Debugging quantum circuits

Abstract

A method of computing using a hybrid quantum-classical computing system comprising a classical computer, a system controller, and a quantum processor includes the steps of identifying a computational problem to be solved and a quantum algorithm to be used to solve the computational problem; detecting a defective two-qubit gate among a plurality of two-qubit gates that may be applied to a pair of qubits in the quantum processor; compiling a computational task to solve the computational problem based on the quantum algorithm into a series of logic gates including single-qubit gates and two-qubit gates that exclude the detected defective two-qubit gates; executing the series of logic gates on the quantum processor; measuring one or more of the qubits in the quantum processor; and outputting a solution to the identified computational problem derived from the measured results of the qubits in the quantum processor.

Description

[Technical field]

[0001] FIELD OF THE DISCLOSURE

[0002] The embodiments described herein relate generally to methods for performing computations in a hybrid computing system, and more particularly to methods for debugging quantum circuits in a hybrid computing system. [Background technology]

[0002] Quantum computers have been shown to improve the performance of certain computational tasks, including hard optimization problems and sensitive cryptographic tasks, compared to what traditional (classical) computers can perform. Running such computational tasks on quantum computers requires improved system stability, faster maintenance operations, and improved uptime that can be achieved by debugging quantum circuits running on quantum computers, in order to provide accurate and useful results.

[0003] Debugging is the process of detecting and removing existing and potential errors (also called "bugs") in a circuit (i.e., a sequence of gate operations) that may cause errors in computations performed using the circuit. However, debugging quantum circuits differs from debugging very large scale integrated (VLSI) circuits in classical computers due to the difference between qubits that represent "0" and "1" states in a quantum computer and bits that represent "0" and "1" in a classical computer. For example, quantum computers are tested by feeding quantum states in which all qubits are prepared in the "0" state into various test quantum circuits and repeatedly measuring the quantum states.

[0004] Therefore, a systematic and efficient method for debugging quantum circuits is needed to improve the error rate of quantum computers. Summary of the Invention

[0005] An embodiment of the present disclosure provides a method of performing a computation using a hybrid quantum-classical computing system comprising a classical computer, a system controller, and a quantum processor, the method including: identifying, by using a classical computer, a computational problem to be solved and a quantum algorithm to be used to solve the computational problem; detecting, by using a classical computer and the system controller, one or more defective two-qubit gates of a plurality of two-qubit gates that may be applied to a pair of qubits in the quantum processor; compiling, by using a classical computer, a computational task for solving the computational problem based on the quantum algorithm into a series of logic gates including a plurality of single-qubit gates and a two-qubit gate of the plurality of two-qubit gates that excludes the detected one or more defective two-qubit gates; executing, by using the system controller, the series of logic gates on the quantum processor; measuring, by using the system controller, one or more of the qubits in the quantum processor; and outputting, by using a classical computer, a solution to the identified computational problem derived from a result of measuring one or more of the qubits in the quantum processor.

[0006] Embodiments of the present disclosure also provide a hybrid quantum-classical computing system that includes a quantum processor comprising a group of trapped ions, each trapped ion of the group of trapped ions having two hyperfine states that define a qubit, one or more lasers configured to illuminate a laser beam provided to the trapped ions in the quantum processor, a classical computer, and a system controller configured to control the illumination of the laser beam from the one or more lasers applied to the trapped ions in the quantum processor. The classical computer and system controller are configured to perform operations including: identifying, through the use of the classical computer, a computational problem to be solved and a quantum algorithm to be used to solve the computational problem; detecting, through the use of the classical computer and the system controller, one or more defective two-qubit gates of the plurality of two-qubit gates that may be applied to a pair of qubits in the quantum processor; compiling, through the use of the classical computer, a computational task for solving the computational problem based on the quantum algorithm into a series of logic gates including a plurality of single-qubit gates and a two-qubit gate of the plurality of two-qubit gates that excludes the detected one or more defective two-qubit gates; executing, through the use of the system controller, the series of logic gates on the quantum processor; measuring, through the use of the system controller, one or more of the qubits in the quantum processor; and outputting, through the use of the classical computer, a solution to the identified computational problem derived from a result of measuring one or more of the qubits in the quantum processor.

[0007] An embodiment of the present disclosure further provides a hybrid quantum-classical computing system, comprising a classical computer, a quantum processor, a system controller, and a non-volatile memory having a number of instructions stored therein. Some instructions, when executed by one or more processors, cause the hybrid quantum-classical computing system to perform operations including: identifying, through the use of a classical computer, a computational problem to be solved and a quantum algorithm to be used to solve the computational problem; detecting, through the use of a classical computer and a system controller, one or more defective two-qubit gates of the plurality of two-qubit gates that may be applied to a pair of qubits in the quantum processor; compiling, through the use of a classical computer, a computational task for solving the computational problem based on the quantum algorithm into a series of logic gates including a plurality of single-qubit gates and a two-qubit gate of the plurality of two-qubit gates that excludes the detected one or more defective two-qubit gates; executing, through the use of the system controller, the series of logic gates on the quantum processor; measuring, through the use of the system controller, one or more of the qubits in the quantum processor; and outputting, through the use of a classical computer, a solution to the identified computational problem derived from a result of measuring one or more of the qubits in the quantum processor. [Brief description of the drawings]

[0008] So that the above-mentioned features of the present disclosure can be understood in detail, a more particular description of the present disclosure briefly summarized above can be made by reference to embodiments, some of which are illustrated in the accompanying drawings. It should be noted, however, that the accompanying drawings illustrate only typical embodiments of the present disclosure and should not be considered as limiting its scope, since the present disclosure may admit of other equally effective embodiments.

