Simultaneous entanglement gates for trapped-ion quantum computers

Abstract

A method for performing simultaneous entanglement gate operations in a trapped ion quantum computer includes: selecting a gate duration value and a detuning frequency of a pulse to be applied individually to a plurality of participating ions in a chain of trapped ions to simultaneously entangle a plurality of ion pairs in the plurality of participating ions through one or more predetermined values ​​of entanglement interactions; determining the amplitude of the pulse based on the selected gate duration value, the selected detuning frequency, and the frequency of the motion mode of the chain of trapped ions; generating the pulse with the determined amplitude; and applying the generated pulse to the plurality of participating ions at the selected gate duration value. Each trapped ion in the chain has two frequency-separated states defining a quantum bit, and the motion modes of the chain of trapped ions each have a different frequency.

Description

Technical Field

[0001] The present disclosure relates generally to methods of performing entangled gate operations in an ion trap quantum computer, and more particularly to methods of constructing pulses to perform multiple entangled gate operations simultaneously. Background Art

[0002] In quantum computing, quantum bits (qubits), analogous to the bits that represent "0" and "1" in classical (digital) computers, need to be prepared, manipulated, and measured (read out) with near-perfect control during computations. Imperfect control of qubits leads to errors that accumulate during computations, limiting the scale of quantum computers that can perform reliable calculations.

[0003] In the physical system proposed to build a large-scale quantum computer, there is a chain of ions (e.g., charged atoms) that are trapped and suspended in a vacuum by electromagnetic fields. These ions have internal hyperfine states that are separated by frequencies in the range of several GHz that can be used as computational states of quantum bits (called "qubit states"). These hyperfine states can be controlled using radiation provided from a laser, or sometimes referred to in this article as interaction with a laser beam. Using this laser interaction, the ions can be cooled to close to their ground state of motion. The ions can also be optically pumped with high precision into one of two hyperfine states (preparation of quantum bits), manipulated between two hyperfine states by a laser beam (single-qubit gate operation), and their internal hyperfine states detected by fluorescence when a resonant laser beam is applied (readout of quantum bits). A pair of ions can be controllably entangled (two-qubit gate operation) through qubit state-related forces using laser pulses that couple the ions to the collective motion modes of the chain of trapped ions, which are generated by the Coulomb interaction between the ions. In general, entanglement occurs when pairs or groups of ions (or particles) are generated, interact or share spatial proximity in a way such that the quantum state of each ion cannot be described independently of the quantum state of the other ions, even when the ions are separated by large distances. As the size of quantum computers increases, the implementation of two-qubit gate operations between a pair of ions increases in complexity, and therefore the errors associated with the implementation and the resources required for implementation (such as laser power) increase.

[0004] To increase the size of quantum computers that are able to implement algorithms to solve problems that are otherwise intractable on classical computers, a process is needed to precisely control qubits to perform the desired computational process with minimal resources. Summary of the invention

[0005] A method for performing simultaneous entanglement gate operations in a trapped ion quantum computer comprises: selecting a gate duration value and a detuning frequency of a pulse to be applied individually to a plurality of participating ions in a chain of trapped ions to simultaneously entangle a plurality of ion pairs in the plurality of participating ions through one or more predetermined values ​​of entanglement interactions; determining an amplitude of the pulse based on the selected gate duration value, the selected detuning frequency, and the frequency of a motion mode of the chain of trapped ions; generating the pulse having the determined amplitude; and applying the generated pulse to the plurality of participating ions at the selected gate duration value. Each trapped ion in the chain has two frequency-separated states defining a quantum bit, and the motion modes of the chain of trapped ions each have a different frequency.

[0006] A method of performing computations using a quantum computer includes executing, by a processor in a digital computer, a software program stored in a non-volatile memory of the digital computer; and generating a solution to a selected quantum algorithm based on a processed result of the quantum computation. The software program executed requires performing at least one calculation, and performing the at least one calculation includes: selecting, by the processor in the digital computer, a quantum algorithm to be implemented on a quantum computer, wherein the quantum computer includes a chain of trapped ions arranged within a quantum register of the quantum computer, the trapped ions in the chain each having two frequency-separated states, the two frequency-separated states each defining a quantum bit, and the motion patterns of the chain of trapped ions each having a different frequency; compiling the selected quantum algorithm into a series of universal logic gates; converting the series of universal logic gates into laser pulses to be applied to a plurality of participating ions within the quantum register; during the process of performing the at least one calculation, calculating, by the processor in the digital computer, parameters of the laser pulses to be applied to the plurality of participating ions within the quantum register; generating laser pulses each having a determined amplitude; performing a quantum calculation by applying the generated laser pulses to the plurality of participating ions for a length of time equal to the gate duration value; determining a result of the quantum calculation by measuring a population of the quantum bit states of the trapped ions in the chain; and processing, by the processor of the digital computer, the determined result of the quantum calculation based on the measured population of the quantum bit states. Calculating the parameters includes determining, by the processor in the digital computer, an amplitude of the laser pulse based on information stored in the digital computer regarding the gate duration value and a frequency of a motion mode of the chain of trapped ions.

[0007] A quantum computing system, comprising: a chain of trapped ions, each of the trapped ions having two hyperfine states and an excited state defining a quantum bit; one or more lasers configured to emit a laser beam, the laser beam being split into two or more non-co-propagating laser beams, the two or more non-co-propagating laser beams being provided to each of the trapped ions; and a controller configured to: select gate duration values ​​and detuning frequencies of pulses to be applied individually to a plurality of participating ions in the chain of trapped ions to simultaneously entangle the plurality of participating ions by one or more predetermined values ​​of entanglement interactions. The invention relates to a method for generating a plurality of ion pairs in a quantum computer system; determining the amplitude of the pulse based on a selected gate duration value, a selected detuning frequency, and a frequency of a motion mode of a chain of trapped ions, wherein the amplitude is derived based on a non-zero entanglement interaction between each of the plurality of ion pairs to be entangled, a decoupling between each pair of ions not to be entangled, and a condition of minimizing power provided to the plurality of participating ions during the selected gate duration value; generating the pulse including the determined amplitude and the detuning frequency; and applying the generated pulse to a first ion and a second ion at the gate duration value. Each of the trapped ions has two frequency-separated states defining a quantum bit, the motion modes of the chain of trapped ions each have a different frequency, and an ion pair in the plurality of ion pairs includes the first ion and the second ion. The two or more non-co-propagating laser beams are configured to cause each of the trapped ions to produce a Rabi flopping between the two hyperfine states via the excited state. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0009] Figure 1 is a partial view of an ion trap quantum computer according to one embodiment.

