplished using inductive coupling that leads to sigma x and sigma z
interactions between respective qubits in the Hamiltonian of the quantum
system
that describes the coupled flux qubits. Direct inductive coupling can be used
to
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couple flux qubits. See, for example, Makhlin et al., 2001, Rev. Mod. Plays.
73,
357, which is hereby incorporated by reference in its entirety.
2.1.2 CHARGE QUBITS
An example of a charge qubit is the superconducting electron box
proposed by Shnirman and Schon, 1998, Phys. Rev. B 57 15400. The box
consists of a superconducting island connected by a Josephson junction to a
superconducting electrode with capacitive coupling C to a gate electrode. A
control voltage Vx is applied using a gate capacitor. The Josephson junction
is
characterized by the Josephson energy E~ (which is related to the Josephson
critical current Ic by E' = to ~ol2~c, and ~o = hl2e is the flux quantum) and
by
the capacitance CJ which determines the charging energy scale. In this system,
charge in the box and phase across the junction are cannonically conjugated
variables. The system will decohere if it is not superconducting, i.e.
currents are
kept below Ic. The bit states are pseudo spin variables that correspond to
charge
states ~,~ > _ ~n> and ~T> _ bra + 1>, where n is an integer number of Cooper
pairs.
2.1.3 ELECTRONS ON HELIUM
Another qubit ~s "electrons on helium". The electrons of this class of
qubit behave like artificial single electron atoms governed by the Bohr model.
The wave functions of the first and second excited state are the bit states of
the
qubit. The first and second excited states in this type of qubit are not
degenerate
(i.e., they do not have the same energy). A vertical potential well V(z) a -
1/z
confines the electrons. The system has analogous behavior to atomic models
with its own Rydberg constants and Bohr radius, aB that depends on the isotope
of
helium used. The system is therefore analogous to a well studied model in
mathematical physics. There is an energy transition from the first state with
expectation value <zo> = 1.5 aB to the expected vertical position of the
second
~30 state <zl> = 6 aB, The energy difference is f,. _ (El Eo)/h in frequency
units.
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Therefore, pulses like those used in NMR studies can be used to elevate the
state
of these individual artificial atoms. The electrons would be arranged in an
artificial crystal structure called a Winger crystal. Each atom would be
addressable, allowing the tuned pulse to interact with the atoms. The qubit-
qubit
interactions are described by a Hamiltonian that has terms proportional to all
the
Pauli matrices and their complex linear combinations. The qubit-qubit
interaction is always on and is only modulated by range. See Lea et al. and
Dykman et al. in Braunstein and Lo (Eds.), 2001, Scalable Quafztum Computers,
Wiley-VCH Berlin, which is hereby incorporated by reference in its entirety.
2.2 QUANTUM COMPUTING
2.2.1 QUANTUM COMPUTING DEFINED
Research on what is now called quantum computing traces back to
Richard Feynman. See, e.g., Feynman, 1982, Int. J. Theor. Phys. 21, 467, which
is hereby incorporated by reference in its entirety. Feynman noted that
quantum
systems are inherently difficult to simulate with classical (e.g.,
conventional, non-
quantum, digital) computers, but that this task could be accomplished by
observing the evolution of a quantum system under controlled circumstances.
Solving a theory for the behavior of a quantum system commonly involves
solving a differential equation related to the system's Hamiltonian. Observing
the behavior of the system provides information regarding the solutions to the
equation.
Quantum computing efforts were initially concentrated Qn building the
formal theory or on "software development" or extension to other computational
problems. Discovery of the Shor algorithm and the Grover algorithm were
important milestones in quantum computing. See, e.g., Shor, 1997, SIAM J. of
Comput. 26, 1484; Grover, 1996, Proc. 28th STOC, 212 (ACM Press, New
York); and Kitaev, LANL preprint quant-ph/9511026, each of which is hereby
incorporated by reference in their entireties. The Shor algorithm permits a
quantum computer to factorize large natural numbers efficiently. Using the
Shor
algorithm, a quantum computer could render obsolete all existing "public-key"
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encryption schemes. In another application of the Shor algorithm, quantum
computers (or even a smaller-scale device such as a quantum repeater) could
enable absolutely safe communication channels where a message, in principle,
cannot be intercepted without being destroyed in the process. See, Briegel et
al.,
preprint quant-ph/9803056, which is hereby incorporated by reference in its
entirety. Showing that fault-tolerant quantum computation is theoretically
possible opened the way for attempts at practical realizations. See, e.g.,
Knill et
al., 1998, Science 279, 342.
Quantum computing generally involves initializing the states of N
quantum bits (qubits), creating controlled entanglements among them, allowing
these states to evolve, and reading out the qubits after the states have
evolved.
Therefore, qubits are the fundamental building blocks of a quantum computer.
As described above, a qubit is conventionally a system having two degenerate
(i.e., of equal energy) quantum states, with a non-zero probability of being
found
in either state. Because of this non-zero probability, N qubits can define an
initial
state that is a combination of 2N classical states. This initial state
undergoes an
evolution, governed by the interactions that the qubits have among themselves
and with external influences. This evolution of the states of N qubits defines
a
calculation or in effect, 2N simultaneous classical calculations. Reading out
the
states of the qubits after evolution is complete determines the results of the
calculations.
2.2.2 BASIC REQUIREMENTS FOR REALIZING QUANTUM COMPUTING
The ability of a qubit to adopt a superposition of its basis states is one
basis for the power harnessed by a quantum computer. However, in order to be
useful in a quantum computer, the qubit must be combined with other qubits to
form a quantum register. In fact, the capacity for a quantum register to
represent
information grows exponentially with the number of qubits in the quantum
register. The computing power and nature of quantum computers are known and
described in the art. See, e.g., Shor, U.S. Patent No. 5,768,297, which is
hereby
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incorporated by reference in its entirety.
In addition to the requirement of combining qubits into a quantum
register, DiVincenzo sets forth a number of requirements necessary to realize
a
physical system that is capable of quantum computation. See DiVincenzo, in
Scalable Quantum Computers, chapter 1, 2001, Wiley-VCH Verlag GmbH,
Berlin, which is hereby incorporated by reference in its entirety. These
requirements include the need to initialize the state of the qubits to a
simple
fiducial state, the need for long relevant decoherence times, a "universal
set" of
quantum gates, and qubit-specific measurement capability.
2.2.3 THE UNIVERSAL SET OF QUANTUM GATES REQUIREMENT
As discussed in Section 2.2.2, above, any physical system capable of
quantum computation must provide a universal set of quantum gates so that the
state of each qubit in the physical system can evolve in a controlled manner.
The
minimum set of gates required to realize a universal set of quantum gates is
set
forth by DiVincenzo in Scalable Quantum. Computers, Wiley-VCH, Berlin, 2001,
Braunstein and Lo, eds. In brief, a universal set of quantum gates includes
single
qubit operations as well as at least one two-qubit operation.
