Efficient evaluation of motion mode characteristics for high-fidelity trapped-ion quantum computing.

Abstract

A method of using an ion trap quantum computer includes performing a first measurement of the bright state population of each ion in an ion chain, wherein each ion is coupled to one of the motional modes of the ion chain while a laser coupling frequency is varying; calculating a mode frequency of the one motional mode among the motional modes based on the bright state population measured in the first measurement; performing a second measurement of the bright state population of each ion in the ion chain; and calculating a coupling strength between each ion and the one motional mode among the motional modes by fitting the bright state population of each ion measured in the second measurement to a value of the bright state population calculated based on the calculated mode frequency of the one motional mode among the motional modes and a non-zero temperature effect of the motional mode.

Description

[Technical Field]

[0001] (Cross-reference of related applications) This application claims priority to U.S. Patent Application No. 18 / 202,270, filed on 25 May 2023, and U.S. Provisional Application No. 63 / 348,421, filed on 2 June 2022, each of which is incorporated herein by reference in its entirety.

[0002] This disclosure relates, in general terms, to a method for performing entangling gate operations in a trapped ion-based quantum computer, and more specifically, to a method for characterizing the motion modes of ion chains. [Background technology]

[0003] In quantum computing, scalability requirements include efficient characterization, calibration, and verification of quantum computing systems, in addition to high-fidelity initialization, logical operations, and readout. In trapped-ion-based quantum computers, quantum information encoded in trapped ions (qubits) is processed via the motion modes of the ions (e.g., collective oscillations), and therefore, efficient and accurate characterization of motion modes leads to efficient and accurate quantum computation.

[0004] Therefore, there is a need for methods and systems that enable efficient and accurate characterization of the motion modes of ionic chains. [Overview of the project]

[0005] Embodiments of the present disclosure provide a method using an ion trap quantum computer. The method comprises the steps of: performing a first measurement of the light state group of each ion in an ion chain comprising a plurality of ions for a fixed duration, wherein each ion is coupled to one of the motion modes of the ion chain, during which a laser coupling frequency for coupling each ion to the one of the motion modes is varied; calculating the mode frequency of the one of the motion modes based on the frequency at which the light state group of each ion measured in the first measurement is maximized; and fitting the maximized light state group of each ion measured in the first measurement to the value of the light state group calculated based on the calculated mode frequency of the one of the motion modes and the non-zero temperature effect of the motion mode, thereby equating each ion The method includes the steps of: calculating the binding strength between an ion and one of the motion modes; performing a second measurement of the light-state group of each ion in the ion chain for a fixed duration, wherein each ion is bound to one of the motion modes that was not bound to the ion in the first measurement, and the laser coupling frequency for binding each ion to one of the motion modes is fixed; and calculating the binding strength between each ion and one of the motion modes by fitting the light-state group of each ion measured in the second measurement to the value of the light-state group calculated based on the calculated mode frequency of one of the motion modes and the non-zero temperature effect of the motion mode.

[0006] Embodiments of this disclosure also provide a method using an ion trap quantum computer. The method includes the steps of: performing a first measurement of the light-state group of each ion in an ionic chain containing multiple ions for a fixed duration, wherein each ion is coupled to one of the motion modes of the ionic chain, during which the laser coupling frequency for coupling each ion to the one of the motion modes is variable; calculating the mode frequency of the one of the motion modes based on the frequency at which the light-state group of each ion measured in the first measurement is maximized; performing a second measurement of the light-state group of each ion in the ionic chain for a plurality of durations, wherein each ion is coupled to one of the motion modes, during which the laser coupling frequency for coupling each ion to the one of the motion modes is fixed; and calculating the coupling strength between each ion and the one of the motion modes by fitting the light-state group of each ion measured in the second measurement to the calculated mode frequency of the one of the motion modes and the value of the light-state group calculated based on the non-zero temperature effect of the motion mode.

[0007] Embodiments of the present disclosure further provide a quantum computing system. The quantum computing system includes an ion chain comprising a plurality of ions, each ion in the ion chain having two hyperfine states that define a qubit; a system controller; and a classical computer having a processor and a non-volatile memory storing a number of instructions, the instructions being, when executed by the processor, the quantum computing system is given the steps of: the system controller performing a first measurement of the set of light states of each ion in the ion chain for a fixed duration, wherein each ion is coupled to one of the motion modes of the ion chain, during which the laser coupling frequency for coupling each ion to the one of the motion modes is varied; and the processor determines that the set of light states of each ion measured in the first measurement is the largest The system controller is made to perform an operation comprising: calculating the mode frequency of one of the motion modes based on the frequency at which it becomes; performing a second measurement of the light state group of each ion in the ion chain, wherein each ion is coupled to one of the motion modes, thereafter the laser coupling frequency for coupling each ion to one of the motion modes is fixed; and calculating the coupling strength between each ion in the ion chain and one of the motion modes of the ion chain based on the light state group measured in the first measurement, the light state group measured in the second measurement, the calculated mode frequency of one of the motion modes, and the non-zero temperature effect of the motion mode. [Brief explanation of the drawing]

[0008] To allow for a more detailed understanding of the features of this disclosure listed above, a more specific description of this disclosure, which is briefly outlined above, can be obtained by referring to embodiments, some of which are shown in the accompanying drawings. However, it should be noted that the accompanying drawings show only typical embodiments of this disclosure and should not be considered to limit the scope of this disclosure, as this disclosure may permit other equally effective embodiments.

[0009] [Figure 1] This is a schematic partial diagram of a trapped ion quantum computing system according to one embodiment. [Figure 2] A flowchart illustrating a basic method for characterizing the Ramdicke parameter according to one embodiment is shown. [Figure 3] A flowchart illustrating an improved method for characterizing the Ramdicke parameter according to one embodiment is shown. [Figure 4] An example of a set of light states at various development times according to one embodiment is shown. [Figure 5A] An example of the time evolution of an average light-state population according to one embodiment is shown. [Figure 5B] An example of the time evolution of an average light-state population according to one embodiment is shown. [Figure 6A] An example of the average relative error when estimating the Ramdicke parameter according to one embodiment is shown. [Figure 6B] An example of the average relative error when estimating the Ramdicke parameter according to one embodiment is shown. [Figure 7] An example of the predicted time expansion of an average light state population according to one embodiment is shown. [Figure 8A] An example of the average relative uncertainty for various values ​​of S(0) and MtSt according to one embodiment is shown. [Figure 8B] An example of the average relative error when estimating ηj,k according to one embodiment is shown. [Figure 8C] An example of measurement time according to one embodiment is shown.