[0010] Figure 2 A schematic diagram of an ion trap for confining ions in a chain is depicted according to one embodiment.

[0011] Figure 3A , Figure 3B and Figure 3C Several schematic collective lateral motion mode structures of a chain of five trapped ions are depicted.

[0012] Figure 4A schematic energy diagram of each ion in a chain of trapped ions is depicted according to one embodiment.

[0013] Figure 5 The qubit state of the ion is described as a point on the surface of a Bloch sphere.

[0014] Fig. 6A and Figure 6B A schematic diagram of the motion sideband spectrum and motion pattern of each ion according to one embodiment is described.

[0015] Figure 7 A flow chart illustrating a method for determining a set of control parameters (EASE protocol) according to one embodiment is described.

[0016] For ease of understanding, the same reference numerals are used to represent the same elements common to the drawings, where possible. In the drawings and the following description, an orthogonal coordinate system including an X-axis, a Y-axis, and a Z-axis is used. For convenience, the direction represented by the arrow in the figure is assumed to be the positive direction. It is conceivable that the elements disclosed in some embodiments can be used beneficially in other embodiments without special statements. DETAILED DESCRIPTION

[0017] Embodiments described herein relate generally to methods and systems for designing, optimizing, and delivering pulses to simultaneously perform entanglement gate operations on multiple ion pairs during quantum computing, and more specifically, to pulses that can be constructed in an efficient manner and that can also reduce the laser power required to perform entanglement gate operations.

[0018] The entire system capable of performing quantum computations using trapped ions will include a classical computer, a system controller, and a quantum register. The classical computer performs support and system control tasks, including: selecting a quantum algorithm to be run by using a user interface such as a graphics processing unit (GPU); compiling the selected quantum algorithm into a series of general logic gates; converting the series of general logic gates into laser pulses to be applied to the quantum register; and pre-calculating parameters for optimizing laser pulses by using a central processing unit (CPU). The software program for performing the tasks of decomposing and executing the quantum algorithm is stored in non-volatile memory within the classical computer. The quantum register includes trapped ions coupled to various hardware, including lasers that manipulate the internal hyperfine states (qubit states) of the trapped ions and acousto-optic modulators that read out the internal hyperfine states (qubit states) of the trapped ions. The system controller receives pre-calculated parameters of power-optimal pulses from the classical computer at the beginning of running the selected algorithm on the quantum register, controls various hardware associated with controlling any and all aspects of running the selected algorithm on the quantum register, and returns a readout of the quantum register, thereby outputting the results of the quantum computation to the classical computer at the end of running the algorithm.

[0019] The methods and systems described herein include a process for converting logic gates into laser pulses applied to a quantum register, and a process for pre-calculating parameters that optimize the laser pulses applied to the quantum register and used to improve the performance of a quantum computer.

[0020] Among the several known sets of universal logic gates by which any quantum algorithm can be decomposed, there is a set of universal logic gates (generally represented as {R,XX}) that originates from the trapped ion quantum computing system described in this article. Here, the R gate corresponds to the manipulation of the individual quantum bit states of the trapped ion, and the XX gate (also called the "entanglement gate") corresponds to the manipulation of the entanglement of two trapped ions. It should be clear to those of ordinary skill in the art that the R gate can be implemented with near-perfect fidelity, while the formation of the XX gate is complex and requires optimization of a given type of trapped ion, the number of ions in the chain of trapped ions, and the hardware and environment in which the trapped ions are trapped (to name just a few factors), which can improve the fidelity of the XX gate and avoid or reduce computational errors in quantum computers. In the following discussion, methods for generating and optimizing pulses for performing calculations based on the formation of XX gates with improved fidelity will be described.

[0021] As the size of quantum computers increases, the complexity of the entanglement gate operations used to perform quantum computations increases, and the complexity of the pulses used to perform these entanglement gate operations also increases. The laser power required to achieve such complex pulses subsequently increases, and therefore the available laser power can limit the scale of achievable quantum computers. The methods and systems described in the present disclosure simplify the construction of pulses and further reduce the laser power required to achieve the pulses, so that quantum computers can be scaled up to a larger scale, allowing them to perform more complex computational operations. This means that entanglement gates are executed faster with a given power budget. Errors commensurate with the delivered laser power will decrease as the required laser power decreases.

[0022] General hardware configuration

[0023] Figure 1 1 is a partial view of an ion trap quantum computer or system 100 according to one embodiment. System 100 includes a classical (digital) computer 101, a system controller 118, and a quantum register, which is a chain 102 of trapped ions (i.e., five shown) extending along the Z axis. Classical computer 101 includes a central processing unit (CPU), a memory, and support circuits (or I / O). The memory is connected to the CPU and can be one or more of readily available memories such as read-only memory (ROM), random access memory (RAM), floppy disk, hard disk, or any other form of local or remote digital storage. Software instructions, algorithms, and data can be encoded and stored in the memory for instructing the CPU. Support circuits (not shown) are also connected to the CPU for supporting the processor in a conventional manner. Support circuits may include conventional caches, power supplies, clock circuits, input / output circuits, subsystems, etc.