A single qubit can be considered a vector ~'I') = a~0) + b~1) parameterized
by two complex numbers, a and b, satisfying ~ a ~ 2 + ~ b ( 2 =1. Operations
on a
qubit must preserve this norm, and thus such operations are described by 2x2
matrices. Some 2x2 matrices are the Pauli matrices
_ 0 1
W =6x=X - 1 0
_ _ _ 0 -i
62 6'' Y a 0
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_ _ 1 0
63 -6z -Z 0 -1
The Pauli matrices 6X, 6y, and 6Z are three single-qubit operations. For
more information on gates, see Nielsen and Chuang, 2000, Quantum
i
Computation and Quantum Information, Cambridge University Press,
Cambridge, UK which is hereby incorporated by reference in its entirety.
2.2.4 SET OF MATRICES AVAILABLE FOR A 2-QUBIT QUANTUM
COMPUTING SYSTEM
Fig. 4 illustrates the set of matrices available for a 2-qubit quantum
computing system, including the possible states of the quantum register.
Matrix
400 illustrates the possible states of the 2-qubit system as correlated with
standard binary notation. The quantum register can simultaneously exist in a
superposition of each of the states, having some complex probability 'yo, yi,
'Yz,
and y3 of being in each of the states, respectively. Matrices 410 and 411
represent
the matrices of the X operator acting on the first and second qubits in a
quantum
register respectively. Matrices 420 and 421 represent the matrices of the Z
operator acting on the first and second qubits in a quantum register,
respectively.
Matrices 430 and 431 represent the matrices of the Y operator acting on the
first
and second qubits in a quantum register, respectively. Matrix 440 represents
the
matrix of the coupling operator acting to couple the first and second qubits
in the
quantum register, wherein the coupling operation represents a controlled phase
operation. In an N qubit quantum register, these matrices can be scaled to
become 2Nx2N matrices acting on the corresponding qubit or qubits.
2.3 PHYSICAL SYSTEMS FOR PERFORMING QUANTUM COMPUTING
Several physical systems have been proposed for the qubits in a quantum
computer. One qubit system uses molecules having degenerate nuclear-spin
states. See United States Patent 5,917,322 to Gershenfeld and Chuang, which is
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hereby incorporated by reference in its entirety. Nuclear magnetic resonance
(NMR) techniques can read the spin states. These systems have successfully
implemented a search algorithm. See, e.g., Mosca, 1998, Nature 393, 344, which
is hereby incorporated by reference in its entirety. See also the number-
ordering
algorithm of Vandersypen et al., preprint quant-ph/0007017 which is hereby
incorporated by reference in its entirety. The number-ordering algorithm is
related to the quantum Fourier transform, an important element of both Shor's
factoring algorithm and Grover's algorithm for searching unsorted databases.
Further proposals for physical systems for quantum computing are described
above in Section 2.1.
2.4 QUANTUM COMPUTING PROGRAMMING LANGUAGES
Proposals for quantum computing programming languages and
architectures have been made. See, e.g., Bettelli et al., 2001, "Toward an
architecture for quantum programming", LANL cs.PL/0103009 v.2, which is
hereby incorporated by reference in its entirety. Bettelli et al. investigates
a
possible approach to the problem of programming quantum computers. The
reference provides a template high level quantum language that complements a
generic general purpose classical language with a set of quantum primitives.
The
underlying scheme involves a run-time environment that calculates the byte-
code
for the quantum operations and sends it to a quantum device controller or to a
simulator.
Bettelli et al., however, fails to address the complexities related to the
different physical embodiments of quantum computers, and thus does not teach
reduction of quantum computing instructions to the byte-code level that is
needed
in order to control a quantum computer. Furthermore, although Bettelli et al.
recognizes that a high level quantum language must allow an automated scalable
procedure for translating and optionally optimizing the high level code down
to a
sequence of low level control instructions for quantum machines, such a
scalable
procedure is not taught in the paper. Furthermore, the Bettelli et al. high
level
language is merely abstract. It provides no details on how such a language
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work with actual physical systems. In summary, Bettelli et al. teaches a high
level programming language that cannot drive an actual quantum computing
system.
Furthermore, current quantum simulators have little basis in any physical
quantum computing proposals. See, for example, QuCalc (Paul Dumais,
Laboratory for Theoretical and Quantum Computing, University of Montreal).
QuCalc is a commonly used Mathematica package (Wolfram Research Inc.,
Champaign IL) that simulates quantum computing operations. QuCalc is based
on qualitative quantum computing. However, QuCalc does not consider the
constraints, limitations, or characteristics of physical quantum computing
systems.
Given the above background, there is a need in the art for a development
tool that addresses the physical parameters required to operate quantum
computing systems and to optimize instructions that are executed in such
systems.
3.0 SUMMARY OF THE INVENTION
The present invention provides a quantum computing integrated
development environment and methods for designing quantum logic with a
plurality of qubits, compiling the quantum logic into a set of quantum machine
language instructions, executing the quantum machine language instructions,
and
outputting the results generated by the execution of the quantum machine
language instructions. In contrast to prior art systems and methods, the
interface
of the present invention allows for the design and testing of quantum
computing
programs that talces into account the unique characteristics of the scalable
quantum device that such programs will be executed on.
Designing quantum logic includes selecting a quantum computing system
and designing a sequence of fundamental operators. The set of fundamental
operators depends on the choice of quantum computing system. Furthermore, a
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mechanism for designing quantum logic can include defining a sequence of
fundamental operators as an abstract operator (abstract quantum gate) and
designing a sequence of abstract operators. In some embodiments of the
invention, a mechanism for designing quantum logic includes performing a
readout operation, and defining conditional operations that can be executed
based
on the desired conditions. In one example, a readout operation includes
performing a readout operation of one or more qubits in a quantum register.
Such
readout operations collapse the quantum state of the qubit to a binary
equivalent.
Conditional behavior can include application of fundamental operators
(fundamental gates) or abstract operators (abstract quantum gates) on one or
more
qubits in the quantum register. The conditional operations can be applied to
one
or more of the collapsed qubits or non-collapsed qubits.
Designing quantum logic can further include setting driver details for a
quantum register. The driver details for the register depend on the choice of
quantum computing system. The driver details may include parameters such as
the minimum duration for application of fundamental operators or the sharpness
of the pulses that can be applied. Designing quantum logic can further include
preparing the initial conditions of each of the qubits in the quantum
computing
system.
Compiling quantum logic to a set of quantum machine language
instructions includes collapsing a set of abstract operators into a set of
fundamental operators. A mechanism for compiling quantum machine language
instructions can further include collapsing a sequence of fundamental
operators in
accordance with a set of rules for optimizing fundamental operators.
The quantum machine language instructions are executed by a quantum
register and are regulated by a control system for interacting with the
quantum
register. A quantum register includes an array of qubits. The basic operations
performed on a quantum register are an initialization operation, evolving the
state
of the quantum register by application of a set of fundamental operators, and
a
readout operation. The control system can interact with the quantum register
to
coordinate and time each of the respective operations, as specified by the
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quantum machine language instructions. In some embodiments of the invention,
the quantum machine language instructions are executed by a simulator of a
quantum computing system (quantum computer).
