Large-scale multi-qubit trap ion gate

Abstract

We provide a large-scale multi-qubit trap ion gate. [Solution] A system (20) for quantum computing includes an array of qubits (40) and a radiation source (28) that simultaneously irradiates multiple qubits in the array with radiation containing a set of spectral components in multiple vibrational sidebands of the internal transition frequencies of the qubits, each having a different complex amplitude. The sidebands are generated by a group of normal modes having a minimum spacing Δf between their respective vibrational frequencies. A controller (32) initializes a multi-qubit gate containing at least five qubits to an initial state and drives the radiation source to irradiate each qubit with radiation containing the respective complex amplitude of the spectral components in a selected set, so as to switch the multi-qubit gate to a target state within a gate time of less than 50 / Δf.

Description

[Technical Field] 【0001】 Cross-references to related applications This application claims the benefit of U.S. Provisional Patent Application No. 63 / 506,142, filed on 5 June 2023, which is incorporated herein by reference. 【0002】 This invention relates generally to quantum computing, and more particularly to large-scale trapped-ion gates in quantum computers. [Background technology] 【0003】 Quantum computers apply the principles of quantum physics to solve computational problems and have the potential to perform certain calculations far more efficiently than existing digital computers. The fundamental element of a quantum computer is the qubit. A quantum computer consists of qubits and gates that operate the qubits, including single-qubit gates, two-qubit gates, and multi-qubit gates. 【0004】 A trapped ion system, in which individual atomic ions function as qubits, is a promising scalable and reliable platform for quantum computing. In a trapped ion system, individual atomic ions are trapped by an electric field in an ultra-high vacuum and cooled to their motion ground state. The motion of the ions within the trap, as well as their internal electronic levels, is controlled with high precision using a laser, microwave, or radio frequency (RF) field. To perform calculations, gates are applied to the internal and motion states of the atomic ions by driving a field with an appropriate spectrum, i.e., frequency, amplitude, phase, and duration. 【0005】 A common approach to quantum computing is to decompose an algorithm into a concatenation of single-qubit gates and two-qubit gates. Multi-qubit gates consisting of three or more qubits, however, have also been proposed. For example, Shapira et al. describe this type of gate in a paper titled "Theory of robust multiqubit nonadiabatic gates for trapped ions" published in Physical Review A 101, 032330 (2020), which is incorporated herein by reference. 【0006】 Multi-qubit gates would be important in the implementation of quantum error correction (QEC) to overcome the problem of physical qubit errors in a quantum computer. In a QEC code, quantum information is not directly stored in individual physical qubits (e.g., individual trapped ions), but rather in logical qubits composed of multiple physical qubits. This type of QEC scheme is described, for example, by "Comparing two-qubit and multiqubit gates within the toric code" published in Physical Review A 105, 022612 (2022) by Schwerdt et al. In this paper, a gate containing five physical qubits is used to encode two logical qubits across a qubit register and significantly raise the fault tolerance threshold compared to stabilizer measurements performed by a series of two-qubit physical gates. 【0007】 Other uses of multi-qubit gates include significantly reducing the depth of a quantum circuit by performing operations on an entire register. For example, in "Synthesis of and compilation with time-optimal multi-qubit gates" published in Quantum 7, 984 (2023), Bassler et al. use multi-qubit gates to generate an N-qubit quantum Fourier transform with 2N entangling gates. As another example, Bravyi et al. describe in "Constant-Cost Implementations of Clifford Operations and Multiply-Controlled Gates Using Global Interactions" published in Physical Review Letters 129, 230501 (2022) a quantum circuit composed of single-qubit operations and global entangling gates generated by an Ising-type Hamiltonian. Further uses of multi-qubit gates include quantum analog and digital simulations, as well as quantum-classical hybrid optimizations, and also the implementation of computational components that include three or more logic gates. 【Summary of the Invention】 【0008】 Embodiments of the invention described herein below provide an improved multi-qubit gate and a method for driving such a gate. 【0009】 Therefore, according to one embodiment of the present invention, a system for quantum computing is provided, comprising an array of qubits having internal transition frequencies from a ground state to an excited state, and having a plurality of normal modes of oscillatory motion among the qubits in the array, each normal mode having a respective oscillatory frequency. A radiation source is configured to simultaneously irradiate a plurality of qubits in the array with radiation comprising a set of spectral components in a plurality of oscillatory sidebands of the internal transition frequency, such that each qubit is irradiated with spectral components by each different complex amplitude. The sidebands are generated by a group of normal modes having a minimum spacing Δf between each oscillatory frequency of the normal modes in the group. A controller is configured to initialize a multi-qubit gate containing at least five qubits in the array to an initial state and to drive the radiation source to irradiate each qubit with radiation by each complex amplitude of the spectral components in a selected set, such that the multi-qubit gate is switched to a target state within a gate time of less than 50 / Δf. 