[0024] An imaging objective 104, such as an objective having a numerical aperture (NA) of, for example, 0.37, collects fluorescence along the Y axis from the ions and maps each ion onto a multi-channel photomultiplier tube (PMT) 106 for measuring individual ions. A non-co-propagating Raman laser beam provided along the X axis from a laser 108 operates on the ions. A diffraction beam splitter 110 generates an array of static Raman beams 112, which are individually switched using a multi-channel acousto-optic modulator (AOM) 114 and are configured to selectively act on individual ions. A global Raman laser beam 116 irradiates all ions simultaneously. A system controller (also referred to as an "RF controller") 118 controls the AOM 114. The system controller 118 includes a central processing unit (CPU) 120, a read-only memory (ROM) 122, a random access memory (RAM) 124, a storage unit 126, and the like. The CPU 120 is a processor of the RF controller 118. ROM 122 stores various programs, and RAM 124 is a working memory for various programs and data. Storage unit 126 includes a non-volatile memory such as a hard disk drive (HDD) or a flash memory, and stores various programs even when power is off. CPU 120, ROM 122, RAM 124, and storage unit 126 are interconnected via bus 128. RF controller 118 executes a control program stored in ROM 122 or storage unit 126, and uses RAM 124 as a working area. The control program will include a software application that includes program code that can be executed by a processor to perform various functions associated with receiving and analyzing data and controlling any and all aspects of the method and hardware for creating the ion trap quantum computer system 100 discussed herein.

[0025] Figure 2 A schematic diagram of an ion trap 200 (also called a Paul trap) for confining ions in a chain 102 is depicted according to one embodiment. The confinement potential is applied by both a static (DC) voltage and a radio frequency (RF) voltage. A static (DC) voltage V is applied to the end cap electrodes 210 and 212. S The ions are confined along the Z-axis (also referred to as the "axial" or "longitudinal" axis). Due to the Coulomb interaction between the ions, the ions in the chain 102 are almost uniformly distributed in the axial direction. In some embodiments, the ion trap 200 includes four hyperbolic electrodes 202, 204, 206, and 208 extending along the Z-axis.

[0026] During operation, a sinusoidal voltage V1 (with amplitude V RF / 2) is applied to a pair of opposing electrodes 202, 204, and a sinusoidal voltage V1 (with an amplitude V RF / 2) A sinusoidal voltage V2 with a 180° phase shift to drive the frequency ωRF Applied to another pair of opposing electrodes 206, 208, a quadrupole potential is generated. In some embodiments, the sinusoidal voltage is applied only to one pair of opposing electrodes 202, 204, while the other pair of opposing electrodes 206, 208 is grounded. The quadrupole potential generates an effective confinement force for each trapped ion in the XY plane (also referred to as "radial" or "lateral") perpendicular to the Z axis, and the confinement force is proportional to the distance from the saddle point (i.e., the position where the RF electric field disappears in the axial direction (Z direction)). The motion of each ion in the radial direction (i.e., the direction in the XY plane) is approximated as a harmonic oscillation (called long-term motion) with a restoring force toward the saddle point in the radial direction, and can be respectively expressed by the spring constant k x and k y to model, as discussed in more detail below. In some embodiments, when the quadrupole potential is symmetric in the radial direction, the spring constants in the radial direction are modeled to be equal. However, in some cases, the motion of ions in the radial direction may be undesirably distorted due to some asymmetry in the physical trap configuration, small DC patch potentials due to inhomogeneities in the electrode surfaces, etc., and due to these and other external distortion sources, the ions may deviate from the center of the saddle point.

[0027] Trapped ion configuration and quantum bit information

[0028] Figure 3A , Figure 3B and Figure 3C Several schematic structures of collective lateral motion modes (also referred to as "motion mode structures") of a chain 102 of, for example, five trapped ions are depicted. Here, due to the static voltage V applied to the end cap electrodes 210 and 212, S The resulting confinement potential is weaker than the confinement potential in the radial direction. The collective motion mode of the chain 102 of trapped ions in the lateral direction is determined by the Coulomb interaction between the trapped ions in combination with the confinement potential generated by the ion trap 200. The trapped ions undergo collective lateral motion (referred to as "collective lateral motion mode", "collective motion mode" or simply "motion mode"), where each mode has a different energy (or equivalently, frequency) associated with it. The motion mode with the pth lowest energy is hereinafter referred to as |n ph > p , where n ph denoting the number of quanta of motion in a motion mode (in units of energy excitation, called phonons), and the number of motion modes P in a given transverse direction is equal to the number N of ions trapped in the chain 102 . FIG. 3A to FIG. 3C Examples of different types of collective lateral motion modes that five trapped ions positioned in chain 102 may undergo are schematically shown. Figure 3A It is the common movement mode with the highest energy|n ph > PSchematic diagram of , where P is the number of motion modes. In the common motion mode |n> P In the oscillation, all ions oscillate in phase along the transverse direction. Figure 3B is the second highest energy tilting motion mode |n ph > P-1 Schematic diagram of . In the tilt motion mode, ions on opposite ends move out of phase in the transverse direction (ie, in opposite directions). Figure 3C It is an advanced sports mode. ph > P-3 Schematic diagram of the energy ratio of the tilt motion mode |n ph > P-1 The lower the energy, the more complex the patterns of ions.

[0029] It should be noted that the above-mentioned specific configuration is only one of several possible examples of traps for confining ions according to the present disclosure, and does not limit the possible configurations, specifications, etc. of the traps according to the present disclosure. For example, the geometry of the electrodes is not limited to the above-mentioned hyperbolic electrodes. In other examples, the trap that generates an effective electric field may be a multilayer trap or a surface trap, wherein the effective electric field causes the ions to move in the radial direction as harmonic oscillations, in which several electrode layers are stacked and RF voltage is applied to two diagonally opposite electrodes, and in which all electrodes are located in a single plane on the chip. In addition, the trap may be divided into a plurality of segments, adjacent pairs of which may be linked by one or more ion shuttles, or coupled by photonic interconnections. The trap may also be an array of individual confinement regions arranged close to each other on a microfabricated ion trap chip. In some embodiments, in addition to the above-mentioned RF component, the quadrupole potential also has a spatially varying DC component.

