Accelerated molecular dynamics simulation method in quantum-classical hybrid computing system

Abstract

A method for performing computations using a hybrid quantum-classical computing system comprising a classical computer, a system controller, and a quantum processor includes the steps of: identifying, using the classical computer, a molecular dynamics system to be simulated; calculating, using the classical computer, a plurality of energies associated with particles of the molecular dynamics system as part of the simulation based on an Ewald summation method, where calculating the plurality of energies includes partially offloading the calculation of the plurality of energies to the quantum processor; and outputting, using the classical computer, a physical behavior of the molecular dynamics system determined from the calculated plurality of energies.

Description

[Technical field]

[0001] (Government Rights) This invention was made with United States Government support under Contract No. DESC0019040 awarded by the United States Department of Energy. The United States Government has certain rights in this disclosure.

[0002] The present disclosure relates generally to a method for performing calculations in a hybrid computing system, and more specifically to a method for obtaining the energy of a physical system having interacting particles by a molecular dynamics (MD) simulation performed in a hybrid computing system including a classical computer and a quantum computer, where the quantum computer operates based on a group of trapped ions, and the hybrid computing system can be referred to as a hybrid quantum-classical computing system. [Background technology]

[0003] In quantum computing, quantum bits, or qubits, are similar to the bits that represent "0" and "1" in classical (digital) computers, and require nearly perfect control to be prepared, manipulated, and measured (read out) during a calculation or computational process. Imperfect control of qubits leads to errors that can accumulate in the computational process, limiting the size of quantum computers that can perform reliable calculations.

[0004] Among the types of physical systems or qubit technologies proposed to build large-scale quantum computers are groups of ions (i.e., charged atoms) trapped and suspended in a vacuum by electromagnetic fields. The ions have internal hyperfine states that are separated by frequencies in the multi-GHz range and can be used as computational states of a qubit (referred to as "qubit states"). These hyperfine states can be controlled using radiation provided by a laser, sometimes referred to herein as interaction with a laser beam. An ion can be cooled to near its motional ground state using such interaction with a laser. An ion can also be optically excited with high precision into one of two hyperfine states (qubit preparation), manipulated between the two hyperfine states by a laser beam (single-qubit gate operation), and its internal hyperfine state detected by fluorescence upon application of a resonant laser beam (qubit readout). A pair of ions can be controllably entangled by a force that depends on the qubit state (two-qubit gate operation) using a laser pulse that couples the ions into a collective motional mode of the group of trapped ions that arises from the Coulomb interaction between the ions. In general, entanglement occurs when pairs or groups of ions (or particles) are created, interact, or share spatial proximity such that the quantum state of each ion cannot be described independently of the quantum states of the other ions, even if the ions are separated by large distances.

[0005] Quantum computers have been shown to improve the performance of certain computational tasks compared to what classical computers can do, including the simulation of physical systems. In a molecular dynamics (MD) simulation of N interacting particles, we calculate the interparticle interaction energies, including long-range interactions. This allows for a computation time of O(N 2) as the number of interacting particles, N, increases. Even when efficient methods such as the Ewald summation method are used, the computational complexity in calculating long-range interactions is O(N 3 / 2 )

[0006] Therefore, there is a need to reduce the computational complexity in MD simulations, especially efficient methods for MD simulations such as the Ewald summation method. Summary of the Invention

[0007] An embodiment of the present disclosure provides a method of performing computations using a hybrid quantum-classical computing system comprising a classical computer, a system controller, and a quantum processor, the method including: identifying, using the classical computer, a molecular dynamics system to be simulated; calculating, using the classical computer, a plurality of energies associated with particles of the molecular dynamics system as part of the simulation based on an Ewald summation method, where calculating the plurality of energies includes partially offloading the calculation of the plurality of energies to the quantum processor; and outputting, using the classical computer, a physical behavior of the molecular dynamics system determined from the calculated plurality of energies.