[0010] For ease of understanding, the same reference numerals are used to indicate identical elements common to the drawings, where possible. The drawings and the following description use a Cartesian coordinate system including the X, Y, and Z axes. For convenience, the direction indicated by arrows in the figures is considered positive. Elements disclosed in some embodiments are intended to be usefully utilized in other implementations without specific description. [Modes for carrying out the invention]

[0011] As quantum computers grow in size, parameters associated with quantum computer systems need to be characterized with high accuracy and efficiency to achieve high-fidelity quantum logic. In trapped-ion-based quantum computers, the strength of entangling between qubits (trapped ions) is mediated by the motion modes of the ion chain, and therefore, it is essential to characterize the coupling strength between each ion and motion mode (called the Ramdicke parameter). Embodiments described herein provide a physical model that accurately predicts both the magnitude and sign of the Ramdicke parameter when motion modes are probed in parallel. Embodiments described herein further provide an improved characterization method that reduces the characterization time by more than an order of magnitude compared to the characterization time of conventional methods.

[0012] A complete system capable of performing quantum computations using trapped ions includes a classical (digital) computer, a system controller, and a quantum processor. The classical computer performs support and system control tasks, including selecting a quantum algorithm to be implemented quantum using a user interface such as a graphics processing unit (GPU), compiling the selected quantum algorithm into a set of universal logic gates, converting the set of universal logic gates into a set of pairwise entungling gate operations and applying them to the quantum processor, and using a central processing unit (CPU) to calculate the amplitude and detuning frequency of laser pulses that produce the set of pairwise entungling gate operations. Software programs for performing the task of decomposing and executing the quantum algorithm are stored in non-volatile memory within the classical computer. The quantum processor includes trapped ions coupled with various hardware, including a laser for manipulating the internal hyperfine states (qubit states) of the trapped ions and an acousto-optic modulator for reading out the internal hyperfine states (qubit states) of the trapped ions. The system controller receives the calculated amplitude and detuning frequency of the laser pulse from the classical computer at the start of execution of the selected algorithm on the quantum processor, controls various hardware related to controlling any and all aspects used to execute the selected algorithm on the quantum processor, and, at the end of algorithm execution, returns the readout from the quantum processor (e.g., the set of qubit states of the trapped ions), and thus the output of the quantum computation results, to the classical computer, and generates and outputs a solution for the selected quantum algorithm based on the processing results of the quantum computation.

[0013] I. General-purpose hardware configuration FIG. 1 is a schematic partial view of a trapped ion quantum computing system 100, or simply system 100, according to one embodiment. System 100 can represent a hybrid quantum classical computing system. System 100 includes 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, which includes a chain 106 of atomic ions (i.e., five shown as circles at approximately equal intervals from each other) that are trapped to form a linear Coulomb crystal extending along the Z-axis. Each ion in ion chain 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, and for example, a positive ytterbium ion 171 Yb + , a positive barium ion 133 Ba + , a positive cadmium ion 111 Cd + , 113 Cd + , and all of them have a nuclear spin I = 1 / 2 and 2 S 1 / 2 hyperfine states. In some embodiments, all ions in ion chain 106 are of the same species and isotope (e.g., 171 Yb + ). In some other embodiments, ion chain 106 includes one or more species or isotopes (e.g., some ions are 171 Yb + , and some other ions are 133 Ba +The ion chain 106 may include (i.e., different isotopes of Yb, different isotopes of Ba). The ions in the ion chain 106 are individually addressed by 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 readily available memories such as read-only memory (ROM), random access memory (RAM), floppy disks, hard disks, or any other form of local or remote digital storage. Software instructions, algorithms, and data can be coded and stored in 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, etc.

[0014] An imaging objective lens 108, such as one with a numerical aperture (NA) of 0.37, collects fluorescence from the ions along the Y-axis and maps each ion onto a multi-channel photomultiplier tube (PMT) 110 (or some other imaging device) for individual ion measurement. A Raman laser beam from a laser 112 positioned along the X-axis performs operations on the ions. A diffraction beam splitter 114 creates an array of Raman laser beams 116 that are individually switched using a multi-channel acousto-optic modulator (AOM) 118. The AOM 118 is configured to act selectively on individual ions by individually controlling the emission of the Raman laser beams 116. A global Raman laser beam 120 does not copropage with the Raman laser beams 116 and irradiates all ions simultaneously from different directions. In some embodiments, individual Raman laser beams (not shown) can be used to irradiate individual ions, each instead of a single global Raman laser beam 120. The system controller (also referred to as the "RF controller") 104 controls the AOM 118 and, therefore, controls the intensity, timing, and phase of the laser pulses applied to the trapped ions in the ion chain 106. The CPU 122 is the processor of the system controller 104. The ROM 124 stores various programs, and the RAM 126 is working memory for various programs and data. The storage unit 128 includes non-volatile memory such as a hard disk drive (HDD) or flash memory and stores various programs even when the power is turned off. The CPU 122, ROM 124, RAM 126, and storage unit 128 are interconnected via the bus 130. The system controller 104 executes the control program stored in the ROM 124 or the storage unit 128 and uses the RAM 126 as a working area. The control program includes a software application that can be executed by the CPU 122 to perform various functions related to receiving and analyzing data, and controlling any all aspects of the methods and hardware used to implement and operate the trap-ion quantum computing system 100 discussed herein.

[0015] II. Trapped Ion Quantum Computer Systems In trap-ion quantum computing systems such as System 100, atomic ions 2 S 1 / 2 Two internal states, such as the hyperfine state, are typically used as computational qubit states, denoted as |0> and |1>. The hyperfine ground state (i.e., 2 S 1 / 2 A lower energy state of the hyperfine state may be selected to represent the qubit state |0>. Hereafter, the terms “internal state,” “hyperfine state,” and “qubit state” may be used interchangeably to represent |0> and |1>. Furthermore, the hyperfine states |0> and |1> may be called the “dark state” and “light state,” respectively. Each ion may be cooled to near the kinetic ground state for any motion mode without phonon excitation (i.e., the kinetic energy of the ion may be reduced) by known laser cooling methods such as Doppler cooling or resolved sideband cooling, and then the qubit state may be prepared in the dark state |0> by optical pumping. When many ions are trapped and form a linear Coulomb crystal as in ion chain 106, the external motion of the ions (e.g., the collective motion of the ions) can be quantized and approximated as a set of coupled quantum harmonic oscillators. The internal and external degrees of freedom of an ion chain consisting of N ions (e.g., the qubit states of individual ions and the collective motion of the ions) are given by the Hamiltonian

number

number

number

number

number

number

[0016] Typical laser-induced multi-qubit gate operations between ions, such as the Mφlmer-Solensen method, use a laser electric field to couple the internal and external degrees of freedom of the participating ions in the ion chain. Hamiltonian

number

number

number

number

[0017] II.A Characterization of Ramdicke Parameters These parameters (Ramdicke parameter η) j,k and mode frequency ω k A conventional method for characterizing ) is sideband spectroscopy using blue sideband (BSB) transitions. The Ramdicke parameter η of the motion mode k for ion j j,k and the mode frequency ω of the motion mode k k To characterize the laser coupling frequency of each pulse,

number

number

number

[0018] Similar to other spectroscopic approaches, conventional mode characteristic evaluation methods use mode frequency ω k It is designed to probe the Ramdicke parameter η, which needs to be characterized. Embodiments described herein, in particular, are designed to probe the Ramdicke parameter η that needs to be characterized. j,k Since there are N × N' different values, the Ramdicke parameter η j,k This method offers an improvement over conventional modal characterization methods when more accurate and efficient characterization is required.