[0030] Figure 4 A schematic energy diagram 400 of each ion in the chain 102 of trapped ions according to one embodiment is depicted. In one example, each ion may be a positive ytterbium ion. 171 Yb + , which has 2 S 1 / 2 The hyperfine state (i.e., two electronic states) has an energy splitting corresponding to ω 01 / 2π=12.642821GHz frequency difference (called “carrier frequency”). The qubit is formed by these two hyperfine states, denoted as |0> and |1>, where the hyperfine ground state (i.e. 2 S 1 / 2 The lower energy state in the hyperfine state is represented by |0>. In the following, the terms "hyperfine state", "internal hyperfine state" and "qubit" are used interchangeably to represent |0> and |1>. By known laser cooling methods, such as Doppler cooling or resolved sideband cooling, each ion can be cooled (i.e., the kinetic energy of the ion can be reduced) to the motional ground state |0>p Nearby, any motion mode p has no phonon excitation (i.e. n ph = 0), and then the qubit state is prepared in the hyperfine ground state |0> by optical pumping. Here, |0> represents a single qubit state of the trapped ion, and |0> with a suffix of p p The motion ground state of the motion mode p of the chain 102 of trapped ions is represented.

[0031] The individual qubit states of each trapped ion can be determined, for example, by exciting the 2 P 1 / 2 energy level (denoted as |e>). Figure 4 As shown, the laser beam from the laser can be split into a pair of non-co-propagating laser beams (a first laser beam with a frequency ω1 and a second laser beam with a frequency ω2) in a Raman configuration, and about the transition frequency ω between |0> and |e> 0e The detuning frequency of single photon transition is Δ=ω1-ω 0e Detuning, such as Figure 4 As shown. The two-photon transition detuning frequency δ includes adjusting the amount of energy provided to the trapped ion by the first and second laser beams, and the combination thereof is used to transfer the trapped ion between the hyperfine states |0> and |1>. When the single-photon transition detuning frequency Δ is much larger than the two-photon transition detuning frequency (also referred to as "detuning frequency") δ = ω1-ω2-ω 01 (hereinafter referred to as ±μ, μ is a positive value), single-photon Rabi frequency Ω 0e (t) and Ω 1e (t) (they are time-varying and determined by the amplitude and phase of the first and second laser beams, and the Rabi oscillations between the states |0> and |e> and between the states |1> and |e> occur at the single-photon Rabi frequency, respectively), and the spontaneous emission rate from the excited state |e>, which induces Rabi oscillations (also called "carrier transitions") between the two hyperfine states |0> and |1> at the two-photon Rabi frequency Ω(t). The intensity (i.e., the absolute value of the amplitude) of the two-photon Rabi frequency Ω(t) is related to Ω 0e Ω 1e / 2Δ is proportional to, where Ω 0e and Ω 1e are the single-photon Rabi frequencies caused by the first and second laser beams, respectively. In the following, this set of non-co-propagating laser beams used to manipulate the internal hyperfine state of the qubit (qubit state) in a Raman configuration 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 will be shown and further described below. Detuning frequency δ = ω1-ω2-ω 01It may be referred to as the detuned frequency of the composite pulse or the detuned frequency of the pulse. The amplitude of the two-photon Rabi frequency Ω(t) determined by the amplitudes of the first and second laser beams may be referred to as the "amplitude" of the composite pulse.

[0032] It should be noted that the specific atomic species used in the discussion provided herein is only 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 therefore not intended to limit the possible configurations, specifications, etc. of ion trap quantum computers 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 + ).

[0033] supply Figure 5 To help visualize the qubit state of the ion, it is represented as a point on the surface of a Bloch sphere 500 having an azimuthal angle φ and a polar angle θ. Application of a composite pulse as described above causes Rabi oscillations to occur between the qubit states |0> (represented as the north pole of the Bloch sphere) and |1> (the south pole of the Bloch sphere). Adjusting the duration and amplitude of the composite pulse causes the qubit state to flip from |0> to |1> (i.e., from the north pole to the south pole of the Bloch sphere), or to flip 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." In addition, by adjusting the duration and amplitude of the composite pulse, the qubit state |0> can be converted to a superposition state |0>+|1>, in which the two qubit states |0> and |1> are added and equally weighted in phase (the normalization factor of the superposition state is omitted below without loss of generality), and the qubit state |1> can be converted to a superposition state |0>-|1>, in which the two qubit states |0> and |1> are equally weighted but in different phases. This application of a composite pulse is called a "π / 2 pulse". More generally, the superposition of 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 state |0>±|1> corresponds to points on the equator with azimuth angles φ of zero and π, respectively. The superposition state corresponding to a point on the equator with azimuth angle φ is represented as |0>+e iφ |1> (eg, |0>±i|1> for φ=±π / 2). The transformation between two points on the equator (ie, a rotation about the Z axis on the Bloch sphere) can be achieved by shifting the phase of the composite pulse.

[0034] In a trapped ion quantum computer, the motion pattern can be used as a data bus to mediate the entanglement between two qubits, which is used to perform XX gate operations. That is, each of the two qubits is entangled with the motion pattern, and then the entanglement is transferred to the entanglement between the two qubits by using motion sideband excitation, as described below. Fig. 6A and Figure 6B Schematically depicts the ions in the chain 102 having a frequency ω according to one embodiment. p Sports Mode |n ph > p A view of the moving sideband spectrum under . Figure 6B As shown, when the detuned 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 oscillation (carrier transition) between the qubit states |0> and |1> occurs. When the detuned frequency of the composite pulse is positive (i.e., the frequency difference between the first and second laser beams is tuned to be higher than the carrier frequency, δ = ω1-ω2-ω 01 =μ>0, called blue sideband), the combined quantum bit motion state |0>|n ph > p and |1>|n ph +1> p Rabi oscillations between |n ph > p The p-th motion mode with n phonon excitation represented by |n ph +1> p Represented by (n ph +1) phonon excited p-th motion mode). When the detuning frequency of the composite pulse is negative (i.e., the frequency difference between the first and second laser beams is tuned to a lower motion mode than the carrier frequency |n ph > p The frequency ω p ,δ=ω1-ω2-ω 01 =-μ<0, called red sideband), the combined quantum bit motion state |0>|n ph > p and |1>|n ph -1> p Rabi oscillations between (i.e., when the qubit state |0> flips to |1>, the transition from motion mode |n ph > p To at least one phonon-excited motion mode |n ph -1> p The π / 2 pulse applied to the blue sideband of the quantum bit will combine the quantum bit motion state |0>|nph > p Convert to |0>|n ph > p and |1>|n ph +1> p The π / 2 pulse applied to the red sideband of the qubit moves the combined qubit |0>|n ph > p Convert to |0>|n ph > p and |1>|n ph -1> p When the two-photon Rabi frequency Ω(t) is less than the detuning frequency δ = ω1-ω2-ω 01 = ±μ, the blue sideband transition or the red sideband transition can be selectively driven. Therefore, by applying the right type of pulse (such as a π / 2 pulse), the qubit can be entangled with the desired motion mode, which can then be entangled with another qubit, resulting in entanglement between the two qubits. In an ion trap quantum computer, entanglement between qubits is required to perform XX gate operations.