[0008] An embodiment of the present disclosure also provides a hybrid quantum-classical computing system, comprising: a quantum processor comprising a first register formed of a plurality of qubits, a second register formed of a plurality of qubits, and a third register formed of a plurality of qubits, each qubit comprising a trapped ion having two hyperfine states; one or more lasers configured to emit a laser beam that is provided to the trapped ions in the quantum processor; a classical computer configured to perform operations; and a system controller configured to execute a control program to control the one or more lasers to perform operations on the quantum processor based on the offloaded calculation of the plurality of energies, the operations including: identifying, using the classical computer, a molecular dynamics system to be simulated; calculating, using the classical computer, a plurality of energies associated with particles of the molecular dynamics system as part of the simulation based on an Ewald summation method, the calculating the plurality of energies comprising partially offloading the calculation of the plurality of energies to the quantum processor; and outputting, using the classical computer, a physical behavior of the molecular dynamics system determined from the calculated plurality of energies.

[0009] An embodiment of the present disclosure further provides a hybrid quantum-classical computing system including a classical computer, a quantum processor comprising a first register formed of a plurality of qubits, a second register formed of a plurality of qubits, and a third register formed of a plurality of qubits, each qubit comprising a trapped ion having two hyperfine states, a non-volatile memory having a number of instructions stored therein that, when executed by one or more processors, cause the hybrid quantum-classical computing system to perform operations, and a system controller configured to execute a control program to control the one or more lasers to perform operations on the quantum processor based on the offloaded calculation of the plurality of energies. The operations include identifying, using the classical computer, a molecular dynamics system to be simulated; calculating, using the classical computer, a plurality of energies associated with particles of the molecular dynamics system as part of the simulation based on an Ewald summation method, where calculating the plurality of energies includes partially offloading the calculation of the plurality of energies to the quantum processor; and outputting, using the classical computer, a physical behavior of the molecular dynamics system determined from the calculated plurality of energies. [Brief description of the drawings]

[0010] 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 described by reference to embodiments, some of which are shown 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.

[0011] [Figure 1] FIG. 1 is a schematic partial view of an ion trap quantum computing system according to one embodiment. [Diagram 2] 2 shows a schematic diagram of an ion trap for confining ions in groups according to one embodiment. [Diagram 3] 4 shows a schematic energy diagram of each ion in a group of trapped ions according to one embodiment. [Figure 4] 1 shows the qubit states of the ions 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] 7 shows a flowchart illustrating a method 700 for performing computations using a hybrid quantum-classical computing system comprising a classical computer and a quantum processor. [Figure 8] 1 shows a flow chart illustrating a method for obtaining the energy of a system with interacting particles by molecular dynamics (MD) simulation, according to one embodiment.

[0012] For ease of understanding, the same reference numbers are used, where possible, to indicate 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

[0013] The embodiments described herein generally relate to a method for performing computations in a hybrid computing system, and more specifically, to a method for obtaining the energy of a physical system having interacting particles by a molecular dynamics (MD) simulation performed in a hybrid computing system including a classical computer and a quantum computer, in which the quantum computer operates based on a group of trapped ions, and in which the hybrid computing system can be referred to as a hybrid quantum-classical computing system.

[0014] A hybrid quantum-classical computing system capable of obtaining interparticle interaction energy of a physical system having interacting particles by molecular dynamics (MD) simulation may include 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 hardware / software components that perform quantum computation. The hybrid quantum-classical computing system performs support tasks including selecting a physical system including a group of interacting particles to be simulated by using a user interface and calculating a portion of the interparticle interaction energy of the physical system by the classical computer, a system control task including converting a series of logic gates into laser pulses, applying them to the quantum processor, performing measurements, and estimating the remaining portion of the interparticle interaction energy of the physical system by the system controller, and further support tasks including summing up the interparticle interaction energy of the physical system by the classical computer. Software programs for performing these tasks are stored in a non-volatile memory in the classical computer.

[0015] Quantum processors can be made from different qubit technologies. In one example, for ion trap technology, the quantum processor includes a trapped ion coupled with various hardware, including a laser for manipulating the internal hyperfine state (qubit state) of the trapped ion, and a photomultiplier tube (PMT) or other type of imaging device for reading out the internal hyperfine state (qubit state) of the trapped ion. A system controller receives instructions for controlling the quantum processor from a classical computer 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 to the classical computer the readout of the quantum processor and thus the output of the results of the calculations performed by the quantum processor.

[0016] The methods and systems described herein include computer simulation routines executed by a quantum processor in a hybrid quantum-classical computing system to perform computer simulations of complex systems, such as complex physical systems including, but not limited to, molecular dynamics. The methods described herein include improvements over conventional computer simulation methods.