[0009] [Figure 1] FIG. 1 is a schematic partial diagram of an ion trap quantum computing system according to one embodiment. [Diagram 2] FIG. 2 shows a schematic diagram of an ion trap for confining ions in groups according to one embodiment. [Diagram 3] FIG. 3 shows a schematic energy diagram of each ion in a group of trapped ions, according to one embodiment. [Figure 4] Figure 4 shows the qubit states of an ion represented as points on the surface of the Bloch sphere. [Diagram 5] 5A, 5B, and 5C show some schematic collective transverse motion mode structures for a group of five trapped ions. [Figure 6] 6A and 6B show schematic diagrams of the motional sideband spectrum and motional modes of each ion according to one embodiment. [Figure 7] FIG. 7 shows a flowchart illustrating a method of performing one or more calculations using a hybrid quantum-classical computing system comprising a classical computer and a quantum processor, according to one embodiment. [Figure 8] FIG. 8 shows a flow chart illustrating a method for detecting a defective two-qubit gate according to one embodiment.

[0010] For ease of understanding, the same reference numbers are used, where possible, to designate identical elements common to the figures. The figures and the following description use a Cartesian coordinate system including an X-axis, a Y-axis, and a Z-axis. Directions represented by arrows in the figures are assumed to be positive for convenience. It is believed that elements disclosed in some embodiments may be beneficially utilized in other implementations without specific specification. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] FIELD OF THE DISCLOSURE The embodiments described herein relate generally to methods for performing computations in a hybrid computing system, and more particularly to methods for debugging quantum circuits in a hybrid computing system.

[0012] A hybrid quantum-classical computing system may comprise a classical computer, a system controller, and a quantum processor. As used herein, the terms "quantum computer" and "quantum processor" may be used interchangeably to refer to the hardware / software components that perform quantum computations. A quantum circuit is a sequence of gate operations that is executed on the quantum processor by the system controller.

[0013] Quantum processors can be made from a variety of qubit technologies. In one example, in the case of ion trap technology, the quantum processor includes trapped ions coupled with various hardware, including lasers for manipulating the internal hyperfine states (qubit states), photomultiplier tubes (PMTs), or other types of imaging devices for reading out the internal hyperfine states (qubit states) of the trapped ions. A system controller receives instructions from a classical computer for controlling the quantum processor, and controls various hardware associated with controlling any and all aspects used to execute the instructions for controlling the quantum processor. The system controller also returns readouts of the quantum processor, and thus outputs the results of calculations performed by the quantum processor, to the classical computer.

[0014] The methods described herein are directed to a quantum processor having N qubits. 2 This involves identifying defective two-qubit gates out of all two-qubit gates with only 3log2N-1 tests.

[0015] (General hardware configuration) FIG. 1 is a schematic partial diagram of an ion-trapped quantum computing system 100, or simply system 100, according to one embodiment. System 100 may be a representative hybrid quantum-classical computing system. System 100 comprises a classical (digital) computer 102 and a system controller 104. Other components of system 100 shown in FIG. 1 are associated with a quantum processor, including a group 106 of trapped ions (i.e., five shown as circles approximately equally spaced from one another) extending along the Z-axis. Each ion in group 106 of trapped ions is an ion, e.g., a positive ytterbium ion, having a nuclear spin I and an electron spin S such that the difference between the nuclear spin I and the electron spin S is zero. 171 Yb + , positive barium ions 133 Ba + , positive calcium ions 111 CD + or 113 CD + all of which have nuclear spin I=1 / 2 and 2 S 1 / 2 In some embodiments, all ions in the group of trapped ions 106 are of the same species and isotope (e.g., 171 Yb + In some other embodiments, the group of trapped ions 106 includes one or more species or isotopes (e.g., some ions are 171 Yb + and some other ions 133 Ba +In yet further embodiments, the group of trapped ions 106 may include various isotopes of the same species (e.g., different isotopes of Yb, different isotopes of Ba). Ions within the group of trapped ions 106 are individually processed with separate laser beams. The classical computer 102 includes a central processing unit (CPU), memory, and support circuits (or I / O) (not shown). The memory is connected to the CPU and may be one or more of readily available memory, either locally or remotely, such as read-only memory (ROM), random access memory (RAM), floppy disk, hard disk, or any other form of digital storage. Software instructions, algorithms, and data may be coded and stored in the memory to instruct the CPU. Support circuits (not shown) are also connected to the CPU to support the processor in a conventional manner. The support circuits may include conventional caches, power supplies, clock circuits, input / output circuits, subsystems, and the like.

[0016] An imaging objective 108, for example a 0.37 numerical aperture (NA) objective, collects fluorescence from the ions along the Y-axis and maps each ion to a multi-channel photomultiplier tube (PMT) 110 (or some other imaging device) for measuring the individual ions. A Raman laser beam from a laser 112, provided along the X-axis, performs operations on the ions. A diffractive beam splitter 114 creates an array of Raman laser beams 116 that are individually switched using a multi-channel acousto-optic modulator (AOM) 118. The AOM 118 is configured to selectively act on individual ions by individually controlling the illumination of the Raman laser beams 116. A global Raman laser beam 116, which is non-co-propagating with the Raman laser beam 116, illuminates all ions at once from different directions. In some embodiments, rather than a single global Raman laser beam 120, individual Raman laser beams (not shown) can be used, each to illuminate an individual ion. A system controller (also called an "RF controller") 104 controls the AOM 118 and thus the intensity, timing, and phase of laser pulses applied to the trapped ions in the group 106 of trapped ions. The CPU 122 is the processor of the system controller 104. The ROM 124 stores various programs, and the RAM 126 is the working memory for various programs and data. The storage unit 128 includes a non-volatile memory, such as a hard disk drive (HDD) or a flash memory, and stores various programs even when the power is turned off. The CPU 122, the ROM 124, the RAM 126, and the storage unit 128 are interconnected via a bus 130. The system controller 104 executes control programs stored in the ROM 124 or the storage unit 128 and using the RAM 126 as a working area.The control programs include software applications containing program code that can be executed by the CPU 122 to perform various functions related to receiving and analyzing data, and controlling any and all aspects of the methods and hardware used to implement and operate the ion trap quantum computing system 100 described herein.