[0035] By controlling and / or guiding the conversion of the combined quantum bit motion state as described above, an XX gate operation can be performed on two quantum bits (the i-th and j-th quantum bits). In general, the XX gate operation (with maximum entanglement) converts the two-qubit state |0> i |0> j 、|0> i |1> j 、|1> i |0> j , and |1> i |1> j :

[0036]

[0037] For example, when two qubits (the i-th and j-th qubits) are initially in the hyperfine ground state |0> (denoted by |0> i |0> j ), and then when a π / 2 pulse on the blue sideband is applied to the i-th quantum bit, the i-th quantum bit and the motion mode |0> i |n ph > p The combined state of is converted to |0> i |n ph > p and |1> i |n ph +1> p superposition, so that the combined state of these two qubits and the motion mode is converted to |0>i |0> j |n ph > p and |1> i |0> j |n ph +1> p When a π / 2 pulse on the red sideband is applied to the jth qubit, the jth qubit and the motion mode |0> j |n ph > p The combined state of is converted to |0> j |n ph > p and |1> j |n ph -1> p of superposition, and the combined state |0> j |n ph +1> p is converted to |0> j |n ph +1> p and |1> j |n ph > p of superposition.

[0038] Therefore, applying a π / 2 pulse on the blue sideband to the i-th qubit and a π / 2 pulse on the red sideband to the j-th qubit can convert these two qubits and the motion mode |0> i |0> j |n ph > p The combined state of |0> i |0> j |n ph > p and |1> i |1> j |n ph > p The two qubits are now in an entangled state. It should be clear to those skilled in the art that the motion mode (whose number of phonon excitations is different from the initial number of phonon excitations n) is ph ) two entangled quantum bit states (i.e., |1> i |0> j |n ph +1> p and|0> i |1> j |n ph -1> p) can be removed by a sufficiently complex pulse sequence, so that at the end of the XX gate operation the initial number of phonon excitations in the pth motion mode is n ph When it remains unchanged, it can be considered that after the XX gate operation, the combined state of the two qubits and the motion mode is disentangled. Therefore, the following will generally describe the qubit state before and after the XX gate operation, excluding the motion mode.

[0039] More generally, by applying a gate with amplitude Ω on the sidebands for a duration τ (called the “gate duration”) (m) and Ω (n) The combined state of the mth and nth qubits switched by a pulse of detuned frequency μ can be expressed by the entanglement interaction χ (m,n) (τ) is described as follows:

[0040] |0> m |0> n →cos(χ (m,n) (τ) / 2)|0> m |0> n -isin(χ (m,n) (τ) / 2)|1> m |1> n

[0041] |0> m |1> n →cos(χ (m,n) (τ) / 2)|0> m |1> n -isin(χ (m,n) (τ) / 2)|1> m |0> n

[0042] |1> m |0> n →-isin(χ (m,n) (τ) / 2)|0> m |1> n +cos(χ (m,n) (τ) / 2)|1> m |0> n

[0043] |1> m |1> n →-isin(χ (m,n) (τ) / 2)|0> m |0> n +cos(χ (m,n) (τ) / 2)|1> m |1> n

[0044] in,

[0045]

[0046] and is the Lamb-Dicke parameter, which quantifies the mth ion and the frequency is ω p is the coupling strength between the pth motion mode of , and P is the number of motion modes (equal to the number N of ions in the chain 102).

[0047] Construction of pulses for simultaneous entanglement gate operation

[0048] The entangled interaction between the two qubits can be used to perform an XX gate operation. The XX gate operation (XX gate) together with the single qubit operation (R gate) forms a set of universal gates {R, XX}, which can be used to build a quantum computer configured to perform the desired computational process. In order to perform an XX gate operation between the mth and nth qubits, construct a gate satisfying the condition χ (m,n) (τ) = θ (m,n) (0<θ (m,n) ≤π / 2)(i.e., the entanglement interaction χ (m,n) (τ) has the desired value θ (m,n) , called the condition for non-zero entanglement interaction), and applies the pulse to the mth and nth qubits. (m,n) =π / 2, the transformation of the combined state of the mth and nth qubits corresponds to the XX gate operation with maximum entanglement. The amplitude of the pulse to be applied to the mth and nth qubits is Ω (m) (t) and Ω (n) (t) are control parameters that can be adjusted to ensure non-zero tunable entanglement of the mth and nth qubits, thereby performing the desired XX gate operation on the mth and nth qubits.

[0049] In order to perform entanglement gate operation on two ion pairs at the same time, for example, a pair of m-th and n-th ions (abbreviated as (m,n)) and a pair of m'-th and n'-th ions (abbreviated as (m',n')), an entanglement gate operation is performed by applying an amplitude of Ω to the m-th, n-th, m'-th, and n'-th ions, respectively. (m) (t),Ω (n) (t),Ω (m′) (t), and Ω (n′) (t) of the pulse. The amplitude of the pulse is Ω (m) (t),Ω (n) (t),Ω (m′) (t), and Ω (n′) (t) is determined so that the ion pairs to be entangled (i.e., (m,n), (m′,n′)) are coupled to each other, and a vibration with amplitude Ω is applied. (m)(t),Ω (n) (t),Ω (m′) (t), and Ω (m′) At the end of the pulse (t), the ion pairs that are not to be entangled (i.e., (m,m′), (m,n′), (n,m′), (n,n′)) are decoupled from each other. That is, for the pairs to be entangled, a non-zero entanglement interaction χ must be satisfied. (l,l′) (τ) = θ (l,l′) ((l,l′)=(m,n),(m′,n′)) condition, for unentangled ion pairs, the condition χ (l,l′) (τ) = 0 ((l,l′)≠(m,n),(m′,n′)) (i.e., the total entanglement interaction between each decoupled pair is zero) (called the decoupling condition).