[0019] Ramdicke parameter η j,k To extract the ion j, measurement data from the light-state population are fitted to a model (referred to as the "baseline model" by the superscript (0)), and the model is conventionally based on the approximate interaction Hamiltonian.

number

number

number

[0020] Here, t is the expansion time,

number

number

number

number

number

[0021] II.B Improvements to the Baseline Model The baseline model is an approximation for two main reasons: (i) spectator motional modes (i.e., unprobezed motional modes) are ignored, and (ii) motional modes are always assumed to be prepared in the motional ground state. For a more accurate estimate of the light-state ensemble, the contribution of spectator motional modes due to non-zero spreading and non-resonant BSB transitions of ion position-wave packets, as well as the effect of non-zero temperatures, can be taken into account. Also, conventional mode characterization methods using (6) use the Mudike parameter η, which is important for multi-qubit gate design and operation. j,k Please note that the relative signs of these terms are not explicitly stated.

[0022] The methods according to the embodiments described herein are provided to improve upon conventional modal characteristic evaluation methods with respect to the following aspects. 1. Parallelization: N × N' different Ramdicke parameters η j,k However, it exists in N-ion chains that have a motion mode of N' that is strongly coupled to the laser. N × N' different Ramdicke parameters η j,k To characterize one at a time, it takes O(N 2 It requires ) operations. To support large-scale quantum computers, parallelization is necessary to reduce the complexity to O(N). 2. Precision: Ramdicke parameter η j,k To characterize the ion j with high accuracy, it is necessary to consider the effects of coupling to other motion modes k'≠k. Coupling arises from both non-zero spreading and non-resonant BSB transitions of the ion's position wave packet. 3. Sign Problem: Ramdicke Parameter η j,k It is necessary to distinguish the relative signs of (6), but in the light state set, the Ramdicke parameter η j,k It depends only on the size, and not on its sign. 4. Efficiency: Mode frequency ω k And if the shot noise is inaccurate, the Ramdicke parameter η j,k The characterization also becomes inaccurate. To reduce uncertainty, measurements over a considerably long period are required.

[0023] Such improvements can be achieved through the following objectives: Objective 1: To find an effective model for better characterizing the dynamics of the light-state ensemble of ions undergoing BSB transitions. Objective 2: Ramdicke parameter η j,k We search for a method and corresponding model that can distinguish the signs of each other. Objective 3: Ramdicke parameter η j,k To find a more efficient parallelization method that minimizes measurement time while keeping the uncertainty in estimation below the target value.

[0024] III. Improvement Model This section discusses various improved models that predict the light-state population of ions that all undergo BSB transitions in parallel. These models predict the light-state population of ions and thereby the Ramdicke parameter η j,k and mode frequency ω k When characterizing the system, it is more accurate than the baseline model conventionally used in (6). Section III.A discusses three effects that occur in parallel BSB transitions that are not considered in the baseline model. Section III.B introduces a total of five models, gradually taking into account the effects discussed in Section III.A and their combinations, until the most sophisticated model is finally arrived at.

[0025] III.A Effects This section discusses three effects in parallel BSB transitions of ions. By considering these effects in the model, the Ramdicke parameter η j,k This will enable more accurate characterization.

[0026] (a) Non-zero temperature Even after using the most sophisticated cooling techniques, the motion mode is unlikely to be in the absolute motion ground state. Therefore, the baseline models described in (4)-(6) generalize to the initial state of any phonon number n. Two composite states |0,n> j,k and |1,n+1> j,k The Rabi frequency between these two combined states is, assuming that no other combined states affect the BSB transition,

number

number

[0027] This generalized Rabi frequency

number

number

number

number

[0028] (b) Debyewaller (DW) effect The spreading of ion position wave packets associated with each mode manifests as a decrease in the Rabi frequency, widely known as the DW effect. The DW effect due to zero-point fluctuations persists even after the motion mode has cooled to the motion ground state.

[0029] When the motor mode k is probed through ion j, the DW effect due to the spectator motor mode k'≠k is,

number

number

number

[0030] For efficient characterization, each of the N ions is used to probe its assigned mode of motion in parallel, which corresponds to the Ramdicke parameter η. j,k To probe all N×N' values ​​of the motion modes, the process is repeated N' times with different permutations of the motion modes. In this case, each observed motion mode k' is also probed through another ion j'(k'), and therefore the number of phonons in motion mode k' is n k’ and n k’ It fluctuates between +1 and +1. Therefore, the average DW reduction coefficient is,

number

number

number

number

number

[0031] If the motion mode k' is probed resonantly over a sufficiently long development time, the number of phonons in motion mode k' is n times half the time. k’ and the remaining half of n k’ It can be approximated as +1. The exception is when the ion j'(k') is at the node of the motion mode.

number

number

[0032] Using (8) to (11), equation (6) is the effective Rabi frequency

number

number

number

number

[0033] (c) Cross-mode coupling When ion j probes motion mode k, a non-resonant BSB transition also occurs with other motion modes k'≠k. The resulting effect of other motion modes on the qubit state is called cross-mode coupling. Cross-mode coupling occurs at the detuning frequency Δ j,k’ The Rabi frequency Ω is much smaller. j,kWhile this can be reduced by using [a specific method], the smaller the Rabi frequency, the slower the BSB transition. Therefore, there is a trade-off between reducing errors due to crossmode coupling and shortening the characteristic measurement time.

[0034] Cross-mode coupling can, in principle, be included in a model that simulates the time evolution of the entire Hamiltonian for N ions and N' motion modes. However, the simulation time increases exponentially with the number of ions N. Therefore, a more realistic approach is to limit the simulated system size to a maximum of three ions and three motion modes by including only the nearest motion modes and the ions probing them in the simulation.

[0035] III.B Five Improvement Models Below, we discuss five models of the light-state population of ions undergoing parallel BSB transitions. These five models are improvements over the baseline model in (6).