【0010】 In the disclosed embodiments, the vibration frequencies of each normal mode within a group extend across a frequency range from the minimum normal mode frequency to the maximum normal mode frequency, and the controller is configured to drive the radiation source to irradiate with radiation over a bandwidth of at least 10% of the frequency range. 【0011】 In some embodiments, the system includes an ion trap, the array of qubits includes an array of ions held within the trap, and the multi-qubit gate includes at least five ions within the array. In one embodiment, the internal transition frequency is an electronic transition frequency, and irradiation includes irradiation with laser radiation. In another embodiment, the internal transition may be an ultrafine frequency or Zeeman frequency driven by a light source with a Raman transition configuration. In yet another embodiment, irradiation includes irradiation with radio frequency (RF) radiation. In the disclosed embodiments, the array of ions is a linear array. 【0012】 In the disclosed embodiments, the multi-qubit gate includes more than 12 qubits in the array. Additionally or alternatively, the gate time is less than 10 / Δf. 【0013】 In some embodiments, the multi-qubit gate is configured to implement quantum error correction codes, such as surface codes. 【0014】 In the disclosed embodiments, the target state of the multi-qubit gate is the target entanglement phase vector. 【0015】 【number】 Characterized by this, the complex amplitude of each spectral component is selected by optimizing the complex amplitudes to generate a target entanglement phase vector, following the discovery of an initial set of complex amplitudes that will produce a zero-entanglement phase. 【0016】 In some embodiments, the target state is a highly connected entanglement state. Additionally or alternatively, the target state includes multiple nonlocal entanglements. 【0017】 According to one embodiment of the present invention, a method for quantum computing is also provided. The method includes preparing an array of qubits having an internal transition frequency from a ground state to an excited state, and having a plurality of normal modes of vibrational motion between the qubits in the array, each normal mode having a respective oscillation frequency. A multi-qubit gate including at least five qubits in the array is initialized to an initial state. The plurality of qubits in the array are simultaneously irradiated with radiation. The radiation includes a set of spectral components in a plurality of vibrational sidebands of the internal transition frequency such that each qubit is irradiated with a spectral component with a different respective complex amplitude. The sidebands are generated by a group of normal modes having a minimum spacing Δf between the respective oscillation frequencies of the normal modes within the group. Each respective complex amplitude of the spectral components in the set is selected to switch the multi-qubit gate to a target state within a gate time less than 50 / Δf. 【0018】 According to one embodiment of the present invention, a method for quantum computing is further provided, which includes preparing an array of qubits having an internal instantaneous transition frequency ω0 from a ground state to an excited state. A multi-qubit gate including a first number N>2 of qubits in the array is initialized to an initial state. Each frequency ω0±ω m and each amplitude r defined by an amplitude vector R = <r1, r2, ···, r M > of a second number M>2 of excitation frequency pairs are selected. A set of N(N - 1) / 2 coupling matrices A m having a dimension M×M representing the interaction between the excitation frequency pairs and the qubit pairs with 1 < n < m < N is defined. The initial amplitude vector r0 is found to satisfy the constraint |r0| = 1 such that for all j = 1, ···, N n,m . The target entanglement phase vector 【0019】 【Number】 is such that 【0020】 【Number】 is selected. The parameters λ and D are for all 1 < n < m < N 【0021】 【Number】 calculated to find the target amplitude vector R = λR0 + D that satisfies 【0022】 【Number】 and 【0023】 【Number】 is. The multi - qubit gate is driven to the target state by irradiating the array of qubits with radiation, and the radiation includes M pairs of excitation frequencies having amplitudes according to the target amplitude vector R. 【0024】 In some embodiments, the vector 【0025】 【Number】 [[ID=:44]] is used not only for the disentanglement between the qubit state and the motion mode, but also for additional linear constraints to ensure resistance to various sources of errors and noise 【0026】 【Number】 needs to be satisfied. In these cases, the vectors 【0027】 【Number】 and 【0028】 【Number】 is found within the null space (kernel) of L. 