[0050] Simultaneous entanglement gate operations can be performed on a greater number of ion pairs. In a simultaneous entanglement gate operation, all ions in these pairs (i.e., each ion will be entangled with another ion) are called "participating ions" or "participating qubits." The number of participating ions in a simultaneous entanglement gate operation is denoted as N in the following. EASE In order to N EASE The participating ions perform simultaneous entanglement gate operations, each with amplitude Ω (m) (t)(m=1,2,…,N EASE ) are applied to the mth ion. Determine the pulse amplitude Ω (m) (t)(m=1,2,…,N EASE ), so that for the ion pair to be entangled (l, l′) the non-zero entanglement interaction condition χ is satisfied (l,l′) (τ) = θ (l,l′) (0<θ (l，l′) ≤π / 2), and the decoupling condition χ is satisfied for the ion pair (l,l′) that is not to be entangled (l，l′) (τ)=0.

[0051] Pulse control parameters, amplitude Ω (m) (t), the condition must also be satisfied that all N trapped ions in the chain 102 that were displaced from their initial positions when the motion mode was excited by the delivered pulse return to their initial positions. The mth qubit in the superposition state |0>±|1> is displaced during the gate duration τ due to the excitation of the pth motion mode and follows the trajectory in the phase space (position and momentum) of the pth motion mode Trajectory The amplitude of the pulse Ω (m) (t) and the detuning frequency μ. Therefore, for a chain 102 of N trapped ions, in addition to the condition of non-zero entanglement interaction χ (m，n) (τ) = θ(m，n) (0<θ (m,n) ≤π / 2), the condition must also be imposed on all P motion modes (p = 1, 2, ..., P) (i.e. trajectory must be closed, which is called the condition for the trapped ion to return to its original position and momentum value (or closure of the phase space trajectory).

[0052] By dividing the gate duration into N seg There are equally spaced segments (k = 1, 2, ..., N seg ), and varies the amplitude of the pulse from one segment to another. (m) (t) to determine the pulse amplitude Ω as the control parameter (m) (t)(m=1,2,…,N EASE ) to satisfy these conditions. (m) (t) is expressed as , the condition for the trapped ions to return to their original positions and momentum values ​​can be rewritten as

[0053]

[0054] Among them, M pk is defined as

[0055]

[0056]

[0057] The conditions for returning the trapped ion to its original position and momentum value (e.g., closure of the phase space trajectory) can be equivalently written in the matrix form Where M is M pk 2P×N seg The coefficient matrix, yes N seg Amplitude vector. Number of segments N seg is selected to be greater than twice the number of motion patterns 2P. Therefore, there is N0 (=N seg -2P) non-trivial (i.e., amplitude is non-zero) amplitude vector The conditions are met for the trapped ion to return to its original position and momentum value.

[0058] The conditions for non-zero entanglement interaction and decoupling can be rewritten as

[0059]

[0060]

[0061] in, is defined as

[0062]

[0063] or equivalently rewritten in matrix form as (if m and n are to be entangled) or 0 (otherwise), where D (m,n) yes N seg ×N seg coefficient matrix, and yes It is worth noting that for the control parameter The conditions for the trapped ion to return to its original position and momentum value, as well as the conditions for non-zero entanglement interaction and decoupling, can in principle be written in the form of what is known as a quadratically constrained quadratic program (QCQP). In general, QCQP is known to be a non-deterministic polynomial time (NP) hard problem (which is at least as hard as any NP problem). However, in the embodiments described here, these conditions form a special case of QCQP and can therefore be converted into a form that is not NP hard, such that a set of N EASE ×N seg Control parameters Using the number N of participating ions EASE This method is used to determine a set of N EASE ×N seg Control parameters The method is called the Efficient Arbitrary Simultaneous Entanglement (EASE) protocol and consists of having the amplitude determined as The gate operation performed by the pulse is referred to as EASE gate in the following text.

[0064] EASE Protocol and EASE Gate

[0065] Figure 7 A method for determining a control parameter according to an embodiment is described. Flowchart of method 700 of (EAS E protocol). In this example, the chain 102 of N trapped ions is a quantum register, where the two hyperfine states of each of the N trapped ions form a qubit.

[0066] In the examples described herein, a desired quantum algorithm is selected by a classical computer (not shown) using a user interface such as a graphics processing unit (GPU) (not shown), and is decomposed into R gate operations (single qubit gate operations) and XX gate operations (also called "entanglement gate operations", or "two qubit operations") on multiple pairs of qubits by a software program within the classical computer. The software program within the classical computer determines, using method 700 (EASE protocol) as further described below, which of the selected qubit pairs (a total of N) are to be performed simultaneously among all the entanglement gate operations. EASE The entanglement gate operation (EASE gate) of N participating qubits is determined, and the EASE The pulses determined by the software program are applied to N participating qubits in the quantum register (a chain of N trapped ions) to induce entanglement between the selected qubit pairs to perform the EASE gate operation. EASE participating qubits to perform EASE gate operations on selected qubit pairs controlled by the system controller.

[0067] At the beginning of the EASE protocol, N EASE Each of the participating qubits is initially labeled with a number n (n = 1, 2, ..., N EASE ), for example, according to N EASE The order in which the participating quantum bits are arranged in the chain 102 of N trapped ions. EASE The participating qubits may initially be labeled in any other order. A qubit labeled with the number n may also be referred to hereinafter as the nth qubit.