Once execution of said machine language instruction set is complete, the
quantum register exists in a quantum superposition of its basis states. Such a
superposition can then be collapsed to a single basis state to provide a
result to
the calculation. The final state of the quantum computing system after
execution
of the quantum machine language instructions provides the result of the
calculation.
Some embodiments of the invention allow a user to choose a desired
hardware platform, and then provide tools that will aid in designing machines
at
the hardware, machine language, logic, and software levels. An embodiment of
the invention allows the user to control each of these aspects, providing an
"integrated development environment" (IDE) in which all phases of
computational engine design may be accomplished.
4.0 BRIEF DESCRIPTION OF THE DRAWINGS
Fig. 1 is a system 10 that is operated in accordance with one embodiment of
the
invention.
Fig. 2 is a flow diagram illustrating interactions amongst components of a
quantum computing, integrated development environment, in accordance with
some embodiments of the invention.
Fig. 3A is an entity-relationship diagram describing a quantum logic design
process, in accordance with some embodiments of the invention.
Fig. 3B is a block diagram illustrating components of an execution portion of
a
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quantum computing, integrated development environment, in accordance with
some embodiments of the invention.
Fig. 3C is a block diagram illustrating components of an output portion of a
quantum computing, integrated development environment, in accordance with
some embodiments of the invention.
Fig. 4 illustrates a collection of fundamental operations associated with a
two-
qubit quantum system, in accordance with the prior art.
Fig. 5 is a block diagram of a quantum computing, integrated development
environment used as a calibration tool for a quantum computing environment, in
accordance with some embodiments of the invention.
Figs. 6A-6B illustrate embodiments of interfaces of the present invention for
the
circuit and machine language design mode for the quantum computing, integrated
development environment.
Figure 7 illustrates another embodiment of the circuit and machine language
design mode for the quantum computing, integrated development environment.
Figs. 8A-8C illustrate embodiments various aspects of the quantum logic design
mode in the quantum computing, integrated development environment.
Figs. 9A and 9B illustrate two embodiments of a run mode interface.
Fig. 10 illustrates an embodiment of an abstract quantum gate.
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Like reference numerals refer to corresponding parts throughout the
several views of the drawings.
5.0 DETAILED DESCRIPTION OF THE INVENTION
Any sequence of quantum logic can be broken down in terms of
fundamental operations or "gates". For information on gates, see Section
2.2.3,
above. Thus, these gates make up an important part of the quantum machine
language of the quantum computer, along with instructions for initialization
and
readout operations. As described in Section 2.2.2, quantum computing systems
must provide a basic set of quantum operations, or fundamental operators,
which
are specific to that system. In order to be suitable for quantum computation,
a
quantum system must be designed to provide 6X operations, hereinafter referred
to
as "X" operations, sz operations hereinafter referred to as "Z" operations, 6Y
operations, herein after referred to as "Y" operations, and an entanglement
operation, or a subset of these operations.
One known quantum computing system is nuclear magnetic resonance
(NMR). An NMR can achieve all necessary fundamental operations. Other
systems that can achieve all necessary fundamental operations include flux
qubits, charge qubits, and electrons on Helium. The computational space
available for a quantum computation grows with the number of qubits associated
with that system as 2N, where N is the number of qubits in the system.
Building
and designing algorithms for quantum systems is a highly complex task as it
involves working with matrices of sizes 2Nx2N.
5.1 REPRESENTATIVE SYSTEM
Fig. 1 illustrates a system 10 that is operated in accordance with one
embodiment of the invention. System 10 includes at least one digital (binary,
conventional) computer 20. Computer 20 includes standard server components
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including a central processing unit 22, memory 24 (including high speed random
access memory as well as non-volatile storage, such as disk storage 14) for
storing program modules and data structures, user input/output device 26, a
disk
controller 12, a network interface card 16 and one or more busses 34 that
interconnect these components. User input/output device 26 includes one or
more user input/output components such as a mouse 36, display 38, and keyboard
8.
Memory 24 includes a number of modules and data structures that are
used in accordance with the present invention. It will be appreciated that at
any
one time during operation of the system, a portion of the modules and/or data
structures stored in memory 24 will be stored in random access memory while
another portion of the modules andlor data structures will be stored in non-
volatile storage. In a typical embodiment, memory 24 includes an operating
system 40. Operating system 40 includes procedures for handling various basic
system services and for performing hardware dependent tasks.
In a typical implementation, the programs and data stored in system
memory 24 further include a quantum computing, integrated development
environment (QC-IDE) module 44 for designing quantum logic, compiling the
quantum logic into quantum machine language instructions, executing the
quantum machine language instructions, and providing as output the results of
the
execution. QC-IDE 44 can be used to develop quantum algorithms, to optimize
quantum algorithms, and to perform quantum computation. QC-IDE 44 includes
a circuit layout interface module 620, a machine language interface module
610,
a pulse magnitudes interface module 611, an initial conditions interface
module
615, a control panel module 630, a global settings interface module 640, a
toolbar
menu module 650, and a system information interface module 660. These
modules will be described in further detail below in conjunction with Figs. 6
through 8. Some embodiments of QC-IDE 44 are used to model quantum
systems such as many-body electron systems, nuclear fusion or nuclear fission,
or
for modeling protein folding systems and the like. In particular, some
embodiments of QC-IDE 44 are useful for modeling the structure of proteins,
nucleic acids and other biological macromolecules in solution as well as
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determining interaction energies between such macromolecules and organic
compounds. Memory 24 further includes at least one time resolved set of
operators 48 that are produced using QC-IDE module 44. The time resolved set
of operators 48 is compiled by compiler module 50 form machine language
instructions 52 which are then executed by execution module 54 and output to a
device by output module 56.
System 10 further includes a quantum computing system 70 that includes
a quantum register 72. The quantum register, in turn, contains a plurality of
qubits 74. A control system for implementing the fundamental operations on .
each of the qubits in the quantum register, and a control processor for
coordinating the operations is required. In system 10, such coordinating
functionality is provided as driver hardware 58 in computer 20.
Although only one quantum computing system 70 is illustrated in
illustrated system 10, in practice, system 10 may have any number of quantum
computing systems 10. Further, there is no requirement that each quantum
computing system 70 in system 10 have the same type of qubits or architecture.
For example, some quantum computing systems 70 in system 10 may include one
or more quantum registers 72 that include flux qubits 74 while other quantum
computing systems 70 in system 10 may include one or more quantum registers
72 that include charge qubits 72. Further, some quantum computing systems 70
in system 10 may include one or more quantum registers 72 that are hybrid
registers, for example, including both flux qubits and charge qubits. Driver
hardware 58 is used to track the characteristics of each of the quantum
computing
systems 70 used in system 10, as described in further detail below.