[0017] 2 shows a schematic diagram of an ion trap 200 (also called a Paul trap) that confines ions in groups 106 according to one embodiment. The confinement potential is applied by both a static (DC) voltage and a radio frequency (RF) voltage. The static (DC) voltage V S is applied to end cap electrodes 210 and 212 to confine ions along the Z axis (also called the "axial" or "longitudinal" direction). The ions in group 106 are approximately evenly distributed in the axial direction due to Coulomb interactions between the ions. In some embodiments, ion trap 200 includes four hyperbolic shaped electrodes 202, 204, 206, and 208 that extend along the Z axis.

[0018] During operation, (amplitude V RF A sinusoidal voltage V1 having a phase shift of 180° (and amplitude V RF / 2) is a sinusoidal voltage V2 having a driving frequency ω RF In some embodiments, a sinusoidal voltage is applied to the other pair of opposing electrodes 206, 208 at 100 Hz to generate a quadrupole potential. In some embodiments, a sinusoidal voltage is applied only to the other pair of opposing electrodes 202, 204, and the other pair of opposing electrodes 206, 208 is grounded. The quadrupole potential generates an effective confinement force in the XY plane perpendicular to the Z axis (also called the "radial" or "transverse") for each trapped ion, which is proportional to the distance from the saddle point (i.e., the location in the axial (Z) direction) where the RF field vanishes. The radial (i.e., in the XY plane) motion of each ion is approximated as a harmonic oscillation (called secular motion) with a restoring force towards the radial saddle point, each with a spring constant k x and ky In some embodiments, the radial spring constants are modeled as equal when the quadrupole potential is radially symmetric. However, if undesired, the radial ion motion may be distorted due to some asymmetry in the physical trapping configuration, small DC patch potentials due to non-uniformities on the surface of the electrodes, etc. These and other external sources of distortion may cause the ion to de-center from the saddle point.

[0019] Although not shown, a different type of trap is a microfabricated trapping chip, and a similar approach to that described above is used to hold or confine ions or atoms in place on the surface of the microfabricated trapping chip. A laser beam, such as the Raman laser beam described above, can be applied to the ions or atoms as they lie just above the surface.

[0020] 3 illustrates a schematic energy diagram 300 of each ion in the group of trapped ions 106 according to one embodiment. Each ion in the group of trapped ions 106 is an ion having a nuclear spin I and an electron spin S such that the difference between the nuclear spin I and the electron spin S is zero. In one example, each ion has a spin energy of ω 01 Nuclear spins I=1 / 2 and I=2π=12.642812 GHz, with energy division corresponding to a frequency difference (called the "carrier frequency") 2 S 1 / 2 A positive ytterbium ion with a hyperfine state (i.e., two electronic states) 171 Yb + In another example, each ion may all have a nuclear spin I=1 / 2 and 2 S 1 / 2 Positive barium ion with hyperfine state 133 Ba + , positive cadmium ions 111 CD + or 113 CD + The qubit may be formed in two hyperfine states, denoted |0> and |1>, and the hyperfine ground state (i.e., 2 S 1 / 2The lower energy state of the hyperfine state is chosen to represent |0>. Hereinafter, the terms "hyperfine state", "internal hyperfine state" and "qubit" may be used interchangeably to represent |0> and |1>. Each ion can be cooled without phonon excitation (i.e., n ph =0) and the ground state of motion of any motion mode m is m (i.e., the kinetic energy of the ions can be reduced), and then the qubit state can be prepared in the hyperfine ground state │0〉 by optical pumping, where │0〉 denotes the individual qubit state of the trapped ion and │0〉 with the subscript m. m represents the motional ground state of motional mode m of the group 106 of trapped ions.

[0021] The individual qubit states of each trapped ion can be, for example, excited 2 P 1 / 2 A 355 nanometer (nm) mode-locked laser can be operated through a level (represented by |e>) at 100 Hz. As shown in Figure 3, the laser beam from the laser is split into a pair of non-copropagating laser beams (a first laser beam with frequency ω1 and a second laser beam with frequency ω2) in a Raman configuration, with a transition frequency ω between |0> and |e> as explained in Figure 3. 0e With respect to the one-photon transition detuning frequency Δ=ω1-ω 0e The two-photon transition detuning frequency δ involves adjusting the amount of energy provided to the trapped ion by the first and second laser beams, which, when used in combination, move the trapped ion between the hyperfine states |0> and |1>. The one-photon transition detuning frequency Δ can be expressed as the two-photon transition detuning frequency (also simply called the "detuning frequency") δ=ω1-ω2-ω 01 (hereafter denoted as ±μ, where μ is a positive value), the single-photon Rabi frequency Ω at which a Rabi flop occurs between states |0> and |e>, and between states |1> and |e>, respectively. 0e (t) and Ω 1eThe two-photon Rabi frequency Ω(t) (which is time dependent and determined by the amplitudes and phases of the first and second laser beams), as well as the spontaneous emission rate from the excited state |e>, the Rabi flop between the two hyperfine states │0> and │1> (called a "carrier transition"), is induced at the two-photon Rabi frequency Ω(t). 0e Ω 1e / 2Δ, where Ω 0e and Omega 1e are the single-photon Rabi frequencies of the first and second laser beams, respectively. Hereinafter, this set of non-copropagating laser beams in a Raman configuration for manipulating the internal hyperfine state of a qubit (qubit state) may be referred to as a "composite pulse" or simply a "pulse", and the resulting time-dependent pattern of the two-photon Rabi frequency Ω(t) may be referred to as the "amplitude" of the pulse or simply a "pulse", which are illustrated and further described below. Detuning frequency δ=ω1-ω2-ω 01 is sometimes referred to as the detuning frequency of the composite pulse or the detuning frequency of the pulse. The amplitude of the two-photon Rabi frequency Ω(t), which is determined by the amplitudes of the first and second laser beams, is sometimes referred to as the “amplitude” of the composite pulse.