[0068] In block 702 (preprocessing), N EASE The participating qubits are grouped into disjoint qubit sets. EASE The participating qubits are relabeled such that the qubits within each disjoint set are labeled with consecutive numbers, and the qubits labeled with the smallest and second smallest numbers within each disjoint set (referred to as the first qubit and the second qubit in that disjoint set) correspond to one of the selected pairs on which the entanglement gate operation is performed. For example, chain 102 may have 11 trapped ions (i.e., qubits initially labeled with numbers 1 to 11), and entanglement gates may be performed simultaneously on qubit pairs (1, 2), (1, 4), (1, 5), (3, 6), and (3, 8). The participating qubits are then the qubits labeled with 1-6 and 8. The first disjoint set may include qubits 1, 2, 4, and 5, and the second disjoint set may include qubits 3, 6, and 8. The qubits in the first disjoint set are relabeled with 1-4, and the qubits in the second disjoint set are relabeled with 5-7.

[0069] To construct the n-th qubit (n=1, 2, ..., N EASE ) with amplitude Ω (n) First, determine the amplitude Ω of the first pulse to be applied to the first qubit (marked with 1). (1) (t) and the amplitude Ω of the second pulse to be applied to the second qubit (labeled with 2) (2) (t). Based on the determined amplitude Ω of the first pulse and the second pulse (1) (t) and Ω (2) (t), determine the amplitude Ω of the third pulse to be applied to the third qubit (marked with 3) (3) (t). The process is then continued until the Nth EASE Quantum bit (with N EASE Mark) EASE Pulse amplitude So far, and thus determine to be applied to all N EASE The amplitude of the pulses of the participating qubits.

[0070] In block 704, as a function of determining the number of qubits to be applied to the nth qubit (n=1, 2, ..., N EASE )'s nth pulse amplitude Ω (n) At the initial step of (t), among the qubits labeled with m (m = 1, 2, ..., n-1), the qubits that are not entangled with the nth qubit (called "disentangled qubits" and labeled with s) are included. That is, the nth qubit and the sth qubit (s ≤ n-1) do not correspond to any of the selected pairs on which the entanglement gate operation is to be performed. The number of disentangled qubits is denoted as N in the following text. s .

[0071] In block 706, the trapped ion is returned to its original position and momentum value after the conditions are met. Amplitude Based on the amplitude of the sth pulse to be applied to the sth qubit, To determine the conditions for decoupling between the nth qubit and the sth disentangled qubit Amplitude Amplitude Will be defined or determined in a previous iteration. The (N0-(n-1)) sets of amplitudes satisfy the conditions for the trapped ion to return to its original position and momentum value, and these amplitude sets can be linearly combined to obtain

[0072] In blocks 704 and 706, it is determined that the EASE )'s nth pulse amplitude Ω (n) After the initial step of (t), if all of the m-th qubits (m=1, 2, ..., n-1) are decoupled from the n-th qubit, the process proceeds to box 708. If a portion of the m-th qubits (m=1, 2, ..., n-1) (including the (n-1)-th qubit) are coupled to the n-th qubit and a pulse to be applied to one of the m-th qubits (e.g., the (n-1)-th qubit) has not yet been determined, the process proceeds to box 710. This occurs for the second qubit in each disjoint set. If a portion of the m-th qubits (m=1, 2, ..., n-1) are coupled to the n-th qubit and a pulse to be applied to all of the m-th qubits has been determined, the process proceeds to box 712.

[0073] In block 708, the set of amplitudes of the nth qubit is saved. In this case, all m-th qubits (m=1, 2, ..., n-1) are decoupled from the n-th qubit. The process returns to block 704 for determining the amplitude Ω of the (n+1)th pulse to be applied to the (n+1)th qubit. (n+1) .

[0074] In block 710, the amplitude Ω of the (n-1)th pulse to be applied to the (n-1)th qubit has not yet been determined. (n-1) (t). Thus, the set of amplitudes determined in block 706 for the nth iteration is calculated Linear combination of And similarly calculate the set of amplitudes determined in the previous iteration for the (n-1)th qubit in block 706 Linear combination of (i.e., the coefficient of determination and ), the condition for non-zero entanglement interaction between the nth and (n-1)th qubits is satisfied, and the average intensity of the nth and (n-1th) pulses within the gate duration τ is obtained and is minimized. The nth and (n-1)th pulses are configured to be power-optimal (i.e., the required laser power is minimized). The process returns to block 704 for determining the amplitude Ω of the (n+1)th pulse to be applied to the (n+1)th qubit. (n+1) .

[0075] In block 712, the amplitude set determined in block 706 is calculated Linear combination of (i.e., the coefficient of determination ), the conditions for non-zero entanglement interaction and decoupling between the nth and mth quantum bits (m = 1, 2, ..., n-1) If the nth and mth qubits are to be entangled, otherwise 0) and the average intensity of the resulting nth pulse within the gate duration τ is minimized. The above nth and (n-1)th pulses are configured to be power-optimal (i.e., the required laser power is minimized). The process returns to block 704 for determining the amplitude Ω of the (n+1)th pulse to be applied to the (n+1)th qubit. (n+1) .

[0076] When constructing EASE The process ends when a pulse from a participating qubit is emitted.

[0077] Applying the above-constructed pulse to the participating qubits implements the entanglement gate operation (XX gate operation) of each pair within the participating qubits in the series of universal gate {R, XX} operations into which the selected quantum algorithm is decomposed. All XX gate operations (XX gates) in the series of universal gate {R, XX} operations are implemented by the above-mentioned method 700, running the selected quantum algorithm defined and implemented by the classical computer together with the single qubit operation (R gate). At the end of running the selected quantum algorithm, the measurement obtained by the imaging objective 104 determines (reads out) the population of the qubit state (trapped ion) within the quantum register (chain of trapped ions 102) and maps it to the PMT 106, so that the result of the quantum calculation within the selected quantum algorithm can be determined and provided as input to a classical computer (e.g., a digital computer). The classical computer can then process the result of the quantum calculation to perform the desired activity or obtain the solution to the problem, which cannot usually be determined by a classical computer alone, or cannot be determined within a reasonable time. Problems that are known to be difficult or unsolvable by today's conventional computers (i.e., classical computers) and that may be solved by using the results obtained from performing quantum computations may include, but are not limited to, simulating the internal chemical structure of complex molecules and materials, and factoring large integers.