5.2 PROCESS FLOW
Fig. 2 is a flow diagram of an embodiment of the invention. Quantum
logic design is derived in design stage 202 using QC-IDE 44. This results in
the
production of a time resolved set of operators 48 that are described in
further
detail below. In compilation stage 204, the quantum logic derived in design
stage
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202 (time resolved set of operators 48) is compiled by compiler module 50 into
a
sequence of quantum machine language instructions 52. Instructions 52 may
include classical machine language instructions that can be executed by a
classical (e.g. digital, computer 20) computer, but typically include at least
one
quantum machine language instruction capable of execution on quantum
computing system 70 (Fig. 1). In execution stage 206, instructions 52 are
executed in a quantum computing system 70 and/or computing system 20.
Finally, in output stage 208, the results of the calculation are provided as
output
by output module 56.
Quantum computing logic that is derived in design stage 202 can be
defined as a sequence of unitary transformations acting on a quantum state.
The
fundamental operations of quantum computing logic include the set of quantum
unitary transformations that a quantum computer can implement. Generally, the
fundamental operations consist of X, Y, Z, and an entanglement operation. In
some embodiments, a ground or readout operation is included.
In some embodiments, methods for designing quantum logic during
design states 202 include creating a time-resolved sequence of fundamental
operators 48, such that the combination, when applied to the initial state of
quantum system 70, evolves the initial state of quantum system 70 to some
final
state. In some embodiments, methods for designing quantum logic include
obtaining the output results 208 illustrated in Fig. 2, adjusting the sequence
of
fundamental operators 48 as required, and iterating the process illustrated in
Fig.
2 until the desired quantum logic has been implemented.
In accordance with some embodiments of the present invention, designing
quantum logic 202 includes controlling the characteristics of driver hardware
58.
Driver hardware 58 is a control system for implementing the fundamental
operations on each of the qubits in the quantum register. Driver hardware 58
includes a time unit setting for defining the resolution or minimum duration
of
each operation in the time resolved set of operators 48. Further, the
sharpness of
the pulses in the time resolved set of operators 48 can be calibrated in
accordance
with the characteristics of driver hardware 58. Optimal driver settings
ultimately
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depend on the physical characteristics of quantum computing system 70. For
example, United States Patent Application No. 09/872,495, incorporated herein
by reference in its entirety, describes current pulses with a frequency on the
order
of a gigahertz, and magnitudes on the order of nanoamperes. Such driver
settings
58 can be useful for phase or flux qubits, but other physical systems may
demand
different driver settings.
In some embodiments of the invention, the target quantum computing
system 70 can be selected before quantum logic 48 is designed. When a target
quantum computing system 70 is selected, the driver hardware 58 details vary
according to the requirements of that platform. However, at any point, the
driver
details 58 for that platform 70 can be modified in order to aid in the design
of an
algorithm that is executed on the designated quantum computing platform 70.
In some embodiments of the invention, designing quantum logic includes
defining the number of qubits 74 required and the possible connections between
them (fundamental operators), using QC-IDE module 44. Defining such
fundamental operators requires (i) selecting the desired operator sequence,
(ii)
setting the appropriate driver conditions, (iii) setting the initial state of
each of the
qubits 74 in the quantum register 72, (iv) compiling the sequence of
operations
into quantum machine language instructions 52, (v) executing the quantum
machine language instructions 52 on quantum computing system 70, and (vi)
assessing the result of the executed sequence of operations using output
module
56. If the output from the calculation does not satisfy the desired output,
the
process is repeated by iteratively re-designing the pulse sequence 48 using QC-
IDE module 44 until the desired results are obtained.
In some embodiments of the present invention, quantum logic 48 includes
one or more abstract quantum gates 1000 (Fig. 10). Each abstract quantum gate
1000 includes a sequence of fundamental operations (gates) 1002 and driver
characteristics 1004. An abstract quantum gate 1000 can be used to design high-
level quantum logic 48. As a sequence of fundamental operations (gates), 'each
abstract quantum gate 1000 can be combined with other abstract quantum gates
1000 to form a sequence of abstract quantum gates, thereby achieving high-
level
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quantum logic 48. In other words, each operation 1002 in an abstract quantum
gate 1000 can be a fundamental operation (gate) or an abstract quantum gate.
Some embodiments of the invention include creating abstract quantum
gates 1000, and designing high level quantum logic 48 that includes a sequence
of abstract quantum gates 1000. An abstract quantum gate 1000 can act upon a
single qubit 74 or a plurality of qubits 74. In some embodiments, an abstract
quantum gate 1000 includes a sequence of abstract quantum gates 1000. This is
particularly advantageous for designing complex quantum logic 48 that involves
many qubits 74.
In some embodiments of the invention, an abstract quantum gate 1000 is
designed by building the desired sequence of fundamental operators (e.g., the
Pauli matrices described in Section 2.2.3, above) and exporting the sequence
as
an abstract quantum gate 1000. Building a sequence of fundamental operators
. (gates) can be accomplished using QC-IDE module 44. Once a sequence of
fundamental operators (gates) 1002 has been designed, the sequence can be
defined as a single abstract gate 1000. In some embodiments of the present
invention, an abstract quantum gate 1000 can then be used with a high-level
quantum logic design tool.
In some embodiments of the invention, memory 24 includes one or more
libraries of abstract operators 1002 (not shown). Abstract operators 1000 in
such
libraries may be incorporated into a time resolved set of operators 48 during
design stage 202. Each library of abstract operators corresponds to a
particular
target quantum computing system 70. In this way, a library of abstract
operators
can be used to define the characteristics of a given quantum computing system
70. As a result, a quantum computing system 70 in system 10 can simulate
another quantum computing system accurately.
5.2 INTRODUCING CONDITIONAL STEPS INTO QUANTUM LOGIC
One aspect of the present invention provides quantum logic 48 (Fig. 1)
that includes a set of conditional actions. These conditions are based on the
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results of prior readout operation of a single qubit 74 or a plurality of
qubits 74.
A readout of a qubit 74 involves collapsing the state of the qubit such that
the
qubit returns a classical "1" or "0" and then measuring the value (0 or 1).
This
aspect of the invention is advantageous because quantum algorithms often
require
conditional actions that are based on the readout of a single qubit 74 or a
plurality
of qubits 74. See, for example, United States Patent 5,768,297 to Shor, which
is
hereby incorporated by reference in its entirety. Error decoding operations
typically involve reading out the state of certain ancillary qubits 74 and
performing operations on other qubits based on those measurements in order to
remove possible error from the information. Further, readout and subsequent
conditional behavior is typically used for quantum teleportation. In United
States
Patent 5,768,297, decoding a logical quantum state requires measuring two
qubits
and then performing a NOT quantum operation on a target qubit based on the
outcome of the readout of the first two qubits.
In one embodiment in accordance with this aspect of the invention,
quantum operations are executed based on the outcome of a prior readout
operation (or set of readout operations). This control logic is stored in the
time
resolved set of logic operators 48. In some embodiments, the readout operation
is
performed on a plurality of qubits 74 and conditional quantum logic based on
the
outcome of the readout operation is designed. This conditional logic is
applied to
a qubit 74 that remains in a quantum state (i.e. to a qubit that has not
undergone a
readout operation). A set of quantum operations that can be executed based on
the readout may include a set of fundamental operators and/or a set of
abstract
operators 1000, available to the respective quantum computing system 70.