[0017] (General hardware configuration) FIG. 1 is a schematic partial diagram of an ion trap quantum computing system 100, or simply system 100, according to one embodiment. System 100 may represent a 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 trapped ions 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 cadmium 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.

[0018] 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 multichannel photomultiplier tube (PMT) 110 (or some other imaging device) for measuring the individual ions. A Raman laser beam from a laser 112 is provided along the X axis to perform operations on the ions. A diffractive beam splitter 114 creates an array of Raman laser beams 116 that are individually switched using a multichannel 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 120 is non-co-propagating with the Raman laser beam 116 and 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 associated with 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.

[0019] FIG. 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 static (DC) and radio frequency (RF) voltages. A static (DC) voltage VS 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 groups 106 are approximately evenly distributed in the axial direction due to Coulomb interactions between the ions. In some embodiments, the ion trap 200 includes four hyperbolic shaped electrodes 202, 204, 206, and 208 that extend along the Z axis.

[0020] 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 toward the radial saddle point, each with a spring constant k, as discussed in more detail below. x and ky In some embodiments, the radial spring constants are modeled as equal when the quadrupole potential is radially symmetric. However, if undesirable, 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.

[0021] A different type of trap, not shown, is a microfabricated trapping chip, where an approach similar 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.

[0022] 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 is a positive ytterbium ion. 171 Yb + ω 01 Nuclear spins I=1 / 2 and I=2π=12.642821 GHz, with energy division corresponding to a frequency difference (called the "carrier frequency") 2 S 1 / 2 In another example, each ion has a hyperfine state (i.e., two electronic states). 133 Ba + , positive cadmium ions 111 CD + or 113 CD + all of which have nuclear spin I=1 / 2 and 2 S 1 / 2 The qubit is formed in two hyperfine states, denoted |0> and |1>, and has a hyperfine ground state (i.e., 2 S1 / 2 The 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 ion 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.

[0023] The individual qubit states of each trapped ion can be excited, for example, 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 Ω1e The 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 due to 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.

[0024] It should be noted that the specific atomic species used in the description provided herein is merely one example of an atomic species that has a stable and well-defined two-level energy structure and optically accessible excited states when ionized, and is not intended to limit the possible configurations, specifications, etc. of the ion trap 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 + ) are included.

[0025] 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 |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.

[0026] (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 where m 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 show 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 shows 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.

[0027] It should be noted that the above specific configuration is only one of several possible examples of a trap for confining ions according to the present disclosure, and is not intended to limit possible configurations, specifications, etc. 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 creates 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 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 in close proximity 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.

[0028] In an ion trap 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 quantization scheme for 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 tuned to the carrier frequency), δ=ω1-ω2-ω 01 =0), a simple Rabi flop (carrier transition) occurs between 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, and the combined qubit motion 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> mThe two-photon Rabi frequency Ω(t) is transformed into a superposition of the detuning frequency δ=ω1-ω2-ω 01 = ±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 entanglement between the two qubits. This entanglement is necessary to perform XX gate operations in an ion trap quantum computer.

[0029] 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

[0030] 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 Since ,does not change at the end of the XX gate operation, it may be considered disentangled. Therefore, the qubit states before and after the XX gate operation are generally described below without including the motional modes.

[0031] More generally, it is transformed by applying a composite pulse of sidebands 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

[0032] 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 universal gates {R, XX} that can be used to build a quantum computer configured to perform a desired computational process. Among several known sets of logic gates into which any quantum algorithm can be decomposed, a set of logic gates, commonly denoted 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 "entanglement gates") correspond to the manipulation of the entanglement of two trapped ions.

[0033] 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., entanglement interaction χ (i,j) (τ) is the desired value θ (i,j) The condition that the entanglement interaction is non-zero is constructed and applied to the i-th and j-th qubits. The transformation of the joint 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 and perform the desired XX gate operation on the i-th and j-th qubits.

[0034] (Hybrid Quantum-Classical Computing System) In a hybrid quantum-classical computing system, a quantum computer can be used as a domain-specific accelerator that may be able to accelerate certain computational tasks, generally beyond the scope of what a classical computer can perform. As mentioned above, the terms "quantum computer" and "quantum processor" can be used interchangeably. Examples of such computational tasks include Ewald summation in molecular dynamics (MD) simulations of physical systems with particles exerting forces on each other through short- and long-range interactions. Examples of such physical systems include ionic fluids, DNA strands, proteins, (poly)electrolyte solutions, colloids, or molecular models with partial charges. The dynamics of such physical systems are dictated by the energetic properties of the physical system, and the main contribution to the energy of a physical system comes from long-range interactions between particles (e.g., Coulomb interactions).