【0029】 In some embodiments, after finding the target amplitude vector R, for all 1 < n < m < N 【0030】 【Number】 such that the optimization process is applied to find an optimized target vector R that locally satisfies the constraint argmin |R opt |. Typically, applying the optimization process involves reducing the residual error opt in the target phase. Additionally or alternatively, applying the optimization process involves iteratively modifying the target amplitude vector to reduce its magnitude while reaching the target entanglement phase vector within a predetermined error. 【0031】 【Number】 In some embodiments, each frequency ω0 ± ω 【0032】 is selected to excite sidebands of the transition frequencies resulting from a group of normal modes of oscillation of the qubits. In the disclosed embodiments, each oscillation frequency of the normal modes within the group extends over a frequency range from the minimum normal mode frequency to the maximum normal mode frequency, and the selected frequencies extend over a bandwidth of at least 10% of the frequency range. Additionally or alternatively, the sidebands are generated by a group of normal modes having a minimum spacing Δf between each oscillation frequency of the normal modes within the group, and the target amplitude vector is calculated such that the multi-qubit gate switches to the target state within a gate time of less than 50 / Δf. m is selected to excite sidebands of the transition frequencies resulting from a group of normal modes of oscillation of the qubits. In the disclosed embodiments, each oscillation frequency of the normal modes within the group extends over a frequency range from the minimum normal mode frequency to the maximum normal mode frequency, and the selected frequencies extend over a bandwidth of at least 10% of the frequency range. Additionally or alternatively, the sidebands are generated by a group of normal modes having a minimum spacing Δf between each oscillation frequency of the normal modes within the group, and the target amplitude vector is calculated such that the multi-qubit gate switches to the target state within a gate time of less than 50 / Δf. 【0033】 In the disclosed embodiments, finding the target amplitude vector involves calculating the distinct complex amplitudes of each excitation frequency pair for each qubit. 【0034】 Additionally or alternatively, the method includes defining the gate time T for a multi-qubit gate, and computing the target amplitude vector, which includes selecting the target amplitude vector such that the multi-qubit gate switches to the target state at the defined gate time. 【0035】 Furthermore, additionally or alternatively, the method includes defining a target unfavorability for a multi-qubit gate, and computing a target amplitude vector, which includes selecting a target amplitude vector such that the multi-qubit gate switches to the target state with an unfavorability less than or equal to the target unfavorability. 【0036】 In the disclosed embodiments, the qubit includes a trapped ion, the internal transition frequency is the electronic transition frequency, and irradiation with radiation includes irradiation with laser radiation. 【0037】 In some embodiments, a multi-qubit gate includes at least five qubits, or more than twelve qubits. 【0038】 In the disclosed embodiments, the multi-qubit gate is configured to implement a quantum error correction code. 【0039】 Typically, finding the initial amplitude vector involves solving a set of quadratic constraints of order N. 【0040】 In some embodiments, multi-qubit gates produce highly connected entangled states and / or multiple nonlocal entanglements. 【0041】 According to one embodiment of the present invention, there is further provided a system for quantum computing, including an array of qubits having an internal transition frequency ω0 from a ground state to an excited state, initializing a multi-qubit gate including the first number N>2 of qubits in the array to an initial state, and driving the multi-qubit gate to a target state by irradiating the array of qubits with radiation. The radiation has respective frequencies ω0±ω m and a second number M>2 of excitation frequency pairs each having an amplitude r M defined by a target amplitude vector R = <r1, r2, ···, r m >. The target amplitude vector R defines a set of N(N - 1) / 2 coupling matrices A n,m having dimension M×M representing the interaction between the excitation frequency pairs and the qubit pairs, with 1 < n < m < N, finding an initial amplitude vector r0 that satisfies the constraint |r0| = 1, selecting a target entanglement phase vector 【0042】 【Number】 and calculating parameters λ and D to find a target amplitude vector R = λR0 + D that satisfies 【0043】 【Number】 for all 1 < n < m < N, 【0044】 【Number】 where 【0045】 【Number】 and 【0046】 【Number】 It is calculated by the act of calculation. 