Any fundamental operator, or defined set of fundamental operators,
available to QC-)DE 44 module can be used as a basis for conditional logic. To
illustrate, an exemplary quantum logic design 48 uses three qubits 74. After
some evolution of the set of three qubits 74 has occurred, the second and
third
qubit are read out. Then, a set of operators are applied, conditional on the
result
of the readout operations as illustrated by the following pseudocode:
if ( (readout of qubit 2 ) and (readout of qubit 3 ) are ifa bit state 1 )
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then apply a quantum operation to qubit(1 j
else
continue without applying any conditional quantum
operations.
In some embodiments of the invention, a set of conditional behavior can
be defined based on a set of readout operations on qubits 74 in quantum
computing system 70.
5.3 COMPILING THE TIME RESOLVED SET OF OPEARATORS
In order to convert quantum logic, expressed in the form of a set of
abstract operators 48, into a set of quantum machine language instructions 52
(Fig. 1), the abstract operations 1002 must first be compiled into an
equivalent set
of fundamental operators. Compiling quantum logic includes converting a set of
abstract operations 1002 into a set of fundamental operations, and
incorporating
the driver settings into the fundamental operations to create a set of quantum
machine language instructions 52.
Converting a set of abstract operators 1000 into a set of fundamental
operations includes optimizing the sequence of fundamental operations. Since
decoherence processes in quantum computing systems 70 render the time
required to execute a calculation of critical importance, optimization of the
set of
fundamental operations becomes important for execution of the quantum logic.
United States Patent Application Number 09/782,886, which is hereby
incorporated by reference in its entirety, describe rules for optimization
(reducing) a set of fundamental operators. In some embodiments of the
invention, these rules include commutation of fundamental operators, removal
of
empty time units, and removal of redundant pulse sequences or replacement of
such pulse sequences by simplified pulse sequences.
Commutation of fundamental operators allows quantum gates that do not
interfere with each other to overlap or change their order in time. For
example,
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an X operation on qubit 74-1, does not interfere with an X operation on qubit
74-
2, and the time-resolved sequence X(1)X(2) is the same as X(2)X(1).
Commutation operations depend are quantum computing system 70 dependent,
since the choice of quantum computing system 70 determines which fundamental
operators commute. For example, the effect of a coupling operation between two
qubits 74 can depend on the nature of the coupling, and the coupling in turn
depends on the quantum computing system 70 used.
Once a desired logic 48 has been developed, it can be defined as an
abstract quantum operator for that quantum computing system 70. A set of
abstract quantum operators can be used to implement high-level quantum logic
such as a quantum Fourier transform (QFT), for example. See, e.g., United
States
Patent Application No. 09/782,886 to Blais, which is hereby incorporated by
reference in its entirety This high level of quantum algorithm development
provides a level of abstraction useful for building such complex quantum
algorithms. Further, due to the sensitivity of quantum computing systems to
possible errors, individual qubit states can be encoded as logical qubits,
wherein a
plurality of physical qubits can be used to encode a single qubit state, such
that
the state is protected from errors during the computation. Such algorithms can
include aspects similar to classical error correction algorithms, See, e.g.,
United
States Patent 5,768,297 to Shor, which is hereby incorporated by reference in
its
entirety.
When high level quantum logic 48 is used for design, some lack of
efficiency results when a set of abstract operators are directly converted to
a set
of quantum machine language instructions 52. For example, in United States
Patent Application No. 09/782,886, a controlled not (CN) gate is defined as
the
following sequence of fundamental operations:
.3~t
CNrs = a 4 ~sCprs~s~s~s~rCprs '
Where r and s are two qubits 74 and Z and X are as defined in Section 2.2.3.
This pulse sequence consists of fundamental quantum gates that are available
in
most solid state quantum computing systems. Here, the CPrs gate is an
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entanglement operation between two qubits having the effect of a ZrZs
operation.
A SWAPl2 quantum gate is defined as:
SWAP12 = CN12CN21CN12 ,
thus, by defining the CNrs operation between two qubits as an abstract
operator,
the SWAPrs operator can be further defined as an abstract quantum operator
using
a sequence of the CNrs abstract quantum operators. Direct conversion of the
sequence described above for the SWAP abstract operator to a sequence of
fundamental operators results in some degree of redundancy. Using optimization
rules such as commutation of operators, certain simplifications can be
automated,
in accordance with some embodiments of the invention. For example, the CNrs
illustrated above can be re-sequenced as:
3~c
2 4 ~'S Cprs~s r~s
where the square brackets offset the operators that can be performed
simultaneously, thus reducing the total required time to execute the CNis
operation. Similar reductions result from the fundamental operators associated
with the SWAP expansion.
In some embodiments of the invention, quantum logic can be designed
using fundamental operators of the quantum computing system 70 directly. In
this case, QC-IDE module 44 can be used to optimize the set of fundamental
operations, and compiling includes combining driver details with the set of
fundamental operators to be executed on the quantum computing system 70.
The quantum machine language 52 used in the compilation process can
vary depending on the target quantum computing system 70. Different quantum
computing systems 70 can have different sets of fundamental operators. A
quantum computing system has operators sufficient to form a universal set.
Some embodiments of the invention can compile quantum logic in terms of
quantum machine language 52 that is specific to a predetermined quantum
computing system 70.
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5.4 QUANTUM MACHINE LANGUAGE INSTRUCTIONS
Once the quantum logic 48 and driver 58 details are compiled, a set of
quantum machine language instructions 52 exist that can be executed. The
nature
of the machine language instructions 52 depend upon the mechanism for
executing those instructions. For example, a mechanism for executing the
instruction set can be a particular quantum computing system 70, or a
simulation
of that system resident in memory 24 of digital computer 20. Thus, the set of
fundamental operators available varies for each quantum computing system.
A quantum machine language instruction set 52 can be executed on those
quantum computing systems 70 described herein. A quantum computing system
70 includes any quantum mechanical system where a set of basis states can be
used to compute in accordance with quantum mechanical principles. A quantum
system useful for quantum computing must provide at least some degree of
control over the information units or qubits 74 of the system. For example,
each
quantum computing system 70 must be able to initialize the state of a qubit
74,
perform a sequence of unitary evolutions of the qubit 74, and perform a
readout
operation on the state of the qubit 74. Quantum computing systems such as this
are termed "quantum registers" 72, where the operations required for quantum
computing is applied to a plurality of qubits 74. Quantum register structures
72
are described, for example, in United States Patent Application No.
09/872,495,
which is hereby incorporated by reference in its entirety.