[0022] It should be noted that the specific atomic species used in the description provided herein is merely an example of an atomic species that has a stable and well-defined two-level energy structure and an optically accessible excited state when ionized, and is not intended to limit the possible configurations, specifications, etc. of the trapped ion quantum computer according to the present disclosure. For example, other ion species include alkaline earth metal ions (Be + , Ca + , Sr + , Mg + , and Ba + ) or transition metal ions (Zn + , Hg + , Cd + ).

[0023] FIG. 4 is provided to help visualize the qubit state of an ion, represented as a point on the surface of a Bloch sphere 400 with azimuthal angle φ and polar angle θ. As described above, application of a composite pulse produces a Rabi flop between qubit states |0> (represented as the north pole of the Bloch sphere) and |1> (represented as the south pole of the Bloch sphere). Adjusting the duration and amplitude of the composite pulse flips the qubit state from |0> to |1> (i.e., from the north pole to the south pole of the Bloch sphere) or flips the qubit state from |1> to |0> (i.e., from the south pole to the north pole of the Bloch sphere). This application of a composite pulse is referred to as a "π pulse." Furthermore, by adjusting the duration and amplitude of the composite pulse, the qubit state │0> can be transformed into a superposition state │0>+│1>, where the two qubit states │0> and │1> are added and equally weighted in phase (the normalization factor of the superposition state is omitted below for convenience), and the qubit state │1> can be transformed into a superposition state │0>-│1>, where the two qubit states │0> and │1> are added and equally weighted but out of phase. This application of the composite pulse is called a “π / 2 pulse”. More generally, the superposition of the two added and equally weighted qubit states │0> and │1> is represented by a point on the equator of the Bloch sphere. For example, the superposition states │0>±│1> correspond to points on the equator with azimuthal angles φ of zero and π, respectively. The superposition state corresponding to a point on the equator with azimuthal angle φ is │0>+e iφ │0>±i│1> (for example, for φ=±π / 2, it is │0>±i│1>). Transformation between two points on the equator (i.e., rotation around the Z axis of the Bloch sphere) can be implemented by shifting the phase of the composite pulse.

[0024] (Tangle formation) 5A, 5B, and 5C show schematic collective transverse motion mode configurations (also simply referred to as "motion mode configurations") of, for example, several groups 106 of five trapped ions, where a static voltage V SThe confining potential due to the axial direction is weak compared to the radial confining potential. The collective transverse motion mode of a group of trapped ions 106 is determined by a combination of the confining potential generated by the ion trap 200 and the Coulombic interactions between the trapped ions. The trapped ions undergo collective transverse motion (referred to as the "collective transverse motion mode", "collective motion mode", or simply "motion mode"), each mode having a different energy (or equivalently, frequency) associated with it. In the following, the mth lowest energy motion mode is referred to as |n ph > m where n ph represents the number of motion quanta (units of energy excitation, called phonons) of the motion mode, and the number M of motion modes in a given transverse direction is equal to the number of trapped ions in the group 106. Figures 5A-5C illustrate schematic examples of different types of collective transverse motion modes that may be experienced by five trapped ions arranged in the group 106. Figure 5A illustrates a typical motion mode |n ph > M Schematic diagram of the general motion mode |n>, where M is the number of motion modes. M In this case, all ions oscillate transversely in phase. Figure 5B shows the second highest energy tilting mode |n ph > M-1 In the tilt motion mode, the ions at both ends move laterally out of phase (i.e., in opposite directions). ph > M-1 Higher order modes of motion, which have lower energies than ph > M-3 FIG.

[0025] It should be noted that the above specific configuration is merely one of several possible examples of a trap for confining ions according to the present disclosure, and does not limit the possible configurations, specifications, etc. of a trap according to the present disclosure. For example, the shape of the electrodes is not limited to the above hyperbolic electrodes. In other examples, the trap that generates an effective electric field that causes the motion of ions in a radial direction as a harmonic oscillation may be a multi-layer trap in which multiple electrode layers are stacked and RF voltage is applied to two diagonal electrodes, or it may be a surface trap in which all electrodes are arranged in a single plane on the chip. Furthermore, the trap may be divided into multiple segments, adjacent pairs of which may be linked to shuttle one or more ions or may be coupled by photonic interconnects. The trap may also be an array of individual trapping regions arranged close to each other on a microfabricated ion trap chip, such as those described above. In some embodiments, the quadrupole potential has a spatially varying DC component in addition to the RF component described above.