[0036] (a) Model 1: Debye Waller (DW) effect Model 1 still assumes zero temperature but takes into account the DW effect. (Average light-state population)

number

number

number

number

number

[0037] Reduced Rabi frequency

number

[0038] (b) Model 2: Non-zero temperature Model 2 takes into account non-zero temperature effects in addition to the DW effects considered in Model 1. Multiple different initial phonon numbers are distributed using a distribution function.

number

number

number

number

number

number

number

number

number

[0039] The sum in (13) is given by a certain threshold probability p th About

number

number

number

number

number

number

number

number

[0040] (c) Model 3: Time-dependent DW (TDDW) effect Model 3 further considers the time dependence of the DW reduction coefficient. This is because, for each motion mode k probed through ion j, the spectator motion mode k'≠k is also probed through another ion j'(k')≠j, and its phonon number increases with time as it is probed. k’ and n k’ This is because it fluctuates between +1 and +1.

number

number

number

number

number

number

[0041] Here, the bright state population considering the TDDW effect [Number] To evaluate this, the time-dependent DW reduction coefficient is replaced with the average DW reduction coefficient in (8), thereby obtaining the reduced Rabi frequency [Number] to be time-dependent. Therefore, the time evolution from 0 to t can be divided into short time steps, and the time evolution operators in (4) and (5) are applied to obtain the reduced Rabi frequency [Number] which is updated at each time step to solve for the bright state population [Number] The phonon number as in (13) is weighted-averaged over the bright state population [Number] to obtain the average bright state population [Number] which is obtained [Number] (d) Model 4: Nearest neighbor (NN)

[0042] Model 4 takes into account the NN motional modes of the probed motional mode and their assigned ions. In other words, it considers the subspace of the probed motional mode k, its NN motional modes k - 1 and k + 1 (the motional modes are arranged in ascending order of mode frequency), and their assigned ions j(k), j(k - 1), and j(k + 1) (two ions, two motional modes for k = 1 and N’). ​

[0043] The interaction Hamiltonian that describes the partial space is [Number] where, in the formula [Number] is. The initial composite state is [Number] By taking the matrix element corresponding to the resonant transition and evaluating the time-evolution operator of this Hamiltonian from time 0 to t, the average bright state population [Number] is obtained as in (13).

[0044] Evaluating the time-evolution operator of the three-ion three-mode Hamiltonian in (15) takes a considerably longer time than simply evaluating trigonometric functions and polynomials as in the conventional model. However, since this model includes NN motional modes, its accuracy is less affected by cross-mode coupling. It should be noted that this appropriately captures the quantum interference between the qubit state and the motional modes beyond the single-ion single-mode model. The predicted bright state population is sensitive to the sign of the Rabi parameter η j,k±1 with respect to the Rabi parameter η j,k of.

[0045] (e) Model 5: TDDW+NN Model 5 incorporates the TDDW effect discussed in model 3 (c) into the NN model n of model 4 (d). This is done by replacing the average DW reduction coefficient in (15) with the TDDW coefficient in (14).

[0046] IV. Method In this section, the Rabi parameter η according to the embodiments described in this specificationj,k and the mode frequency ω k Provide two methods, a "basic method" and an "improved method", for characterizing. The measured bright state population of the N - ion qubit undergoing BSB transitions can have different sensitivities to the Rabi Dicke parameters for different methods. The Rabi Dicke parameter η j,k has N×N' different values, so parallelization of measurements is required. Conventional mode characterization methods are mainly designed only to probe the mode frequency ω k The basic method discussed below is a modified version of the conventional mode characterization method for probing the values of the Rabi Dicke parameter η j,k in parallel. The improved method can determine the Rabi Dicke parameter η j,k more accurately and quickly.

[0047] The methods described herein are designed to characterize the Rabi Dicke parameter η j,k with high precision, so a rough estimate of the Rabi Dicke parameter is assumed before implementing this method. An estimate of η j,k within one digit and an estimate of the mode frequency ω k within a few kHz are sufficient.

[0048] IV.A Basic method FIG. 2 is a flowchart showing a basic method 200 for characterizing the Rabi Dicke parameter η j,k which quantifies the coupling strength between ion j and the motional mode k. Here, the N ions in the ion chain are labeled by j, and the N' motional modes of the ion chain that are strongly coupled to the laser are labeled by k. Thus, the number of Rabi Dicke parameters η j,k to be determined is N×N'.

[0049] The basic method 200 includes two steps. The first step in block 210 is to use N ions to measure all the mode frequencies ω kmeasuring and, simultaneously, determining N’ out of N×N’ Lamb-Dicke parameters

Number

Number

Number

Number

Number

[0050] The second step of block 220 involves determining the remaining (N - 1)×N’ Lamb-Dicke parameters

Number

Number

[0051] Specifically, the i-th round of block 210 begins in subblock 212, and each ion j (=1,2,…,N) is assigned to one of the probe motion modes k (=1,2,…,N') that includes motion modes not probed in the previous round. The ions assigned to probe motion mode k in the i-th round are j i This is represented as (k). Of the N' motion modes strongly coupled to the laser, in subblock 212, N ions are assigned to probe N motion modes, and no ions are assigned to probe (N'-N) motion modes.

[0052] The i-th round of block 210 proceeds to subblock 214, and each ion j i (k) (=1,2,…,N) is initialized to the dark state |0>. In the examples described herein, the dark state |0> is ion j i This is the hyperfine ground state of (k). Each ion j i (k) may be initialized to near the ground state of any motion mode without phonon excitation by known laser cooling methods such as Doppler cooling or resolved sideband cooling (i.e., cooled so that the kinetic energy of the ions is reduced), and then initialized to a qubit state prepared in the hyperfine ground state |0> by optical pumping.

[0053] The i-th round of block 210 proceeds to subblock 216, and each ion j in the blue sideband (BSB) transition i (k) Light state group P j,k (t) Frequency scanning measurement, fixed time τ (0) It is executed by each ion j i (k) (=1,2,…,N) is the laser coupling frequency

number

number

number

number

number

number

number

number

number

[0054] The i-th round of block 210 proceeds to subblock 218, and each ion j i (k) and the Ramdicke parameter for the assigned motor mode k

number

number

number

number

[0055] Subblocks 212-218 are for each round

number

number

[0056] Mode frequency ω k To measure this accurately, mode assignment in subblock 212

number

number

[0057] The i-th round of block 220 begins with subblock 222, where each ion j (=1,2,…,N) is assigned to one of the motion modes k. In subblock 222, the ions are assigned to different permutations of motion modes (e.g., different combinations of ion j and motion mode k). The ions assigned to motion mode k in the i-th round are assigned to j i It is represented as (k).

[0058] The i-th round of block 220 proceeds to subblock 224, and each ion j i (k) (=1,2,…,N) is initialized to the dark state |0>. This ion initialization is the same as in subblock 214.

[0059] The i-th round of block 220 proceeds to subblock 226, and each ion j in the blue sideband (BSB) transition i (k) Light state group P j,k (t) is a fixed time τ (0) Measured at [location]. Frequency scanning measurements are not performed in subblock 226. Each ion j i (k) (=1,2,…,N) is the laser coupling frequency

number

number

[0060] The i-th round of block 220 proceeds to subblock 228, and each ion j i (k) and the Ramdicke parameter for the assigned motor mode k

number

number

number

number

[0061] Each round

number

number

number

number

[0062] IV.B Improvement method Figure 3 shows the Ramdicke parameter η. j,k This flowchart shows an improved method 300 for characterizing the laser, which quantifies the binding strength between ion j and motion mode k. Here, N ions in the ion chain are labeled j, and N' motion modes of the ion chain that strongly bind to the laser are labeled k. Therefore, the Ramdicke parameter η to be determined is... j,k The number of items is N × N'.