[0035] In MD simulations, the bulk material analyzed based on the simulations is typically modeled as an infinite system in which a finite system of N interacting particles (called "primitive cells") is replicated with the imposition of periodic boundary conditions. The N interacting particles may have long-range interactions with each other (e.g., Coulomb interactions). It is widely accepted that foreshortening long-range interactions introduces non-physical artifacts when calculating inter-particle interaction energies. Thus, the calculation of inter-particle interaction energy requires the summation of all pairwise long-range interactions between the N interacting particles, which would take O(N 2 ), the Ewald summation method has a computational complexity of O(N 3 / 2 ), and has become a standard method for efficiently simulating swarms of particles with long-range interactions.

[0036] In the embodiments described herein, a method is provided for performing MD simulations using Ewald summation with a hybrid quantum-classical computing system, referred to as the "Quantum Enhanced Ewald (QEE) summation method." The QEE summation method is faster than the traditional Ewald summation method, O(N 3 / 2 ) compared to O(N 5 / 4 (logN) 3 ) overall computational complexity.

[0037] It should be noted that the exemplary embodiments described herein are merely some possible examples of hybrid quantum-classical computing systems according to the present disclosure, and do not limit the possible configurations, specifications, etc. of hybrid quantum-classical computer systems according to the present disclosure. For example, hybrid quantum-classical computing systems according to the present disclosure may be applied to other types of computer simulations or image / signal processing where cyclic shift and phase kickback operations contribute to the computational complexity and may be accelerated by the use of quantum processors.

[0038] Herein, they are considered as N interacting classical particles that evolve according to the laws of classical physics, each of which has a well-defined position and momentum at any point during the simulation.

[0039] The particle interaction energy U due to pairwise interactions, e.g. the Coulomb interaction coul The sum of

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[0040] In the Ewald summation method, the charge distribution ρ(r) at position r in the primitive cell, for example, the sum of N charges (each of which is a Dirac delta function δ(rr (j) )):

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[0041] Therefore, the interparticle interaction energy U coul is the screened charge distribution ρ S Short-range interparticle interaction energy U due to (r) short

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[0042] Long-range interaction energy U long Now, the Fourier transform of the charge density

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[0043] Long-range interaction energy U long Electric form factor in

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[0044] FIG. 7 shows a flowchart 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.

[0045] In block 702, a molecular dynamics system to be simulated by the classical computer 102, e.g., a group of interacting particles, is identified by use of a user interface, e.g., a graphics processing unit (GPU) of the classical computer 102, or is retrieved from the memory of the classical computer 102, and information about the molecular dynamics system is retrieved from the memory of the classical computer 102.

[0046] Specifically, the size of the primitive cell (e.g., edge length L x , L y , and L z), the number of interacting particles in the primitive cell, N, and the positions r of the N interacting particles in the primitive cell. (j) (j=0,1,…,N-1), the charge distribution ρ(r) at position r in the primitive cell, the type of interparticle interaction (e.g., Coulomb interaction) between the N interacting particles, and the screening function W α (rr (j) ), and charge q j Position of r (j) The number of qubits to encode , and the position r (j) The desired upper error limit ε (e.g., edge length L x , L y , and L z m x , m y , and m z finite length) is selected and stored in the memory of the classical computer 102.

[0047] In block 704, the classical computer 102 calculates a number of energies associated with the particles of the molecular dynamics system as part of the simulation based on the Ewald summation method. The calculation of the energies is partially offloaded to the quantum processor to be performed in the process of block 706. Specifically, the short-range interparticle interaction energy U short and self-energy U self is calculated by conventional calculation methods known in the art. In block 706, the long-range interparticle interaction energy U long Electron form factor in

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[0048] In block 706, the system controller 104 and the quantum processor calculate the electron form factor for the inverse vector k selected in block 704.