[0026] In a trapped ion quantum computer, the motional mode can act as a data bus mediating the entanglement between two qubits, which is used to perform XX gate operations. That is, each of the two qubits is entangled with a motional mode, and as described below, the entanglement is transferred to the entanglement between the two qubits by using a motional sideband excitation. Figures 6A and 6B show an example of a trap ion quantum computer with a frequency ω m Mode of motion with ph > M 6B, when the detuning frequency of the composite pulse is zero (i.e., the frequency difference between the first and second laser beams is equal to the carrier frequency δ=ω1-ω2-ω 01 =0), a simple Rabi flop (carrier transition) occurs between the qubit states │0〉 and │1〉. If the detuning frequency of the composite pulse is positive (i.e., the frequency difference between the first and second laser beams is tuned higher than the carrier frequency, then δ=ω1-ω2-ω 01=μ>0, called the blue sideband), combined qubit motional state │0>│n ph > m and │1>│n ph +1> m (i.e., when the qubit state │0〉 flips to │1〉, │n ph > m From the m-th motion mode with n-phonon excitation represented by │n ph +1> m (n ph +1) a transition to the mth motional mode occurs with phonon excitation. If the detuning frequency of the composite pulse is negative (i.e., the frequency difference between the first and second laser beams is greater than the frequency of the motional mode │n ph > m Frequency ω m If the frequency is tuned lower than the carrier frequency by 01 =-μ<0, called the red sideband), combined qubit motion state │0>│n ph > m and │1>│n ph -1> m (i.e., when the qubit state flips from │0〉 to │1〉, the motional mode │n ph > m From the above, the motion mode with one less phonon excitation │n ph -1> m A π / 2 pulse in the blue sideband applied to the qubit induces a transition to the combined qubit motional state │0>│n ph > m │0>│n ph > m and │1>│n ph +1> m A π / 2 pulse in the red sideband applied to a qubit transforms it into a superposition of combined qubit motional states │0>│n ph > m │0>│n ph > m and │1>│n ph -1> m The two-photon Rabi frequency Ω(t) is transformed into a superposition of the detuning frequency δ=ω1-ω2-ω01 = ±μ, one can selectively drive the blue or red sideband transitions. Thus, a qubit can be entangled in a desired motional mode by applying an appropriate type of pulse, such as a π / 2 pulse, and then entangled with another qubit, resulting in the entanglement between two qubits required to perform XX gate operations in a trapped ion quantum computer.

[0027] As described above, an XX gate operation can be performed on two qubits (i-th and j-th qubits) by controlling and / or directing the transformation of the combined qubit motional state. In general, an XX gate operation (with maximal entanglement) can be performed on a two-qubit state |0> i |0> j , |0> i |1> j , |1> i |0> j and |1> i |1> j are converted as follows, respectively:

number

[0028] Thus, applying a π / 2 pulse in the blue sideband to the i-th qubit and a π / 2 pulse in the red sideband to the j-th qubit results in two qubits and the motional mode |0〉 i |0> j |n ph > m The combination state of |0> i |0> j |n ph > m and |1> i |1> j |n ph > m and the two qubits are now in an entangled state. As will be apparent to those skilled in the art, the initial number of phonon excitations, n ph (i.e., |1> i |0> j |n ph +1> m and |0> i |1> j |n ph -1> mSince the two-qubit state entangled with the motional mode having phonon excitations of m can be removed by a sufficiently complex pulse sequence, the combined state of the two qubits and the motional mode after the XX gate operation is the initial number of phonon excitations in the mth motional mode, n ph It should be clear that since does not change at the end of the XX gate operation, it is disentangled. Therefore, the qubit states before and after the XX gate operation are generally described below without involving the motional modes.

[0029] More generally, it is transformed by applying a pulse in the sideband for a duration τ (called the "gate duration"), resulting in an amplitude Ω (i) and Ω (j) The combined state of the ith and jth qubits with detuning frequency μ is expressed by the entanglement interaction χ (i,j) It can be written in terms of (τ) as follows:

number

number

number

[0030] The entanglement interaction between the two qubits described above can be used to perform XX gate operations. The XX gate operations (XX gates), together with the single qubit operations (R gates), form a set of gates {R,XX} that can be used to build a quantum computer configured to perform a desired computational process. Of the several known sets of logic gates into which any quantum algorithm can be decomposed, a set of logic gates commonly represented as {R,XX} is unique to the trapped ion quantum computing system described herein. Here, the R gates correspond to the manipulation of the individual qubit states of the trapped ions, and the XX gates (also referred to as "two qubit gates") correspond to the manipulation of the entanglement of two trapped ions.

[0031] To perform an XX gate operation between the i-th and j-th qubits, the condition χ (i,j) (τ)=θ (i,j) (0<θ (i,j) ≦π / 8) (i.e., the entanglement interaction χ (i,j) (τ) is the desired value θ (i,j) (which is called the condition for non-zero entanglement) is constructed and applied to the i-th and j-th qubits. The transformation of the combined state of the i-th and j-th qubits above is expressed as θ (i,j) = π / 8 corresponds to the XX gate operation with maximum entanglement. The amplitude Ω of the pulse applied to the i-th and j-th qubits (i) (t) and Ω (j) (t) is a control parameter that can be adjusted to ensure non-zero tunable entanglement of the i-th and j-th qubits to perform the desired XX gate operation on the i-th and j-th qubits.

[0032] (Debugging quantum circuits) Described herein is an embodiment of a method for performing one or more computations in a trapped ion quantum computing system 100 using a hybrid quantum-classical computing system that includes a classical computer, such as classical computer 102, and a quantum processor, such as group of trapped ions 106. In the method described herein, a systematic "debug" process (i.e., identifying errors in the quantum processor and removing errors in the circuitry that performs the computations) is performed so that the computations can be performed with reduced errors.

[0033] 7 shows a flow chart illustrating a method 700 for performing one or more calculations using a hybrid quantum-classical computing system comprising a classical computer and a quantum processor. In this example, the quantum processor is based on a group 106 of trapped ions, each of whose two hyperfine states forms a qubit. Thus, the trapped ions form the qubits that provide the computing core of the quantum processor or quantum computer.

[0034] In block 702, a computational problem to be solved and a quantum algorithm to be used to solve the computational problem are identified by the classical computer 102, for example, by use of a user interface, such as a graphics processing unit (GPU) of the classical computer 102, or retrieved from a memory of the classical computer 102. The computational task to solve the computational problem based on the quantum algorithm is then decomposed by the classical computer 102 in block 708 and compiled into a quantum circuit by using a set of universal quantum logic gates (i.e., a series of logic gates). Among several known sets of universal quantum logic gates, a set of universal quantum logic gates, commonly represented as {R,XX}, is unique to the trapped ion quantum computing system described herein. Here, the R gates correspond to single qubit gate operations (i.e., manipulation of an individual qubit state of a trapped ion, also referred to as a "single qubit gate") and the XX gates correspond to two qubit operations (i.e., manipulation of the entanglement of two trapped ions, also referred to as a "two qubit gate"). It should be clear to those skilled in the art that while R gates (single qubit gates) can be implemented with nearly perfect fidelity, the formation of XX gates (two qubit gates) is complex and there may be one or more defective two qubit gates among the available XX gates. If such defective two qubit gates are used in executing a quantum algorithm, calculation errors will occur. Thus, defective two qubit gates are detected in block 704 and, if necessary, calibrated in block 706 or excluded in the compilation of the quantum circuit used to execute the identified quantum algorithm in block 708.