[0063] Improvement method 300 also includes two steps. The first step of block 310 is similar to the first step of block 210 of basic method 200, using N ions to determine all mode frequencies ω of N' motion modes. k This is a frequency scanning measurement to calculate the Ramdicke parameter η. However, in the first step of block 310, j,k This is not calculated. The first step is to ensure that all N' motion modes are assigned ions to probe in at least one round each.

number

[0064] The second step in block 320 is the Ramdicke parameter η j,k A set of light states P for calculating the light state set P j,k This is a time-scanning measurement of (t). The second step is repeated N' rounds.

[0065] Specifically, the i-th round of Block 310.

number

[0066] The i-th round of block 310 proceeds to subblock 314, and each ion j i (k) (=1,2,…,N) is initialized to the dark state |0>. This ion initialization is the same as subblock 214 of basic method 200.

[0067] The i-th round of block 310 proceeds to subblock 316, and each ion j in the blue sideband (BSB) transitioni (k) Light state group P j,k (t) Frequency scanning measurement, fixed time τ (0) It is executed by each ion j i (k) (=1,2,…,N) is the laser coupling frequency

number

number

number

number

number

number

number

number

number

[0068] Subblocks 312-316 are for each round

number

number

[0069] The i-th round of block 320 begins in subblock 322, where each ion j (=1,2,…,N) is assigned to one of the motion modes k (=1,2,…,N'). In subblock 322, the ions are assigned to different permutations of motion modes (e.g., different combinations of ion j and motion mode k). The ions assigned to probe motion mode k in the i-th round are j i It is represented as (k).

[0070] The i-th round of block 320 proceeds to subblock 324, and each ion j i (k) (=1,2,…,N) is initialized to the dark state |0>. This ion initialization is the same as subblock 224 of basic method 200.

[0071] The i-th round of block 320 proceeds to subblock 326, and each ion j in the blue sideband (BSB) transition i (k) Light state group P j,k (t) Time scanning measurement, fixed laser coupling frequency

number

number

number

number

number

[0072] The i-th round of block 320 proceeds to subblock 328, and each ion j i (k) and the Ramdicke parameter for the assigned motor mode k

number

number

number

[0073] Figure 4 shows the light state group P.j,k (t) resonates perfectly in parallel at various development times (Δ j,k An example of a BSB transition (=0) is shown. In this example, the number of ions N is set to be equal to the number of motion modes N' that are strongly coupled to the laser (N=N'=5), and the Rabi frequency of the qubit state is,

number

[0074] In each round (i=1,…,N'), subblocks 322-328 are executed in parallel for N ions, repeated for N' rounds, comprehensively pairing N ions with N' motion modes and N'×N Ramdicke parameters.

number

[0075] IV.C Measurement Time Scale In the method described above, the trapped ion quantum computer undergoes a cycle of ion cooling, qubit state preparation, BSB transition, and measurement of the ion's light state ensemble. The time scales for cooling, state preparation, and measurement may be on the order of 10 ms, 10 μs, and 100 μs, respectively. The BSB transition requires a time on the order of milliseconds because the Rabi frequency of the qubit state must be sufficiently small to suppress cross-mode coupling.

[0076] If the number of ions N is equal to the number of motion modes N' that are strongly coupled to the laser (N'=N), this corresponds to a commonly used laser alignment setting and the Ramdicke parameter η according to basic method 200. j,k and mode frequency ω k Total time T required to characterize (0) teeth,

number

number

number

number

number

[0077] The lower limit of the above parameters is the Ramdicke parameter η j,kThis is determined by the target accuracy in the measurement. In particular, the minimum required for the baseline method (improvement method 300)

number

[0078] In basic method 200, the mode frequency ω k When the uncertainty is large, the Ramdicke parameter η j,k The uncertainty also increases, but this is because both parameters are in the light state ensemble.

number

number

number

number

[0079] Figures 5A and 5B show the Ramdicke parameter η from the BSB transition, respectively. 1,1 and laser coupling frequency

number

number

number

number

number

number

[0080] Fitting the measured light-state population to models 1-5 is not a simple task. This is because the mean light-state population...

number

number

number

[0081] While this section discusses more accurate and efficient estimation of the Ramdicke parameter, it should be noted that the method described herein can also be readily used for better mode frequency estimation, for example, for various laser coupling frequencies.

number

[0082] V. Examples This section demonstrates, through examples, that the three objectives of efficient mode characterization described in Section II can be achieved using the improved models and methods described herein. More specifically, (i) the Ramdicke parameter η j,k (ii) Comparison of the accuracy of models 1-5 when measuring and the baseline model, and (ii) Model 4 is the Ramdicke parameter η j,k Demonstration showing that the relative signs of can be distinguished, and (iii)η j,k This document outlines the requirements under which the improvement method 300 significantly reduces the characteristic evaluation measurement time compared to the basic method 200, given a given target accuracy in estimation.

[0083] To perform numerical testing, we numerically simulate parallel BSB transition measurements. The BSB Hamiltonian in the dialogue image is:

number

number

number

number

number

number

number

number

number

number

[0084] VA accuracy First, we compare the performance of the baseline model and models 1-5 to see if they adequately capture the qubit ensemble expansion using numerical simulations of the light-state ensemble. Here, as an example, all ions are driven simultaneously at the same qubit state Rabi frequency.

number

number

[0085] Figures 6A and 6B show the Ramdicke parameter η obtained by using various models, respectively, as a function of the qubit state Rabi frequency Ω0 and the number of ions N in which the qubit state Rabi frequency Ω0 is fixed at 2π × 2kHz. j,k An example of the mean relative error when estimating is shown. The labels are in the order of baseline and models 1-5 as described in Section III. Here, the relative error is:

number

number

[0086] Models 2-5 exhibit power law behavior, and the relative error is:

number

number

[0087] It is found that including NN motion modes in the model reduces errors from cross-mode coupling. Models 4 and 5 have significantly smaller errors than models 2 and 3 for N < 5. However, for longer ionic chains, the errors do not differ much. For example, η j,k±1 ga η j,k±2 If it is smaller than η, then mode k±2 is η j,k The impact of this mode on the measurement error is equal to or greater than the impact of NN mode k±1. In such cases, the NN model may be modified to include the more influential mode, at the cost of increasing the fitting computation time.

[0088] Models incorporating the TDDW effect achieve the highest accuracy. For example, in Figure 6B, for N=7, the errors of models 3 and 5 are smaller than those of models 2 and 4, at 1 / 2.5. The TDDW effect may be more important for characterizing the Ramdicke parameter with higher accuracy in longer ionic chains.