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[0049] In block 708, the classical computer 102 calculates the particle interaction energy U coul =U short +U long -U self Specifically, the long-range particle interaction energy U long is calculated based on the results of block 706, and the total interparticle interaction energy is calculated by subtracting the short-range interparticle interaction energy U short and self-energy U self The long-range particle interaction energy U long is the electric form factor

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[0050] In block 710, the classical computer 102 determines the physical behavior of the molecular dynamics system from the inter-particle interaction energy calculated in block 708. Specifically, the classical computer 102 calculates the inter-particle interaction energy U coul =U short +U long -U selfThe calculated sum of particles may be output to a user interface, such as a graphics processing unit (GPU) of the classical computer 102, and / or stored in memory of the classical computer 102. For example, the calculated sum of particle interaction energies may be represented in a table on a display coupled to the GPU, or as a graphical representation of the particles.

[0051] 8 is a flow chart illustrating a method 800 for calculating multiple energies associated with particles of a molecular dynamics system as part of a molecular dynamics (MD) simulation as shown in block 706 above. In this example, the quantum processor is based on a group 106 of trapped ions, with the two hyperfine states of each of the trapped ions forming a qubit. Thus, the trapped ions form the qubits that provide the computational core of the quantum processor or quantum computer.

[0052] In block 802, the system controller 104 causes the quantum processor (i.e., the group of ions 106) to enter an initial superposition state |ψ0>=|ψ> index |k>|ψ> data is set to.

[0053] To encode particle index j (=0,1,2,…,N-1),

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[0054] A second register (hereafter referred to as the "inverse vector register") is formed of O(Γ) qubits for encoding the inverse vector k selected in block 704. The inverse vector register can be set by an appropriate combination of single-qubit operations, with the O(Γ) qubits of the inverse vector register all prepared in state |0>.

[0055] The third register (hereafter also called the “data register”) is made up of O(NΓ) qubits and stores the charge-location-encoded states

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[0056] In block 804, the system controller 104 determines the charge position encoding state |ψ> data The data register of is cyclically shifted based on the index register |ν>.

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[0057] The cyclic shift operation S may be implemented by the system controller 104 applying a combination of single-qubit and two-qubit gate operations to the qubits in the index and data registers.

[0058] In block 806, the system controller 104 shifts the cyclically shifted superposition state |Ψ CS The index and data registers in |Ψ are stored in a phased cyclic shifted superposition state |Ψ based on the inverse vector register |k PCS > (k) This transformation, called the phase kickback operation, transforms the electron form factor

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[0059] Therefore, the cyclic shift superposition state │Ψ CS The phase kickback operation applied to the first block of data registers (i.e., j=0) in CS > into a phased cyclic shift superposition state │Ψ PCS > (k) Convert to.

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[0060] In block 808, the system controller 104 determines the phased cyclic shift superposition state |Ψ PCS >> (k) The index register and the data register in the phase overlap state |Ψ P >>(k) is converted to

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[0061] In block 810, the phased superposition state |Ψ is determined by the system controller 104. P > (k) is the final superposition state |Ψ F > (k) is converted to

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[0062] This transformation can be performed by applying the Hadamard operation H to each qubit in the index register.

[0063] In block 814, the system controller 104 determines the final superposition state |Ψ F >> (k) Amplitude A F (k) is in state │0>K>│0>,

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[0064] At block 816, the measured amplitude A F (k) is returned to the classical computer 102. The measured amplitude A F (k) modulus squared |A F (k)| 2 is calculated, and the long-range interparticle interaction energy U long The amplitude A measured for a sufficiently large number of inverse vectors k is then converted to F (k) squared |A F (k)| 2 If not, the process returns to block 802 to calculate another inverse vector k. If the method 800 finds amplitudes A for a sufficiently large number of inverse vectors k, F (k),|A F (k)| 2 Once the calculation of is completed, the process proceeds to block 708 of the method 700.

[0065] The maximum of k to be considered, i.e., K, is typically chosen to ensure that the simulation is accurate to within a desired upper error limit, δ. Optimizing K with respect to the desired upper error limit, δ, in an MD simulation reduces the number of operations to O(N 3 / 2 ) for three-dimensional (3D) systems. In the hybrid quantum-classical approach, when optimizing K with respect to a desired upper bound error δ, the number of operations scales as O(N 5 / 4 (logN) 3 )

[0066] The method described herein for obtaining the energy of a system with interacting particles by molecular dynamics (MD) simulation improves the computational complexity by using a quantum processor in the Ewald summation calculation over classical computational methods.