[0035] At block 704, one or more defective two-qubit gates are detected by the system controller 104 among the two-qubit gates that may be applied to the pair of qubits in the quantum processor, as described further below. For example, in a quantum processor having 32 qubits, the average fidelity of the two-qubit gates may be about 95%. The number of defective two-qubit gates may be one, two, or three. It should be noted that the methods of detecting one or more defective two-qubit gates described herein may be applied to any average fidelity of the two-qubit gates and any number of defective two-qubit gates among all available two-qubit gates in the quantum processor.

[0036] In block 706, the system controller 104 optionally calibrates and corrects one or more of the defect-containing two-qubit gates in the quantum processor detected in block 704 by methods known in the art. Defect-containing two-qubit gates are typically caused by control errors due to lack of knowledge of how the trapped ions (i.e., qubits) behave during operation of the two-qubit gate. Thus, adjustment of control parameters associated with the hardware in the ion trap quantum computing system 100, such as the amplitude, phase, and / or duration of the laser pulses applied to the qubits during two-qubit gate operation, or the trapping potential of the ion trap 200, can reduce or eliminate errors in the defect-containing two-qubit gates. In some embodiments, multiple single-qubit gates are applied to the qubits to calibrate the defect-containing two-qubit gates.

[0037] At block 708, the classical computer 102 compiles (i.e., decomposes) a computational task for solving a computational problem based on the quantum algorithm identified at block 702 into a quantum circuit using a set of universal logic gates. In compiling the quantum circuit, the defective two-qubit gate detected at block 704 is not filtered out (i.e., is not used), or, if the defective two-qubit gate was modified at block 706, the modified two-qubit gate is used.

[0038] At block 710, the quantum circuit is executed on the quantum processor by the system controller 104. The execution of the quantum circuit may be performed by applying laser pulses, the amplitude and phase of which are appropriately adjusted by methods known in the art, to the qubits in the quantum processor. Following the execution of the quantum circuit by the system controller, one or more of the qubits in the quantum processor are measured by methods known in the art. In some embodiments, a quantum computation task is decomposed into multiple executions of the quantum circuit. The process then returns to block 704 to detect one or more defective two-qubit gates, compile and execute one or more quantum circuits to complete a computation based on the identified quantum algorithm, and the process proceeds to block 712.

[0039] At block 712, the classical computer 102 processes one or more measurements of qubits in the quantum processor obtained at block 710 to derive a solution to the computational problem identified in block 704 and outputs the solution to a user interface, such as a graphics processing unit (GPU) of the classical computer 102, and / or stores the solution in memory of the classical computer 102. For example, the calculated solution may be displayed in a table or as a graphical representation of particles on a display connected to the GPU.

[0040] 8 shows a flow chart illustrating a method 800 for detecting a defective two-qubit gate as shown in block 706 above. In this example, the number of qubits in the quantum processor is N=2. n and each qubit is an n-digit binary number (q1q2…q n ) For example, a quantum processor is indexed by 8(=2 3 ) qubits. The qubits are then indexed as (000), (001), (010), (011), (100), (101), (110), and (111). The qubits are further grouped according to their index into 2n classes represented as (i, b), where the binary number of the ith (i∈{0, ..., n-1}) digit in the index is b∈{0,1}. Each class (i, b) has 2 n-1 It contains 8(=2 3 In an example quantum processor with 10,0,10,11 qubits, the qubits are grouped into six classes: (0,0) ∈ {(000), (001), (010), (011)}, (0,1) ∈ {(100), (101), (110), (111)}, (1,0) ∈ {(000), (001), (100), (101)}, (1,1) ∈ {(010), (011), (110), (111)}, (2,0) ∈ {(000), (010), (100), (110)}, and (2,1) ∈ {(001), (011), (101), (111)}.

[0041] In block 802, the system controller 104 performs a two-qubit gate between all pairs of qubits in class (i, b). n-1 There are qubits, so in total there are 2 n-2 (2 n-1 -1) two-qubit gates are performed. The two-qubit gates can be performed by applying appropriately tuned laser pulses of amplitude and phase to the corresponding pairs of qubits. The amplitude and phase of the laser pulses can be tuned by methods known in the art.

[0042] At block 804, the system controller 104 measures the error syndromes of the two-qubit gates of all pairs of qubits in class (i,b). An "error syndrome," as described herein, is information about whether the two-qubit gates collectively contain an error and can be extracted by measuring one or more qubits in class (i,b) and / or one or more ancillary qubits entangled with one or more qubits in class (i,b). In some embodiments, four XX gates are applied to each qubit pair in class (i,b) and all qubits are measured.

[0043] The process returns to block 802 for a different class (i, b). After the syndrome measurements for all 2n classes have been performed, the process proceeds to block 806.

[0044] In block 806, a group of candidate defective two-qubit gates is selected by the classical computer 102 based on the error syndromes measured for all 2n classes. n 2 between all pairs of qubits out of n-1 (2 n Of the m (m-1) two-qubit gates, some of the two-qubit gates may be identified as free from the m error syndromes measured in blocks 802 and 804. For example, in a quantum processor identified as including a single defective two-qubit gate, the number of two-qubit gates that may be identified as free from m (m=0, 1, ..., n-1) of the 2n error syndromes is 2 n-1 (2 n -1)-2 n-1-m Therefore, the number of candidates for defective gates is N C is 2 n-1-m and at most 2 n-1 (=N / 2).