[0089] It should be noted that we are assuming the physical distance between adjacent ions is fixed. Therefore, as the number of ions N increases, the spacing between mode frequencies decreases, which means that cross-mode coupling becomes tighter, given that the Rabi frequency of the qubit states is fixed.

[0090] VB code problem Ramdicke parameter η for other Ramdicke parameters j,k The sign of θ directly affects quantum computation fidelity because it determines the gate pulse design on many trap-ion quantum computers. Unfortunately, conventional mode characterization methods do not allow the sign of the qubit ensemble to be independent in the baseline model in (6), thus limiting the Ramdicke parameter η. j,k The signs of the two are indistinguishable. Here, the Ramdicke parameter η j,k We will show that the signs of these can be distinguished using an NN model (Model 4).

[0091] First, use BSB transitions η j,k To distinguish the sign of η, it is necessary to consider multiple ions, but this is only when the relative motion between different ions is accounted for by the Ramdicke parameter η. j,k This is because the sign of is clearly defined. In single mode, η j,k It should also be noted that if the signs are different, the ions will have different relative directions of motion, but the qubit ensemble will undergo exactly the same development. η is only considered when at least two ions and two modes are considered simultaneously. j,k The sign of the symbol determines whether the symmetry of the involvement of the two ions in one mode is the same as or opposite to the symmetry in the other mode, and this difference affects the qubit ensemble.

[0092] By irradiating two ions with the same two-tone beam, each tone resonating at its respective mode frequency, the two ions are driven to couple in parallel to two different modes, thereby causing BSB transitions to two modes to occur simultaneously on both ions. The predicted development will be that one has the same symmetry and the other has the opposite symmetry, making them significantly different from each other. This affects which symmetry, and therefore the Ramdicke parameter η, is affected. j,k This makes it possible to determine whether the sign is correct directly from the signal generated by the measurement.

[0093] Figure 7 shows the average light state population.

number

number

[0094] Ramdicke parameter η 1,1The collective curve when = ±0.0119 is clearly distinguishable and can be seen to be accurately predicted by the NN model (Model 4). This shows that by carefully selecting the parameters and comparing the observed development with the development predicted by the NN model, all four possible BSB transitions between the two ions and the two modes are simultaneously induced by the Ramdicke parameter η j,k The ability to reliably distinguish between the two signs is crucial.

[0095] VC characteristic evaluation measurement time The characteristic evaluation measurement times for the basic method 200 and the improved method 300 given by (16) and (17), respectively, are as follows: (i) in the basic method 200

number

number

number

[0096] To align with Section VA, M t M t It is fixed at =20,

number

number

number

[0097] First, the Ramdicke parameter η j,k Basic methods needed to reduce uncertainty: 200 shots S (0) and the number of shots S for improvement method 300 t We calculate the following. Here, the simulated bright state group is the mode frequency ω k Assuming that the parameters are fully known, we use Model 2 to fit the uncertainty given by the combination of photons and phonon shot noise. Here, we use Ω0 = 2π × 10kHz, but the effect of the shot noise does not significantly affect Ω0.

[0098] Figure 8A shows S (0) and M t S t Examples of average relative uncertainty for various values ​​of S are shown. The uncertainty is proportional to the reciprocal of the square root of the number of shots. (0) =M t S t In that case, the improvement method is always more efficient than the basic method. j,k The uncertainty of becomes smaller. As explained in Section IV, the improvement method is that the qubit ensemble is ηj,k This includes being extremely sensitive to the value of .

number

number

number

[0099] Next, we calculate the Rabi frequency Ω0 of the qubit state, and thereby determine the BSB transition time.

number

number

[0100] The qubit ensemble is up to the leading order in (6).

number

number

number

[0101] Figure 8B shows η as a function of Ω0. j,k An example of the average relative error when estimating multiple Δ is shown. j,k Consider the value. Using this figure, η j,kWhen a predetermined target accuracy is given in the measurement, Ω0 and δω satisfy the target accuracy. k The value of can be determined. For example, if the relative uncertainty is 10 -3 If lower values ​​are desired, a reasonable selection of the basic method 200 {improvement method 300} is Ω0 / 2π = 7 {10} kHz and δω k / 2π = 12{100}Hz, which means,

number

number

number

[0102] Here, using all the parameters of the determined method, a comparison is made between the characterization measurement times of the basic method 200 and the improved method 300 given in (16) and (17). Specifically, the cooling, state preparation, and state detection times are assumed to be 4 ms, 100 μs, and 150 μs, respectively, and these times are added to the BSB transition time to obtain the cycle time per shot. Table 1 shows the set of parameters for the two methods. Overall, η for 5 ion chains j,k When estimating 10 -3To achieve relative measurement uncertainty of the order of , the characterization measurement time is T = 586 seconds for the improved method, which is T for the basic method. (0) = 1.11 × 10 4 It is shorter than a second, approximately 1 / 19. The savings in the improvement method stem from the fact that in frequency scanning, the number of shots decreases, resulting in lower accuracy. [Table 1] Table 1 shows the basic method 200 (left) and η for 5 ion chains. j,k The relative uncertainty is 10 -3 The parameters for improvement method 300 (right) that achieve the order are shown below. <·> represents i=1,…,M t This is the average over the period. According to (16) and (17), the characteristic evaluation measurement time for the basic method 200 and the improved method 300 is T, respectively. (0) = 1.11 × 10 4 s and T = 586s.

[0103] Finally, to distinguish the advantages of having fewer shots and lower frequency scanning accuracy, Figure 8C shows δω k Examples of measurement times for the two methods for various values ​​of are shown. This is because the uncertainty δω is greater at the mode frequency. k The document emphasizes that allowing this can significantly reduce the time required for characterizing and measuring the improvement methods.

[0104] VI. Trade-offs between basic methods and improvement methods The problem of efficient and highly accurate evaluation of motion mode characteristics leads to optimization across multiple correlated parameters due to various trade-offs. For example, using lower laser power (and therefore lower Ω0) reduces errors due to cross-mode coupling, but at the cost of longer BSB transition times, requiring better frequency scanning accuracy.

[0105] The choice of method and model can also be viewed in terms of trade-offs. For example, a parallelized method may have a complexity of O(N). 2This reduces the computation time from O(N) to O(N), but at the cost of introducing additional considerations into the model, such as DW effects (more precisely, time-dependent) from other modes being probed in parallel. Generally, more accurate models can be used at the cost of longer computation times. To take advantage of this trade-off, highly parallelized and efficient algorithms for fitting routines can be explored to perform the conventional computation portion of this method relatively quickly, which is especially true for long ion chains, where computation tends to be slow.