【0047】 The present invention will be fully understood from the following detailed description of its embodiments, in conjunction with the drawings. [Brief explanation of the drawing] 【0048】 [Figure 1] This is a block diagram illustrating a quantum computing system according to one embodiment of the present invention. [Figure 2] This is a block diagram illustrating a schematic array of trap ions configured as qubits in a quantum computer according to one embodiment of the present invention. [Figure 3] This flowchart schematically illustrates a method for selecting parameters to drive a multi-qubit gate according to one embodiment of the present invention. [Figure 4] This graph schematically illustrates a simplified example of the selection of spectral component amplitudes used when driving a multi-qubit gate using the method shown in Figure 3, according to one embodiment of the present invention. [Figure 5A] This figure shows the physical and logical arrangements, respectively, of an array of trap ions that implement surface coding for use in quantum error correction, according to one embodiment of the present invention. [Figure 5B] This figure shows the physical and logical arrangements, respectively, of an array of trap ions that implement surface coding for use in quantum error correction, according to one embodiment of the present invention. [Figure 6] This graph schematically illustrates the ion driving amplitude in the physical array shown in Figure 5A, according to one embodiment of the present invention. [Figure 7] This graph schematically illustrates the amplitudes of the spectral components of the radiation used to drive the physical array shown in Figure 5A, according to one embodiment of the present invention. [Figure 8]This graph schematically illustrates the amplitude of the vibrational motion of ions over time in the physical array shown in Figure 5A, according to one embodiment of the present invention. [Modes for carrying out the invention] 【0049】 overview In trapped ion systems, entanglement gates are typically generated by driving ions with an electromagnetic field that creates phonon-mediated qubit interactions. This type of driving method utilizes the vibrational sidebands of the ion's internal transition frequencies. In small multi-qubit gates, the trapped ions have only a few normal modes of vibration, and therefore it is relatively easy to select a set of excitation frequencies and amplitudes that will lead to a desired target entanglement phase and gate time (i.e., the time required to drive the gate from its initial state to the target entanglement state). 【0050】 As the number of qubits increases, however, the number and complexity of the normal modes of oscillations increase rapidly. Choosing a set of sideband frequencies and amplitudes to drive transitions in multi-qubit gates robustly (i.e., with high fidelity) and quickly (with short gate times) is a difficult optimization problem with quadratic constraints. Even for gates of around 4 qubits, finding the optimal set of drive frequencies and amplitudes is challenging. 【0051】 Some embodiments of the present invention described herein address this difficulty by providing a systematic method for selecting the drive frequency and amplitude for a gate comprising an array of N qubits such that N > 2. In these embodiments, N 2The difficult optimization problem with an order constraint is reduced to a special instance with polynomial complexity, with only a quadratic constraint on the order of N, which is solved to find a solution for a certain instance of a bipartite multi-qubit gate (i.e., a gate in which an entanglement phase is defined for each pair of qubits and the qubits are driven in parallel to the target entanglement phase). This special solution can then be transformed into an optimized generalized solution using linear transformations and local optimizations. Thus, an optimized set of drive frequencies and amplitudes can be quickly derived, which would enable driving multi-qubit gates, including gates with more than 12 qubits, to perform the desired bipartite entanglement operation in short gate times. 【0052】 To implement this type of solution, in some embodiments of the present invention, the respective frequencies are ω0±ω m And each amplitude r m However, the amplitude vector r = applied to each qubit <r1,r2,···,r M A number of excitation frequency pairs, M > 2, are selected, defined by >. (where ω0 is the instantaneous internal transition frequency of the qubit from the ground state to the excited state.) While it is possible to apply the same amplitude vector to all qubits, embodiments of the present invention use different amplitude vectors r such that the complete set of amplitudes can be represented by an N × M dimensional matrix r. n This relates to the more general case where the operation is applied independently to each qubit. (Cases where all ions are driven by the same global beam, or where several ions are driven by a superimposed beam, are special cases of independent driving described herein.) 【0053】 A combination matrix A with M × M dimensions and N(N-1) / 2 dimensions. n,m The set is defined to represent the interaction between excitation frequency pairs and qubits n and m in the array, based on the normal modes of qubit oscillations. Specifically, 【0054】 【Number】 and O is 【0055】 【Number】 is an N×M matrix such that is the involvement of the nth ion in the jth motion mode. A j represents the interaction between the excitation frequency pair and the jth mode of motion. A n,m The matrix A j is constructed as a linear combination of matrices. 【0056】 Target entanglement phase vector 【0057】 【Number】 for all 1 < n < m < N[[ID=^35]] 【0058】 【Number】 is realized by applying amplitude vectors r1, ···, r N Finding the vectors, however, is a difficult problem as explained above. 【0059】 A useful representation of the problem is the vector 【0060】 【Number】 that is, constructed by considering the vector consisting of all vectors of the amplitudes driving the various ions. 