[0045] In block 808, the first qubit (q1q2...q n ) and the second qubit (q'1q'2...q' n ) are candidates for defect-containing two-qubit gates in classes (i0,b0), (i1,b1), …(i m-1 ,b m-1 ), the binary number of the corresponding digit (i.e., the i-th digit) of the first and second qubits is set to the binary number b in class (i,b). That is, the binary numbers of the i0-th digit of the first qubit and the second qubit are both b0, the binary numbers of the i1-th digit of the first qubit and the second qubit are both b1, and the binary numbers of the i2-th digit of the first qubit and the second qubit are both b2. m-1 The th bit value is both b m-1 For each of the remaining (nm) digits of the first qubit and the second qubit, the binary number of the digit of the first qubit is set to be complementary to the binary number of the corresponding digit of the second qubit (i.e., the first qubit q l The lth digit of is set to be 0, and the second qubit q' l the lth digit of is 1, or vice versa).

number

[0046] In block 810, the system controller 104 C A binary search in the selected group of candidate defective two-qubit gates is performed to identify the defective two-qubit gate. C Start by dividing the selected group of candidate defect-containing two-qubit gates into a first subgroup and a second subgroup, each of which has a set of mutually exclusive N C / 2 defect-containing two-qubit gate candidates (maximum 2n-1 The binary search continues by dividing the subgroup whose error syndrome indicates an error into two subgroups, each of which includes N defective two-qubit gates (N qubit gates) and measures the error syndrome of the first subgroup. If the error syndrome of the first subgroup does not indicate an error, then the error syndrome of the second subgroup is measured. The binary search continues by dividing the subgroup whose error syndrome indicates an error into two subgroups, each of which includes N defective two-qubit gates (N qubit gates). C / 4 defect-containing two-qubit gate candidates (maximum 2 n-2 The binary search continues in this manner until one or more defective gates are identified. If one defective gate is identified, the step of dividing the group of candidate defective gates into two subgroups is repeated up to n-1 times. The one or more defective gates identified in block 810 are returned to classical computer 102 and the process proceeds to block 708.

[0047] The embodiment described herein is a method for performing quantum computations while debugging quantum circuits. Using the method described herein, it is possible to debug approximately N 2 A single defective two-qubit gate out of the two-qubit gates can be identified with only 3log2N-1 tests. Two defective two-qubit gates can be identified with 3.25log2N tests on average. Three defective two-qubit gates can be identified with about 4.947log2N tests on average.

[0048] It should be noted that the above specific illustrative embodiments are merely some possible examples of a hybrid quantum-classical computing system according to the present disclosure, and are not intended to limit possible configurations, specifications, etc. of a hybrid quantum-classical computing system according to the present disclosure. For example, the quantum processor in the hybrid quantum-classical computing system is not limited to the above group of trapped ions. For example, the quantum processor may be a superconducting circuit including a micrometer-sized loop of superconducting metal interrupted by a number of Josephson junctions that act as qubits (called flux qubits). The junction parameters are designed during fabrication so that a persistent current flows continuously when an external magnetic flux is applied. Since only an integer number of flux quanta can pass through each loop, a persistent clockwise or counterclockwise current is generated in the loop to compensate (shield or enhance) the non-integer external magnetic flux applied to the loop. The two states corresponding to the persistent clockwise and counterclockwise currents are the lowest energy states and differ only in their relative quantum phase. The higher energy states correspond to much larger persistent currents and are therefore well separated in energy from the lowest two eigenstates. The two lowest eigenstates are used to represent the qubit states |0> and |1>. The individual qubit states of each qubit device can be manipulated by applying a series of microwave pulses of appropriately tuned frequency and duration.

[0049] While the forgoing is directed to specific embodiments, other and further embodiments may be devised without departing from the basic scope thereof, which is determined by the following claims.

Claims

1. 1. A method of performing a computation using a hybrid quantum-classical computing system comprising a classical computer, a system controller, and a quantum processor, comprising: identifying, by use of the classical computer, a computational problem to be solved and a quantum algorithm to be used to solve the computational problem; detecting, by use of the classical computer and the system controller, one or more defective two-qubit gates of a plurality of two-qubit gates that may be applied to pairs of qubits in the quantum processor; compiling, by using the classical computer, a computational task for solving the computational problem based on the quantum algorithm into a series of logic gates including a plurality of single-qubit gates and a two-qubit gate of the plurality of two-qubit gates that excludes the one or more detected defective two-qubit gates; executing the set of logic gates on the quantum processor using the system controller; measuring one or more of the qubits in the quantum processor through use of the system controller; outputting, by use of the classical computer, a solution to the identified computational problem derived from the measured results of the one or more of the qubits in the quantum processor; A method comprising:

2. detecting the one or more defective two-qubit gates performing, by the system controller, two-qubit gates between all pairs of qubits in each class of multiple classes of qubits in the quantum processor; measuring, by the system controller, error syndromes of the two-qubit gate between all pairs of qubits in each class of the plurality of classes of qubits in the quantum processor; selecting, by the classical computer, a group of candidate defective two-qubit gates among all pairs of qubits in the quantum processor based on the measured error syndromes; performing, by the system controller, a binary search in the selected group of candidate defective two-qubit gates to identify one or more defective two-qubit gates in the selected group of candidate defective two-qubit gates; The method of claim 1 , comprising:

3. each class of the plurality of classes of qubits comprises half of the qubits in the quantum processor; The plurality of classes includes 2n classes, ｎ The method of claim 2 , wherein x is the number of qubits in the quantum processor.