[0106] Another important trade-off related to trapped ions is the interval between mode frequencies versus the physical distance between adjacent ions. As the distance between adjacent ions decreases, the interval between mode frequencies increases, which reduces the cross-mode coupling effect, so η j,k This makes it possible to reduce the error when measuring. As a result, as shown in Figure 6B, the exponential increase in error due to N, assuming that the distance between adjacent ions is fixed, can be mitigated. However, when the inter-ion distance becomes small, the laser beam width cannot be arbitrarily reduced, so optical crosstalk increases.

[0107] Embodiments described herein provide a method for characterizing motion modes. In particular, the method is based on an effective physical model that describes the dynamics of ions in an ion chain and the motion modes of the ion chain more accurately than conventional physical models, thereby enabling accurate and efficient characterization of motion modes. Compared to conventional methods, the method described herein utilizes time-scanning measurements that enable faster and more accurate characterization of motion modes, and parallelism in which motion modes are simultaneously probed by multiple ions for faster and more accurate characterization of motion modes.

[0108] Appendix A, B, C, and D are attached, and their contents are all considered to be part of this application and are therefore incorporated herein.

[0109] While the above describes a specific embodiment, other further embodiments can be devised without departing from its basic scope, and the scope of such embodiments is determined by the following claims.

Claims

1. A method using an ion trap quantum computer, A step of performing a first measurement of the light-state population of each ion in an ionic chain containing multiple ions for a fixed duration, wherein each ion is coupled to one of the motion modes of the ionic chain, and during this time, the laser coupling frequency for coupling each ion to the one of the motion modes is varied. A step of calculating the mode frequency of one of the motion modes based on the frequency at which the light-state group of each ion measured in the first measurement is maximized, A step of calculating the binding strength between each ion and one of the motion modes by fitting the light-state group, which is the largest of each ion measured in the first measurement, to the value of the light-state group calculated based on the calculated mode frequency of one of the motion modes and the non-zero temperature effect of the motion mode, A step of performing a second measurement of the light-state group of each ion in the ion chain for a fixed duration, wherein each ion is coupled to one of the motion modes that was not coupled to each ion in the first measurement, and the laser coupling frequency for coupling each ion to the one of the motion modes is fixed during this time. A step of calculating the binding strength between each ion and one of the motion modes by fitting the light-state group of each ion measured in the second measurement to the calculated mode frequency of one of the motion modes and the value of the light-state group calculated based on the non-zero temperature effect of the motion mode, Methods that include...

2. A step of selecting a quantum algorithm to be implemented for the plurality of ions using a processor in a digital computer, The steps include: compiling the selected quantum algorithm into a series of universal logic gates using the processor in the digital computer; The steps include: using the processor in the digital computer to convert the series of universal logic gates into a series of pairwise entanglement gate operations and applying them to the plurality of ions in the ion chain; The steps include: using the processor in the digital computer to calculate the amplitude and detuning frequency of the laser pulse, and generating the series of pairwise entungling gate operations based on the calculated coupling strength between the motion mode and the ion; The system controller applies the calculated laser pulse, having the amplitude and detuning frequency, to the plurality of ions in the ion chain. The system controller measures the set of qubit states of the plurality of ions in the ion chain, The steps of processing quantum information corresponding to the qubit states of the plurality of ions in the ion chain based on the measured collection of qubit states using the processor in the digital computer, The steps include: generating and outputting a solution for the selected quantum algorithm based on the quantum information processed by the processor in the digital computer; The method according to claim 1, further comprising:

3. A step of initializing each ion in the ion chain to its ultrafine ground state before the first and second measurements of each ion. The method according to claim 1, further comprising:

4. The method according to claim 1, wherein the first measurement of all ions in the ionic chain is performed simultaneously.

5. The method according to claim 1, wherein the second measurement of all ions in the ionic chain is performed simultaneously.

6. The method according to claim 1, wherein the calculation of the binding strength between the ions in the ionic chain and the mode of motion of the ionic chain is further based on the Debye-Waller effect of the ions.

7. The method according to claim 1, wherein the calculation of the binding strength between the ions in the ionic chain and the mode of motion of the ionic chain is further based on the cross-mode binding effect of the mode of motion of the ionic chain.

8. A method using an ion trap quantum computer, A system controller performs a first measurement of the light-state population of each ion in an ion chain containing multiple ions for a fixed duration, wherein each ion is coupled to one of the motion modes of the ion chain, and during this time, the laser coupling frequency for coupling each ion to the one of the motion modes is varied. A step of using a processor in a digital computer to calculate the mode frequency of one of the motion modes based on the frequency at which the light state group of each ion measured in the first measurement is maximized; The steps of calculating the binding strength between each ion and one of the motion modes by fitting the light-state group, which is the maximum for each ion measured in the first measurement, to the value of the light-state group calculated based on the calculated mode frequency of one of the motion modes and the non-zero temperature effect of the motion mode, using the processor in the digital computer; The steps include: performing a second measurement of the light-state group of each ion in the ion chain using the system controller for a fixed duration, wherein each ion is coupled to one of the motion modes that was not coupled to each ion in the first measurement, and the laser coupling frequency for coupling each ion to the one of the motion modes is fixed during this time; A step of calculating the binding strength between each ion and one of the motion modes by fitting the light-state group of each ion measured in the second measurement to the value of the light-state group calculated based on the calculated mode frequency of one of the motion modes and the non-zero temperature effect of the motion mode, using the processor in the digital computer. The steps include: selecting a quantum algorithm to be implemented for the plurality of ions using the processor in the digital computer; The steps include: compiling the selected quantum algorithm into a series of universal logic gates using the processor in the digital computer; The steps include: using the processor in the digital computer to convert the series of universal logic gates into a series of pairwise entanglement gate operations and applying them to the plurality of ions in the ion chain; The steps include: using the processor in the digital computer to calculate the amplitude and detuning frequency of the laser pulse, and generating the series of pairwise entungling gate operations based on the calculated coupling strength between the motion mode and the ion; The system controller applies the calculated laser pulse, having the amplitude and detuning frequency, to the plurality of ions in the ion chain. The system controller measures the set of qubit states of the plurality of ions in the ion chain, The steps of processing quantum information corresponding to the qubit states of the plurality of ions in the ion chain based on the measured collection of qubit states using the processor in the digital computer, The steps include: generating and outputting a solution for the selected quantum algorithm based on the quantum information processed by the processor in the digital computer; Methods that include...

9. A method using an ion trap quantum computer, A step of performing a first measurement of the light-state population of each ion in an ionic chain containing multiple ions for a fixed duration, wherein each ion is coupled to one of the motion modes of the ionic chain, and during this time, the laser coupling frequency for coupling each ion to the one of the motion modes is varied. A step of calculating the mode frequency of one of the motion modes based on the frequency at which the light-state group of each ion measured in the first measurement is maximized, A step of performing a second measurement of the light-state group of each ion in the ion chain for a plurality of durations, wherein each ion is coupled to one of the motion modes, and the laser coupling frequency for coupling each ion to the one of the motion modes is fixed during this time. A step of calculating the binding strength between each ion and one of the motion modes by fitting the light-state group of each ion measured in the second measurement to the calculated mode frequency of one of the motion modes and the value of the light-state group calculated based on the non-zero temperature effect of the motion mode, Methods that include...