5.5 QUANTUM LOGIC DESIGN PROCESSES
Figs. 3A, 3B and 3C illustrate quantum logic design processes in
accordance with various embodiments of the invention. Fig. 3A illustrates
operation sequence design tools found in some embodiments of QC-IDE module
44. These tools include tools for specifying driver details, specifying
initial
conditions of quantum computing system 70, and compiling an instruction set 48
into an instruction set 52 (Fig. 1). In some embodiments of the invention, the
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initial conditions of the qubits 74 in the quantum computing system 70 are set
to
the ~0> state by default.
The set of quantum machine language instructions 52 dictates which
operations are to be performed in the quantum register 72 in a time-resolved
manner. Once compiled, the quantum machine language instructions 52 are
executed by a control system (execution module 54) and driver (driver hardware
58), which makes use of the control aspects provided by a quantum register 72,
as
shown in Fig. 3B. In particular, Fig. 3B shows that instruction set 52 can be
simulated on digital computer 20 using simulation module 60. Alternatively,
the
instruction set 52 can be executed on a quantum computer 70. In some
embodiments, simulation module 60 is an ordinary differential equation solver.
When simulation module 60 is used, a superposition of states of the quantum
computing system are prepared based on input from the initial conditions.
Since
the initialization operation available in a quantum computer 70 can only
initialize
a qubit to either the ~0> or ~1> state, initialization to a superposition of
states is
physically unrealistic. For simulation purposes, however, it is sometimes
useful
to bypass the initialization process and initialize the quantum computing
system
directly to a desired state.
Fig. 3C illustrates how the results of the execution of quantum machine
language instructions 52 are provided as output. Useful forms of output
include
the final state of register 72, in terms of classical values, such as 0 or 1.
Further,
in instances where quantum machine language instructions 52 are simulated
using simulation module 60, the evolution of the quantum state of quantum
register 72 can be monitored on a plot that compares the normalized magnitudes
of the superposition of states. The reason simulation provides more data than
actual computation on a quantum computer 70 is that the readout operation on
quantum computer 70 collapses the states of qubits 74 into the classical
values
"0" or "1". Since no physical readout in required by simulation module 60,
there
is no need to collapse the quantum states of the simulated qubits and
therefore,
the matrices that represent such qubits can be output.
In some embodiments of the invention, quantum computing system 70
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can only be initialized to a classical state of either ~0> or ~1>. Thereafter
system
70 evolves to a superposition of basis states. In this case, a set of abstract
operators are used to provide quantum logic for evolving quantum computing
system 70 to a superposition of states useful for the calculation, prior to
actually
performing the desired quantum calculation.
5.6 SIMULATING A QUANTUM SYSTEM ON A CLASSICAL COMPUTER
As described above, in some embodiments of the present invention a
classical computer 20 can be used to design, compile, execute, and provide
output
for the quantum computing integrated development environment. Thus, in some
embodiments of the invention, a quantum computing system is simulated using a
classical computer 20.
Embodiments of the invention in which the quantum computing system is
simulated include the time-dependent Schrodinger equation (TDSE) in the
Hilbert space generated by N two level systems (qubits). A Hilbert space
represents all the possible values of one or more qubits. The Hamiltonian of a
N
qubit system can be represented as:
H~t~_~~0~~~lt~x +'~~~~~t~y +'~jlt~6~~'+'~'lkm~t~z~zn~
j=1 k<rn
where the first three terms are the Pauli matrices X, Y, and Z, combined with
the
driver details, ~ and s respectively, and the last term is a controlled-phase
type
coupling between qubits k and nz. The effect of an entanglement operation
depends on the particular embodiment of the invention. The states in the
Hilbert
space are labeled in the regular binary form, with "qubit 1" always the
rightmost
digit and "qubit N" always the leftmost.
In some embodiments of the invention, executing machine language
instruction set 52 includes simulating a quantum computing system 70. The
quantum register in such a simulated environment evolves according to the
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application of the available set of fundamental operators. As described above,
the simulated evolution of a quantum register can be described by solving the
time-dependent Schrodinger equation. The Hamiltonian of the system contains
all of the time-resolved behavior of the quantum system, including the
sequencing of fundamental operators as well as potential sources of error or
dissipation, and is represented by a 2Nx2N matrix, where N represents the
number
of qubits in the system. Each of the fundamental operators can be described by
a
2Nx2N unitary matrix, each of which correlates with a specific evolution of
the
state of the quantum register.
In some embodiments of the invention, a simulation of a quantum system
includes preparing a 2Nx2N time-dependent matrix representing the Hamiltonian
of the system to be solved, where N represents the number of qubits in the
system, and numerically solving the Schrodinger equation using the prepared
time-dependent Hamiltonian. A data structure useful for storing the
Hamiltonian
information can be a "Sparse Matrix" data type in which all elements in the
Hamiltonian are stored in a hash table, keyed by matrix entry value by row and
column, and each element in the matrix stores the time-dependent complex
numbers that represent a fundamental operator that is being applied. Some of
the
fundamental operators have matrices with entries only along the diagonal. A
data
structure useful for these fundamental operators can be a "diagonal matrix"
data
type, where the data type need only maintain information regarding 2N states,
which is the number of elements along the diagonal. Since the elements are
known to be placed linearly along the diagonal of the matrix, a sparse matrix
data
structure would reduce efficiency. Thus, the Hamiltonian can be generated by
summing each of the matrices for each of the fundamental operators being
applied to the system. In some embodiments of the invention, potential sources
of decoherence can be taken into account and further incorporated in the
Hamiltonian.
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5.7 CALIBRATING A QUANTUM SYSTEM
Some embodiments of the invention can be used to calibrate a quantum
computing system 70. Such embodiments include functionality for (i)
initializing
a quantum register 72, (ii) evolving register 72 to some superposition of
basis
states, (iii) evolving the state of quantum register 72, and (iv) reading out
the
result of the evolution. This functionality is useful for calibrating a single
qubit
74 in a quantum register 72. In such a calibration, a qubit 74 is initialized
and
subsequently read out in order to gather information regarding inherent
decoherence processes in the quantum computing system 70. Furthermore, after
initialization, a sequence of fundamental operators can be applied to the
qubit,
before the readout operation is applied. Through a process of repeated
measurement, a statistical analysis of that particular qubit 74 in the quantum
computing system 70 can be gathered as related to each of the fundamental
operations applicable to a single qubit 74 for the given quantum computing
system 70. The procedure can be extended to the calibration of a plurality of
qubits 74. Furthermore interaction operators between qubits can be calibrated
as
well using the systems and methods of the present invention.
Fig. 5 illustrates an application of the QC-IDE as a calibration tool for a
quantum computing environment. State 550 represents the initial state of the
quantum register for the calibration. This state depends on the number of
qubits
94 involved in the calibration. State 550 represents the initial state of the
register
as prepared by the control system. Typically, the register can begin in some
single classical state rather than in some superposition of states. Evolution
of the
initial state 550 of the quantum computing system can then be accomplished in
operation 555, where some sequence of fundamental operators is used to evolve
the state of the quantum computing system. Once the sequence of fundamental
operators has been applied, a readout operation 560 can be performed on the
quantum computing system. The output from the register can thus be correlated
with the input state and sequence of applied fundamental operators to
determine
information about the quantum system.