【0061】 【Number】 is also defined as an NM×NM matrix consisting of N×N blocks of size M×M, and these have the values 【0062】 【Number】 All are zero except for the (n,m) block and the (m,n) block that take 【0063】 【Number】 takes 【0064】 Therefore, in some embodiments, the solution process is, for all 1 < n < m < N, the constraint 【0065】 【Number】 satisfies, that is, for all qubit pairs, the entanglement phase 【0066】 【Number】 starts from finding an initial non-trivial amplitude vector R0 that satisfies 【0067】 As described above, solving this zero-phase instance involves only some quadratic constraints on the order of N. N 2 The reduction from quadratic constraints of the order of N to quadratic constraints of N is to solve the zero-phase instance j for all interaction matrices A 【0068】 and all N qubits 【Number】 and is realized by setting 【0069】 【Number】 【0070】 Once this initial solution is found, for all 1 < n < m < N 【0071】 【Number】 To find the neighborhood amplitude vector R = λR0 + D that satisfies, the parameters λ and D can be calculated by a linear solution process. (In the sense that the magnitude of vector D is small compared to the magnitude of λR0, vector R is "nearby" within the multi-dimensional solution space defined by the N·M vector elements of R) The solution space is for all 1 < n < m < N 【0072】 【Number】 such that the optimization target vector R that locally satisfies the constraint argmin |R opt | is then optimized, for example, in a gradient descent process. opt The solution R 【0073】 represents a set of spectral components in each sideband of the instantaneous internal transition frequency ω0 and indicates the respective complex amplitudes (including magnitude and phase) of the spectral components irradiated on each of the qubits. The simultaneous irradiation of these spectral components onto the qubits in the array excites the selected normal modes of vibration and switches the multi-qubit gate from the initial state to the target entanglement phase vector opt having a target state. This operation is the unitary evolution operator 【0074】 【Number】 until local qubit rotations are performed, X 【0075】 【Number】 and X n X mThis is a correlated XX rotation for the nth and mth qubits. 【0076】 The gate time of a multi-qubit gate is governed by the minimum interval Δf between the vibrational frequencies of each group of normal modes excited by the irradiated radiation. In the adiabatic limit with gate time T >> 1 / Δf, the coupling matrix A j The matrix is ​​diagonal, and an amplitude vector R that will satisfy the constraints can be easily found; however, in this case, the long gate time makes the multi-qubit gate impractical for actual quantum computation. Therefore, in some embodiments of the present invention, the coupling matrix is ​​chosen to support faster gate times, e.g., T < 50 / Δf, or even T < 10 / Δf. The coupling matrix in such cases is generally full-rank, but the methods described above can be applied to find the optimal amplitude vector R that will enable the desired fast gate time. Constraints on maximum infidelity and tolerance to errors and noise can also be added to the solution process to ensure that the resulting amplitude vector will drive a multi-qubit gate with high fidelity and robustness. 【0077】 The oscillation frequencies of each normal mode used in a multi-qubit gate extend over a certain frequency range from the minimum normal mode frequency to the maximum normal mode frequency. To achieve fast switching (T<50 / Δf), the bandwidth of the radiation used to drive the gate is at least 10% of this frequency range and may cover the entire frequency range. 【0078】 The solution presented above uses frequency-domain analysis and optimization, but the principles of the present invention may alternatively be carried out in the time domain. In this case, for example, the waveform used to excite the qubits in the array may be defined in terms of time bins, where the optimal amplitude is calculated for each bin. This type of initial waveform is calculated to achieve a zero-entanglement phase, followed by an optimization process to reach the target phase while satisfying constraints on gate time, fidelity, and other parameters. 【0079】 Multi-qubit gates driven according to this method may be used for a variety of computational tasks. The principles of the present invention may be applied when creating multi-qubit gates for general-purpose quantum computing and / or to perform a part of a computational task or circuit together with other gates (which may contain one, two, or more qubits). As described above, this scheme performs a number of bipartite entanglement phases in parallel within a multi-qubit gate. A number of N-qubit operations can be performed using this type of bipartite parallel operation. In addition, some N-qubit operations that cannot be performed in a single step using a multi-qubit gate can be performed as part of a computational circuit (for example, by performing separate rotations between adjacent gates in the circuit). Thus, multi-qubit gates according to embodiments of the present invention can be used to create general-purpose quantum computing schemes with reduced quantum circuit depth (requiring only a few circuit layers for a given global operation) compared to schemes known in the art. The smaller depth of the quantum circuit enables faster circuits with potentially better overall fidelity. 