10. A step of selecting a quantum algorithm to be implemented for the plurality of ions using a processor in a digital computer, The steps include: compiling the selected quantum algorithm into a series of universal logic gates using the processor in the digital computer; The steps include: using the processor in the digital computer to convert the series of universal logic gates into a series of pairwise entanglement gate operations and applying them to the plurality of ions in the ion chain; The steps include: using the processor in the digital computer to calculate the amplitude and detuning frequency of the laser pulse, and generating the series of pairwise entungling gate operations based on the calculated coupling strength between the motion mode and the ion; The system controller applies the calculated laser pulse, having the amplitude and detuning frequency, to the plurality of ions in the ion chain. The system controller measures the set of qubit states of the plurality of ions in the ion chain, The steps of processing quantum information corresponding to the qubit states of the plurality of ions in the ion chain based on the measured collection of qubit states using the processor in the digital computer, The steps include: generating and outputting a solution for the selected quantum algorithm based on the quantum information processed by the processor in the digital computer; The method according to claim 9, further comprising:

11. A step of initializing each ion in the ion chain to its ultrafine ground state before the first and second measurements of each ion. The method according to claim 9, further comprising:

12. The method according to claim 9, wherein the first measurement of all ions in the ionic chain is performed simultaneously.

13. The method according to claim 9, wherein the second measurement of all ions in the ionic chain is performed simultaneously.

14. The method according to claim 9, wherein the calculation of the binding strength between the ions in the ionic chain and the mode of motion of the ionic chain is further based on the Debye-Waller effect of the ions.

15. The method according to claim 9, wherein the calculation of the binding strength between the ions in the ionic chain and the mode of motion of the ionic chain is further based on the cross-mode binding effect of the mode of motion of the ionic chain.

16. A method using an ion trap quantum computer, A system controller performs a first measurement of the light-state population of each ion in an ion chain containing multiple ions for a fixed duration, wherein each ion is coupled to one of the motion modes of the ion chain, and during this time, the laser coupling frequency for coupling each ion to the one of the motion modes is varied. A step of using a processor in a digital computer to calculate the mode frequency of one of the motion modes based on the frequency at which the light state group of each ion measured in the first measurement is maximized; A system controller performs a second measurement of the light-state population of each ion in the ion chain for a plurality of durations, wherein each ion is coupled to one of the motion modes, and the laser coupling frequency for coupling each ion to the one of the motion modes is fixed during this time. A step of calculating the binding strength between each ion and one of the motion modes by fitting the light-state group of each ion measured in the second measurement to the value of the light-state group calculated based on the calculated mode frequency of one of the motion modes and the non-zero temperature effect of the motion mode, using the processor in the digital computer. The steps include: selecting a quantum algorithm to be implemented for the plurality of ions using the processor in the digital computer; The steps include: compiling the selected quantum algorithm into a series of universal logic gates using the processor in the digital computer; The steps include: using the processor in the digital computer to convert the series of universal logic gates into a series of pairwise entanglement gate operations and applying them to the plurality of ions in the ion chain; The steps include: using the processor in the digital computer to calculate the amplitude and detuning frequency of the laser pulse, and generating the series of pairwise entungling gate operations based on the calculated coupling strength between the motion mode and the ion; The system controller applies the calculated laser pulse, having the amplitude and detuning frequency, to the plurality of ions in the ion chain. The system controller measures the set of qubit states of the plurality of ions in the ion chain, The steps of processing quantum information corresponding to the qubit states of the plurality of ions in the ion chain based on the measured collection of qubit states using the processor in the digital computer, The steps include: generating and outputting a solution for the selected quantum algorithm based on the quantum information processed by the processor in the digital computer; Methods that include...

17. A quantum computing system, An ionic chain containing multiple ions, wherein each ion in the ionic chain has two hyperfine states that define a qubit, System controller and A classic computer has a processor and non-volatile memory that stores a large number of instructions, The system comprises, and when the instruction is executed by the processor, the quantum computing system The steps include: performing a first measurement of the light-state group of each ion in the ion chain using the system controller for a fixed duration, wherein each ion is coupled to one of the motion modes of the ion chain, and during this time, the laser coupling frequency for coupling each ion to the one of the motion modes is varied; The processor performs the steps of calculating the mode frequency of one of the motion modes based on the frequency at which the light state group of each ion measured in the first measurement is maximized, The steps include: performing a second measurement of the light-state group of each ion in the ion chain using the system controller, wherein each ion is coupled to one of the motion modes, and the laser coupling frequency for coupling each ion to the one of the motion modes is fixed; The processor performs the steps of calculating the binding strength between each ion in the ion chain and one of the motion modes of the ion chain, based on the light state group measured in the first measurement, the light state group measured in the second measurement, the calculated mode frequency of one of the motion modes, and the non-zero temperature effect of the motion mode. A quantum computing system that performs operations including those mentioned above.

18. The quantum computing system according to claim 17, wherein the second measurement is performed for a fixed duration.

19. The quantum computing system according to claim 17, wherein the second measurement is performed over a plurality of durations.

20. The aforementioned operation is, A step of selecting a quantum algorithm to be implemented for the plurality of ions using a processor in a digital computer, The steps include: compiling the selected quantum algorithm into a series of universal logic gates using the processor in the digital computer; The steps include: using the processor in the digital computer to convert the series of universal logic gates into a series of pairwise entanglement gate operations and applying them to the plurality of ions in the ion chain; The steps include: using the processor in the digital computer to calculate the amplitude and detuning frequency of the laser pulse, and generating the series of pairwise entungling gate operations based on the calculated coupling strength between the motion mode and the ion; The system controller applies the calculated laser pulse, having the amplitude and detuning frequency, to the plurality of ions in the ion chain. The system controller measures the set of qubit states of the plurality of ions in the ion chain, The steps of processing quantum information corresponding to the qubit states of the plurality of ions in the ion chain based on the measured collection of qubit states using the processor in the digital computer, The steps include: generating and outputting a solution for the selected quantum algorithm based on the quantum information processed by the processor in the digital computer; The quantum computing system according to claim 17, further comprising:

21. The aforementioned operation is, A step of initializing each ion in the ion chain to its ultrafine ground state before the first and second measurements of each ion. The quantum computing system according to claim 17, further comprising:

22. The quantum computing system according to claim 17, wherein the calculation of the binding strength between the ions in the ionic chain and the motion mode of the ionic chain is further based on at least one of the Debye-Waller effect of the ions and the cross-mode binding effect of the motion mode of the ionic chain.

Images