[0078] Because the above detailed method of implementing the EASE gate is completely linear, the EASE protocol can be used to solve any linear method of pulses that implement the XX gate. For example, the linear power optimal pulse construction method described in U.S. Provisional Application No. 62 / 851,280 (entitled "Amplitude, Frequency, And Phase Modulated Entangling Gates For Trapped-Ion Quantum Computers") (which is incorporated herein by reference) can be used in accordance with the EASE protocol to produce simultaneous amplitude and frequency modulated pulses that implement multiple XX gates simultaneously, which can be compared to the amplitude modulation method used and described above.

[0079] The EASE protocol described herein can determine pulses in an efficient manner to perform simultaneous entanglement gate operations on multiple pairs of qubits without errors or approximations. That is, the overhead for determining the pulses (e.g., the number of time periods) increases only linearly with respect to the number of participating qubits. This is in contrast to previously proposed nonlinear and approximate methods, which require overhead that increases exponentially with the number of participating qubits. In addition, the pulses constructed by the EASE protocol are optimal when used for a single XX gate operation because the laser power required to perform the gate operation is minimized when amplitude modulation is used to achieve the desired entanglement. Therefore, with given available resources, such as the laser power to achieve the pulses or the computational resources to determine the pulses, quantum computers can be scaled up to larger sizes with faster execution speeds.

[0080] While the foregoing is directed to particular embodiments, other and further embodiments may be devised without departing from the basic scope thereof, and the scope of the same is determined by the claims that follow.

Claims

1. A method for performing simultaneous entangled gate operations in a trapped ion quantum computer, the method comprising: Based on the first condition, a set of amplitudes of each of the plurality of pulses is calculated to simultaneously entangle a plurality of ion pairs in a plurality of participating ions in a chain of trapped ions, wherein, Each trapped ion in the chain has two frequency-separated states that define a qubit, and The motion modes of the chains of trapped ions each have a different frequency; selecting an amplitude from a calculated set of amplitudes for each pulse in the plurality of pulses based on a second condition; and performing a simultaneous entanglement gating operation on the plurality of ion pairs by applying the plurality of pulses each having a selected amplitude to the plurality of participating ions at a selected gate duration value, wherein Each of the plurality of participating ions receives at least one of the plurality of pulses, The first condition includes the trapped ions in the chain of trapped ions being substantially returned to their original positions and momentum values, The second condition includes that a non-zero entanglement interaction exists between each ion pair of the plurality of ion pairs to be entangled, and each ion pair not to be entangled is decoupled.

2. The method according to claim 1, wherein: The non-zero entanglement interaction has a value between zero and π / 2.

3. The method according to claim 2, wherein: The selection of the amplitude is also based on the condition that the power provided to the plurality of participating ions during the selected gate duration value is minimal.

4. The method according to claim 1, wherein: The selection of the amplitude is also based on the condition that the power provided to the plurality of participating ions during the selected gate duration value is minimal.

5. The method according to claim 1, wherein: Calculating the set of amplitudes includes dividing the selected gate duration value into a plurality of time periods.

6. The method according to claim 1, further comprising the steps of: Executing, by a processor in a digital computer, a software program stored in a non-volatile memory of the digital computer, wherein the executed software program requires performing at least one calculation, and performing the at least one calculation comprises: selecting, by said processor in said digital computer, a quantum algorithm to be implemented on said chain of trapped ions; Compile the chosen quantum algorithm into a series of universal logic gates; converting the series of universal logic gates into pulses to be applied to a plurality of participating ions in the chain of trapped ions; measuring the qubit state of ions in the chain of trapped ions; and processing, by the processor of the digital computer, quantum information corresponding to qubit states of trapped ions in the chain of trapped ions based on the measured qubit states; and A solution of the selected quantum algorithm is generated based on the processing result of the quantum calculation.

7. A quantum computing system, comprising: a chain of trapped ions, each with two hyperfine states and an excited state defining a qubit; one or more lasers configured to emit a laser beam, the laser beam being split into two or more non-co-propagating laser beams, the two or more non-co-propagating laser beams being provided to each trapped ion, wherein the two or more non-co-propagating laser beams are configured to cause each trapped ion to Rabi oscillate between the two hyperfine states via the excited state; and a controller including a non-volatile memory having a plurality of instructions stored therein, which, when executed by a processor, cause the quantum computing system to perform operations including: Based on the first condition, a set of amplitudes for each of the plurality of pulses is calculated to simultaneously entangle a plurality of ion pairs in a plurality of participating ions in a chain of trapped ions, wherein each trapped ion has two frequency-separated states defining a quantum bit, and The motion modes of the chains of trapped ions each have a different frequency; selecting an amplitude from a calculated set of amplitudes for each pulse in the plurality of pulses based on a second condition; and A simultaneous entanglement gating operation is performed on the plurality of ion pairs by applying the plurality of pulses, each having a selected amplitude, to the participating ions at a selected gate duration value, wherein Each of the plurality of participating ions receives at least one of the plurality of pulses, The first condition includes the trapped ions in the chain of trapped ions being substantially returned to their original positions and momentum values, The second condition includes that a non-zero entanglement interaction exists between each ion pair of the plurality of ion pairs to be entangled, and each ion pair not to be entangled is decoupled.

8. The quantum computing system according to claim 7, wherein: Each trapped ion has 2 S 1 / 2 Ultra-fine state 171 Yb + ,and The laser is a 355nm mode-locked laser.

9. The quantum computing system according to claim 7, wherein: The non-zero entanglement interaction has a value between zero and π / 2.

10. The quantum computing system according to claim 9, wherein: The selection of the amplitude is also based on the condition that the power provided to the plurality of participating ions during the selected gate duration value is minimal.

11. The quantum computing system according to claim 7, wherein: The selection of the amplitude is also based on the condition that the power provided to the plurality of participating ions during the selected gate duration value is minimal.

12. The quantum computing system according to claim 7, wherein: Calculating a set of amplitudes for each of the plurality of pulses includes dividing the selected gate duration value into a plurality of time periods.

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