4. The group of candidates for defect-containing two-qubit gates is at most 2 ｎ－１ The method of claim 3 , further comprising two-qubit gates.

5. The group of candidates for defect-containing two-qubit gates is ｎ－１－ｍ 4. The method of claim 3, comprising: two-qubit gates, where m is the number of measured error syndromes that are defective.

6. The binary search is dividing the selected group of candidate defective two-qubit gates into two subgroups; measuring an error syndrome of one of the two subgroups; The method of claim 2 , comprising:

7. correcting, by the system controller, the one or more detected defective two-qubit gates. The method of claim 1 further comprising:

8. repeating the steps of detecting the one or more defective two-qubit gates, executing the series of logic gates, and measuring one or more of the qubits in the quantum processor. The method of claim 1 further comprising:

9. a quantum processor comprising a group of trapped ions, each trapped ion of said group of trapped ions having two hyperfine states defining a qubit; one or more lasers configured to illuminate a laser beam provided to trapped ions in the quantum processor; Classical computers and a system controller configured to control irradiation of the laser beam from the one or more lasers applied to the trapped ions in the quantum processor; 1. A hybrid quantum-classical computing system comprising: the classical computer and the system controller, identifying, by use of the classical computer, a computational problem to be solved and a quantum algorithm to be used to solve the computational problem; detecting, by use of the classical computer and the system controller, one or more defective two-qubit gates of a plurality of two-qubit gates that may be applied to pairs of qubits in the quantum processor; compiling, by using the classical computer, a computational task for solving the computational problem based on the quantum algorithm into a series of logic gates including a plurality of single-qubit gates and a two-qubit gate of the plurality of two-qubit gates that excludes the one or more detected defective two-qubit gates; executing the set of logic gates on the quantum processor using the system controller; measuring one or more of the qubits in the quantum processor through use of the system controller; outputting, by use of the classical computer, a solution to the identified computational problem derived from the measured results of the one or more of the qubits in the quantum processor; 1. A hybrid quantum-classical computing system configured to perform operations including:

10. detecting the one or more defective two-qubit gates performing, by the system controller, two-qubit gates between all pairs of qubits in each class of multiple classes of qubits in the quantum processor; measuring, by the system controller, error syndromes of the two-qubit gate between all pairs of qubits in each class of the plurality of classes of qubits in the quantum processor; selecting, by the classical computer, a group of candidate defective two-qubit gates among all pairs of qubits in the quantum processor based on the measured error syndromes; performing, by the system controller, a binary search in the selected group of candidate defective two-qubit gates to identify one or more defective two-qubit gates in the selected group of candidate defective two-qubit gates; 10. The hybrid quantum-classical computing system of claim 9, comprising:

11. each class of the plurality of classes of qubits comprises half of the qubits in the quantum processor; 11. The hybrid quantum-classical computing system of claim 10, wherein the plurality of classes comprises 2 log N classes, where N is a number of qubits in the quantum processor.

12. 12. The hybrid quantum-classical computing system of claim 11 , wherein the group of candidate defective two-qubit gates includes at most N / 2 two-qubit gates.

13. The group of candidates for defect-containing two-qubit gates is ｎ－１－ｍ 12. The hybrid quantum-classical computing system of claim 11 , comprising:

14. The binary search is dividing the selected group of candidate defective two-qubit gates into two subgroups; measuring an error syndrome of one of the two subgroups; 11. The hybrid quantum-classical computing system of claim 10, comprising:

15. The operation is correcting, by the system controller, the one or more detected defective two-qubit gates.

10. The hybrid quantum-classical computing system of claim 9, further comprising:

16. The operation is repeating the steps of detecting the one or more defective two-qubit gates, executing the series of logic gates, and measuring one or more of the qubits in the quantum processor.

10. The hybrid quantum-classical computing system of claim 9, further comprising:

17. Classical computers and A quantum processor; A system controller; a non-volatile memory having a number of instructions stored therein; 11. A hybrid quantum-classical computing system comprising: identifying, by use of the classical computer, a computational problem to be solved and a quantum algorithm to be used to solve the computational problem; detecting, by use of the classical computer and the system controller, one or more defective two-qubit gates of a plurality of two-qubit gates that may be applied to pairs of qubits in the quantum processor; compiling, by using the classical computer, a computational task for solving the computational problem based on the quantum algorithm into a series of logic gates including a plurality of single-qubit gates and a two-qubit gate of the plurality of two-qubit gates that excludes the one or more detected defective two-qubit gates; executing the set of logic gates on the quantum processor using the system controller; measuring one or more of the qubits in the quantum processor through use of the system controller; outputting, by use of the classical computer, a solution to the identified computational problem derived from the measured results of the one or more of the qubits in the quantum processor; A hybrid quantum-classical computing system that performs operations including:

18. detecting the one or more defective two-qubit gates performing, by the system controller, two-qubit gates between all pairs of qubits in each class of multiple classes of qubits in the quantum processor; measuring, by the system controller, error syndromes of the two-qubit gate between all pairs of qubits in each class of the plurality of classes of qubits in the quantum processor; selecting, by the classical computer, a group of candidate defective two-qubit gates among all pairs of qubits in the quantum processor based on the measured error syndromes; performing, by the system controller, a binary search in the selected group of candidate defective two-qubit gates to identify one or more defective two-qubit gates in the selected group of candidate defective two-qubit gates; 20. The hybrid quantum-classical computing system of claim 17, comprising:

19. each class of the plurality of classes of qubits comprises half of the qubits in the quantum processor; The plurality of classes includes 2n classes, ｎ 20. The hybrid quantum-classical computing system of claim 18, wherein x is the number of qubits in the quantum processor.

20. The binary search is dividing the selected group of candidate defective two-qubit gates into two subgroups; measuring an error syndrome of one of the two subgroups; 20. The hybrid quantum-classical computing system of claim 18, comprising:

Images