[0067] It should be noted that the specific illustrative embodiments described above 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 methods described herein may be applied to other simulation problems, such as simulating trapped ions in a quantum computer, to help design better quantum computers. Furthermore, the quantum processor in a 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 that includes 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 such 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 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 two lowest 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 application of a series of microwave pulses, the frequency and duration of which are appropriately adjusted.

[0068] 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: using said classical computer to identify a molecular dynamics system to be simulated; using the classical computer to calculate a plurality of energies associated with particles of the molecular dynamics system as part of the simulation based on an Ewald summation method, the calculating of the plurality of energies comprising partially offloading the calculation of the plurality of energies to the quantum processor; outputting, using the classical computer, a physical behavior of the molecular dynamics system determined from the calculated energies; Including, the plurality of energies include short-range inter-particle interaction energies, self-energies, and long-range inter-particle interaction energies of the particles of the molecular dynamics system; The step of calculating the plurality of energies further comprises the steps of calculating the short-range inter-particle interaction energy and the self-energy; The method of claim 1, wherein the step of partially offloading the step of calculating the plurality of energies includes calculating, by the system controller and the quantum processor, an electron form factor used to calculate the long-range inter-particle interaction energy.

2. calculating the sum of the short-range inter-particle interaction energy, the self-energy and the long-range inter-particle interaction energy; The method of claim 1 , wherein the long-range inter-particle interaction energy is calculated based on the calculated electronic form factors.

3. the quantum processor comprises a first register formed of a plurality of qubits, a second register formed of a plurality of qubits, and a third register formed of a plurality of qubits; The step of calculating the electron form factor by the quantum processor comprises: setting, by the system controller, the quantum processor to an initial state, in which the first register is in a superposition state of equal indices of the particles, the second register encodes an inverse vector from which the electron form factor is calculated, and the third register is in a charge-position encoding state to encode the charge and position of the particles of the molecular dynamics system; converting, by the system controller, the third register into a cyclic shift state based on the first register; converting, by the system controller, the first register and the third register into a phased cyclic shift superposition state based on the second register; converting, by the system controller, the first register and the third register into a phased superposition state; transforming, by the system controller, the first register into the equal superposition state of the index of the particle; measuring, by the system controller, the amplitude of the quantum processor; The method of claim 1 , comprising:

4. 4. The method of claim 3, wherein transforming the third register to the cyclic shift state comprises applying a cyclic shift operation to the third register based on the first register.

5. 5. The method of claim 4, wherein transforming the first register and the third register into a phased superposition state comprises applying an inverse of the cyclic shift operation to the third register based on the first register.

6. 4. The method of claim 3, wherein the step of converting the first register and the third register into the phased cyclic shift superposition state includes a phase kickback operation for a first block of the third register based on the second register.

7. 1. A hybrid quantum-classical computing system, comprising: a quantum processor comprising a plurality of qubits, each qubit comprising a trapped ion having two hyperfine states; one or more lasers configured to emit a laser beam that is delivered to trapped ions in the quantum processor; A classical computer, using said classical computer to identify a molecular dynamics system to be simulated; using the classical computer to calculate a plurality of energies associated with particles of the molecular dynamics system as part of the simulation based on an Ewald summation method, the calculating of the plurality of energies comprising partially offloading the calculation of the plurality of energies to the quantum processor; outputting, using the classical computer, a physical behavior of the molecular dynamics system determined from the calculated energies; a classical computer configured to perform operations including: a system controller configured to execute a control program to control the one or more lasers to perform operations on the quantum processor based on the offloaded calculations of the plurality of energies; Equipped with the plurality of energies include short-range inter-particle interaction energies, self-energies, and long-range inter-particle interaction energies of the particles of the molecular dynamics system; The step of calculating the plurality of energies further comprises the steps of calculating the short-range inter-particle interaction energy and the self-energy; The hybrid quantum-classical computing system, wherein the partially offloading step of calculating the plurality of energies includes calculating, by the system controller and the quantum processor, an electron form factor used to calculate the long-range inter-particle interaction energy.

8. The operation is calculating the sum of the short-range inter-particle interaction energy, the self-energy and the long-range inter-particle interaction energy; 8. The hybrid quantum-classical computing system of claim 7, wherein the long-range interparticle interaction energy is calculated based on the calculated electron form factors.