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5.8 THE INTERFACE MODE OF THE QC-IDE
Figs. 6 through 8 illustrate various aspects of the interface mode of QC-
IDE 44 in accordance with one embodiment of the present invention. Fig. 6A
illustrates the circuit layout interface module 620, machine language
interface
610, pulse magnitudes interface 611, initial conditions interface 615, control
panel 630, global settings interface 640, toolbar menus 650, and system
information interface 660.
Fig. 6A illustrates an example of a quantum program that implements a 2-
qubit quantum CNOT operation. The quantum CNOT operation involves two
qubits (620-1 and 620-2). One of the two qubits acts as a control and the
other
qubit acts as a target. The CNOT operation requires a coupling mechanism 620-
1,2 between the respective qubits (Fig. 6A). The circuit illustrated in
circuit
layout interface module 620 represents a general quantum computing scheme,
and can be designed to reflect the physical characteristics of any quantum
computing system 70.
Machine language interface 610 in Fig. 6A illustrates an example of a
pulse sequence for implementing a quantum CNOT operation. The horizontal
axis of chart 613 in interface 610 represents time units, where each number on
the
horizontal axis represents a successive time period (duration). Each row of
chart
613 represents a qubit gate to be applied to a designated qubit. For example,
row
613-1 of chart 613 is denoted "Q1 6x". This means a 6x gate is applied to
qubit
74-1 at each time period in which a pulse appears in row 613-1 in chart 613. A
pulse is represented by a raised vertical line in a given row at a given time
period.
For example, there is a pulse in time period 2 in row 614 of chart 613. This
means that a ~x gate is to be applied to qubit 74-2 during time period 2. In
the
example of Fig. 6A, the CNOT operation is represented as follows:
CNOT1,2 - e'3~4X2(~/2) C1,2(~/2) Z2(~c/2) X2(~/2)Z2(~/2) Zl(~t/2) Cl,z(~/2),
where XT(0) represents a single qubit bit-flip operation applied to qubit r
for a
phase 0, Zr represents a single qubit phase operation applied to qubit r for a
phase
0, Cr,s(0) represents a two-qubit controlled phase operation, which entangles
the
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states of qubits r and s again over a phase A, and e'3'~ø represents a global
phase.
The implementation and optimization of the quantum CNOT operation
will now be described above in detail. The rows in chart 613 represent, from
the
top, Xr(6), Yr(0), Zr(0), ground or readout operations, and Cr,s(0) operations
for
qubits 1 and 2 respectively. A raised bar in a row indicates that the
respective
gate is turned on during that time unit, representing a pulse of that
operation on
the respective qubit. The magnitudes of the pulses can be defined in pulse
magnitudes interface 611.
Machine language interface 610 represents the quantum machine
language to be executed on quantum computer 70. Once it is compiled, it
contains all relevant information that is important for the program to
execute. In
Fig. 6A, the hardware settings and pulse details can be defined by accessing
the
"Settings and Magnitudes" buttons 698 in driver panel 699 in machine language
interface 610.
The "Settings and Magnitudes" buttons 698 respectively open global
settings interface 640 and pulse magnitudes interface 611. Global settings
interface 640 allows the user to control the steepness of the applied pulses.
The
user can also define the time units to work in. Such time units are
illustrated in
Fig. 6A as 1.0 nano-seconds (ns). Pulse magnitudes interface 611 allows the
user
to set the default area under the applied pulses, which permits a degree of
freedom for the respective quantum gate.
Initial conditions interface 615 permits the user to prepare a desired initial
state for quantum system 70 by setting the complex states of each of the
qubits 74
respectively. The state of a qubit 74 is defined as ~Qr> = a~0> + (3~1>, where
a
and (3 are complex numbers having the form a+ib, and a and b are real numbers.
Referring to Fig. 6A, the initial conditions for qubit Q1 are defined as
follows:
Ql: [(0.49337)+i(0.52027)] ~0> + [(0.34163)+i(0.6076)] ~l>.
Initial conditions interface 615 includes a random button for assigning
arbitrary
numbers to qubit states. This function is useful in preparing the initial
state of
quantum register 72 in a superposition of states for understanding the logic
of the
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respective operation.
Toolbar 650 allows the user to access standard features common in
software such as "New", "Open", "Save", and "Help", as well as tools that are
specific to QC-IDE module 44 that are useful for circuit layout interface
module
620, such as "Cursor", "Add Qubit", and 'Add Connection".
Control panel 630 is an embodiment of an interface for opening and
closing the respective interfaces illustrated in Fig. 6A. In an embodiment of
the
invention, control panel 630 has a closed state, in which it can be reduced in
size
to expand the visible work space, and an open state, in which the features and
controls that it provides are accessible. Fig. 7 illustrates the open state
for
Control Panel 630.
System information interface 660A (Fig. 6A) includes information about
the circuit and logic that is being applied. Interface 660A includes the title
of the
working document, the system type, illustrated as System = Generic, and the
form of coupling, illustrated as Couplings = Controlled Phase. System
information interface 660A allows the user to define parameters of the desired
quantum computing platform 70. For example, in some cases, the quantum
CNOT operation can be chosen for the coupling operations such that Couplings =
CNOT.
Fig. 6B illustrates an embodiment of the system design interface 660B.
System design interface allows the user to define useful aspects of the system
and
is related to global settings interface 640 and system information interface
660A
from Fig. 6A.
Fig. 7 illustrates an example of the creation of a quantum gate for use in
the Logic Design interface of QC-IDE module 44. As illustrated in Fig. 6A,
circuit layout interface module 620 and machine language interface 610 are
used
to define a basic sequence of pulses that implement a set of logic 48 on
quantum
computer 70. Chart 613 in machine language interface 610 in Fig. 7 illustrates
a
quantum CNOT operation. Fig. 7 illustrates an example of the export library
component interface 670, which is used for defining and exporting a machine
language sequence as a single quantum logic gate for use in the logic design
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interface (an embodiment is illustrated in Fig. 8A). Export library component
interface 670 includes a text area 671 for the file name, a display 672 of the
icon
to be used for the library component, a button 673 for selecting desired icon
to be
used, a text area 674 for the title of the library component, a text area 675
for
describing the library component, and some text 676 that describes the system
information for the library component. The library component title,
description,
and icon can be useful for conveying information in the logic design
interface.
Fig. 7 further illustrates an example of the open mode of control panel
630. The example of control panel 630 illustrated in Fig. 7 includes an OS
button,
for viewing machine language interface 610, a conditions button for viewing
initial conditions interface, 615 from Fig. 6, and a run mode button for
compiling,
executing, and viewing the results of the respective machine language (an
embodiment of the run mode interface is illustrated in Figs. 9A and 9B).
Fig. 8A illustrates an embodiment of the logic design interface 780.