9. The quantum processor further comprising a first register, a second register, and a third register, each of the first register, the second register, and the third register formed from a plurality of qubits of the quantum processor; The step of calculating the electron form factor by the quantum processor comprises: setting, by the system controller, the quantum processor to an initial state, in which the first register is in a superposition state of equal indices of the particles, the second register encodes an inverse vector from which the electron form factor is calculated, and the third register is in a charge-position encoding state to encode the charge and position of the particles of the molecular dynamics system; converting, by the system controller, the third register into a cyclic shift state based on the first register; converting, by the system controller, the first register and the third register into a phased cyclic shift superposition state based on the second register; converting, by the system controller, the first register and the third register into a phased superposition state; transforming, by the system controller, the first register into the equal superposition state of the index of the particle; measuring, by the system controller, the amplitude of the quantum processor; 8. The hybrid quantum-classical computing system of claim 7, comprising:

10. converting the third register to the cyclic shift state comprises applying a cyclic shift operation to the third register based on the first register; 10. The hybrid quantum-classical computing system of claim 9, wherein transforming the first register and the third register into a phased superposition state comprises applying an inverse of the cyclic shift operation to the third register based on the first register.

11. 10. The hybrid quantum-classical computing system of claim 9, wherein transforming the first register and the third register into the phased cyclically shifted superposition state comprises a phase kick-back operation on a first block of the third register based on the second register.

12. 1. A hybrid quantum-classical computing system, comprising: Classical computers and a quantum processor comprising a plurality of qubits, each qubit comprising a trapped ion having two hyperfine states; a non-volatile memory having a number of instructions stored therein that, when executed by one or more processors, cause the hybrid quantum-classical computing system to: using said classical computer to identify a molecular dynamics system to be simulated; using the classical computer to calculate a plurality of energies associated with particles of the molecular dynamics system as part of the simulation based on an Ewald summation method, the calculating of the plurality of energies comprising partially offloading the calculation of the plurality of energies to the quantum processor; outputting, using the classical computer, a physical behavior of the molecular dynamics system determined from the calculated energies; a non-volatile memory for performing operations including: a system controller configured to execute a control program to perform operations on the quantum processor based on the offloaded calculation of the plurality of energies; Equipped with the plurality of energies include short-range inter-particle interaction energies, self-energies, and long-range inter-particle interaction energies of the particles of the molecular dynamics system; The step of calculating the plurality of energies further comprises the steps of calculating the short-range inter-particle interaction energy and the self-energy; The hybrid quantum-classical computing system, wherein the partially offloading step of calculating the plurality of energies includes calculating, by the system controller and the quantum processor, an electron form factor used to calculate the long-range inter-particle interaction energy.

13. The operation is calculating the sum of the short-range inter-particle interaction energy, the self-energy and the long-range inter-particle interaction energy; 13. The hybrid quantum-classical computing system of claim 12, wherein the long-range interparticle interaction energy is calculated based on the calculated electron form factors.

14. The quantum processor further comprising a first register, a second register, and a third register, each of the first register, the second register, and the third register formed from a plurality of qubits of the plurality of qubits of the quantum processor; The step of calculating the electron form factor by the quantum processor comprises: setting, by the system controller, the quantum processor to an initial state, in which the first register is in a superposition state of equal indices of the particles, the second register encodes an inverse vector from which the electron form factor is calculated, and the third register is in a charge-position encoding state to encode the charge and position of the particles of the molecular dynamics system; converting, by the system controller, the third register into a cyclic shift state based on the first register; converting, by the system controller, the first register and the third register into a phased cyclic shift superposition state based on the second register; converting, by the system controller, the first register and the third register into a phased superposition state; transforming, by the system controller, the first register into the equal superposition state of the index of the particle; measuring, by the system controller, the amplitude of the quantum processor; 13. The hybrid quantum-classical computing system of claim 12, comprising:

15. 15. The hybrid quantum-classical computing system of claim 14, wherein transforming the third register to the cyclic shift state comprises applying a cyclic shift operation to the third register based on the first register.

16. 16. The hybrid quantum-classical computing system of claim 15, wherein transforming the first register and the third register into a phased superposition state comprises applying an inverse of the cyclic shift operation to the third register based on the first register.

17. 15. The hybrid quantum-classical computing system of claim 14, wherein transforming the first register and the third register into the phased cyclically shifted superposition state comprises a phase kickback operation on a first block of the third register based on the second register.

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