Logic design interface 780 allows the user to design high-level quantum logic
using a standard quantum circuit view. The qubits are represented on
horizontal
rows that represent increasing time from left to right. In some embodiments,
quantum logic gates are added to each of the qubit lines by clicking on the
respective time step and qubit line. In some embodiments of the invention, by
right-clicking the mouse pointer on the respective qubit line at the desired
position, a drop-down menu appears displaying a list of library components. An
embodiment of a drop down menu 781 that lists the available library components
is illustrated in Fig. 8A.
Logic design interface 780 of Fig. 8A illustrates an example of quantum
teleportation circuit where the initial state of qubit Q1 is teleported to
qubit Q3.
The circuit for quantum teleportation is well known in the art. See, e.g.,
Nielsen
and Chuang, 2000, Quafatufm Computation and Quamtufm Information, Cambridge
University Press, Cambridge UK, p.26-28, which is hereby incorporated by
reference. As illustrated, the teleporation circuit comprises a quantum
circuit that
includes Hadamard and CNOT operations, as well as readout, X, and Z
operations.
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Referring again to Figs. 6 and 7, the quantum CNOT operation can
include a sequence of elementary pulses or machine language operations. Since
a
single logic gate in logic design interface 780 can represent a plurality of
elementary pulses, a single time unit can also represent a plurality of time
units.
In some embodiments, a single time unit in logic design interface 780
represents
five elementary time units. The length of the time-lines for the qubits in
logic
design interface 780 can be controlled by length button 782.
The teleportation circuit illustrated in logic design interface 780 includes
readout operations on qubits Q1 and Q2. If the value resulting from the
respective readout operation yields a ~1>, then a further gate is applied to
the
target qubit Q3 (Fig. 8A). For example, referring again to Fig. 8A, the X and
Z
logic gates applied to qubit Q1 are conditional operations based on the value
of
the readout operations executed on qubits Q1 and Q2. If the readout operation
on
qubit Q2 results in a value of (1>, then the X operation is applied to qubit
Q1, and
if the readout operation on qubit Q1 results in a value of ~1>, then the Z
operation
is applied on qubit Q1. These conditional operations are achieved in the
quantum
circuit illustrated Fig. 8A by selections made in conditions option on drop-
down
menu 781. In an embodiment of the invention, conditions option on drop-down
menu 781 will only appear when the user has opened drop-down menu 781 on a
readout operation. Conditional operations in quantum circuits in the present
invention are described in detail in Section 5.2, above.
Fig. 8B illustrates the ground conditionals interface 782, where any form
of classical logic can be applied to the outcome of the readout operation. For
example, the statement illustrated in Fig. 8B reads in pseudo-code:
If (Ground on qubit Q2 at time unit 5 results in ~1>),
then (apply X operation on qubit Q3 at time unit 6).
Fig. 8C illustrates an embodiment of the control statement browser
interface 783, where a user can view the conditional logic statements that are
applied for the respective quantum circuit. Referring to the quantum circuit
illustrated in Fig. 8A, an embodiment of the invention includes two
conditional
operations each based on the readout operations on qubit Q1 and Q2,
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respectively, which are illustrated in Fig. 8C as condl and cond2 in the left
hand
panel. In an embodiment, when one of the conditionals of the respective
circuit
is selected, the conditional logic of that conditional appears in the main
panel of
control statement browser interface 783. Fig. 8C illustrates an example of the
conditional logic for cond2 from the teleportation circuit illustrated in Fig.
8A.
Fig. 9A illustrates an embodiment of run mode interface 800 (Fig. 1,
output module 56) that includes run console interface 835, final states
interface
891, OS interface 892, and state magnitude interface 893. Run mode interface
800 is an embodiment of the output results interface, illustrated as element
208 in
Fig. 2, used to display the execution of quantum logic. In an embodiment, run
console interface 835 acts as the main control interface for displaying and
reviewing the execution of a calculation. Run console interface 835 can
include a
plot views panel 835-1, for displaying various output interfaces, and a time
controls panel 835-2, for controlling the position of a time cursor that aids
in
viewing and understanding the output results. Both state magnitudes interface
893 and final states interface 891 are embodiments of interfaces for viewing
the
results of execution of the quantum logic, whereas OS interface 892 is useful
for
comparing the results against the input pulses or machine language of the
logic.
In some embodiments of the present invention, final states interface 891
(Fig. 9A) includes three components: (i) the initial state of quantum register
72,
(ii) the value of quantum register 72 at the time cursor, and (iii) the final
state of
quantum register 72 after the calculation. Changing the position of the time
cursor will change the corresponding information stored in quantum register
72.
This intermediate value is useful for tracking the quantum logic through
execution. State magnitude interface 893 provides a graphical representation
of
the information in quantum register 72 in the form of a plot of state
population
versus time. The output illustrated in Fig. 9A in state magnitude interface
893
illustrates an example of a quantum CNOT operation applied between two qubits
having an arbitrary initial state. Tracing state lines in state magnitude
interface
893 demonstrates that states 893-01 and 893-11, corresponding to quantum
states
~01> and ~11> respectively, exchange probabilities, whereas the states 893-00
and
893-10, corresponding to quantum states ~00> and ~10> respectively, do not
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change in probability. This demonstrates the CNOT logic where the control
qubit
is Q1 and the target qubit is Q2 such that the state is represented as ~Q2
Q1~.
Fig. 9B illustrates another embodiment of run mode interface 800. The
run mode interface 800 of Fig. 9B illustrates an example of output from a
quantum teleportation circuit, such as that illustrated logic design interface
780 of
Fig. 8A. Run mode interface 800 (Fig. 9B) includes final states interface 891-
1
and intermediate states interface 891-2, which are similar to final states
interface
891 illustrated in Fig. 9A. .Final states interface 891-1 and intermediate
states
interface 891-2 include final global phase panels 891-1-P and 891-2-P,
respectively, which apply a global phase defined by the user to the final
state of
the quantum register. For example, intermediate states interface illustrates a
global phase of el'~2, where the number 1.570796 can be entered by the user
and
in this example represents ~/2, having been applied to the final state of the
quantum register, allowing the final output to take the same form as the
initial
state of the quantum register. In the example of the teleportation circuit
illustrated in Fig. 8A, the state information stored in qubit Q1 is
transferred to
qubit Q3, where the state is represented by ~Q3 Q2 Q1>. In an example of the
teleportation circuit the final states of qubit Q1 and qubit Q2 are not
important.
The present invention can be implemented as a computer program product
that includes a computer program mechanism embedded in a computer readable
storage medium. For instance, the computer program product could contain the
program modules shown in Fig. 1. These program modules may be stored on a
CD-ROM, magnetic disk storage product, or any other computer readable data or
program storage product. The software modules in the computer program
product may also be distributed electronically, via the Internet or otherwise,
by
transmission of a computer data signal (in which the software modules are
embedded) on a carrier wave. The software modules in the computer program
product may also be distributed by hardcopy printout or other means.
While the present invention has been described with reference to a few
specific embodiments, the description is illustrative of the invention and is
not to
be construed as limiting the invention. Various modifications may occur to
those
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skilled in the art without departing from the true spirit and scope of the
invention
as defined by the appended claims.