【0080】 Multi-qubit gates according to embodiments of the present invention can be used to realize a general-purpose quantum computing gate set that is highly efficient (since only a few circuit layers are required for a given global operation) and (since any unitary operation can be adequately approximated using circuits including single-qubit gates and multi-qubit gates as described herein). The general-purpose gate set can be used, for example, in algorithmic tasks including fault-tolerant circuits, surface codes and toric codes, Ising spin models, prime factorization, and database retrieval. 【0081】 Furthermore, using multi-qubit gates according to embodiments of the present invention requires fewer quantum gates to perform a given algorithmic task, and accordingly, the resulting circuit executes faster. Such implementations provide improved coherence with respect to circuit time and better overall fidelity. 【0082】 In addition to implementing parallel gate operations using bipartite multi-qubit gate operations, this method enables highly connected entanglement states, i.e., a substantial entanglement phase φ between multiple ions and two or more other ions. n,m This is also useful when creating gates that produce states having [a certain characteristic]. The entanglement phases are "substantial" in the sense that each has a size that is at least 50% of the size of the maximum entanglement phase. For example, at least 10%, or possibly more than 20%, of the ions may have a substantial entanglement phase with two or more other ions, or possibly three or more ions. 【0083】 Additionally or alternatively, this method can also be used to create gates that generate multiple nonlocal entanglements, i.e., entanglements between non-directly adjacent qubits in parallel. Specifically, this can be used to create gates that generate an effective entanglement phase φ as defined above. n,m There are multiple pairs of non-adjacent qubits (n,m) having such that nm is significant (e.g., mn≧4). 【0084】 In some embodiments, such gates are configured to implement quantum error correction schemes, such as surface coding. Examples of such implementations are described below. In alternative embodiments, this method may be applied when driving quantum simulations. 【0085】 In the description provided, for clarity and specificity, the transition frequency ω is assumed to be the instantaneous frequency of a suitable electronic transition in a trapped ion system excited using laser radiation. The principle of the present invention may also be applied, if necessary, to other types of quantum gates based on other trapped ion transitions, such as transitions between spin states of a Zeeman splitting manifold or between states of a hyperfine splitting manifold, as well as to other types of quantum gates that may be used not only for microwave excitation or high-frequency excitation but also for Raman coupling. 【0086】 Furthermore, while the embodiments described herein relate particularly to a trapped-ion quantum computing system, the principles of the present invention may alternatively be applied, as needed, to other types of qubit arrays, such as superconducting (SC) qubits or arrays of trapped neutral atoms inside an optical resonator. In a trapped-ion system, the qubits utilize the internal electronic degrees of freedom of the trapped ions (such as electron spin), while the interactions between qubits are mediated by bosons based on harmonic phonon modes. SC qubits utilize, for example, transmons, and their interactions are mediated by bosons based on photon excitations of a waveguide resonator in which all SC qubits are coupled. In alternative embodiments of the present invention, multi-qubit gates in SC may similarly be driven using a set of frequency components selected using the optimization method described herein. 【0087】 System Description Figure 1 is a schematic block diagram illustrating a quantum computing system 20 according to one embodiment of the present invention. An atomic source 22 injects a stream of neutral atoms, such as calcium atoms, into a vacuum chamber 26 in an ultra-high vacuum. A radiation source 28 directs several beams of radiation into the vacuum chamber 26, including a beam tuned to ionize the atoms injected by source 22. (In the example presented, as described above, the system 20 is assumed to be based on electronic transitions, and the radiation source 28 is assumed to include a laser emitting a beam of coherent radiation, although ionization may be performed, for example, alternatively, using a non-coherent beam.) The resulting atomic ions are trapped in an ion trap 24, such as a pole trap, which uses an RF field to confine the ions along a designated line in the vacuum chamber 26. A magnetic field may also be applied to the ion trap 24 to separate the different spin components of the electronic states of the ions at the Zeeman level. 【0088】 The electronic qubit control and computation processor 32 drives the radiation source 28 to direct an additional beam towards the trapped ions in order to perform quantum computation operations and then read out the computation results. Typically, the results are read out by adjusting the laser beam to the absorption line of one of the qubit states and then measuring the resulting fluorescence emission using the photodetector 30. The processor 32 receives the computation results and drives the laser source 28 to perform additional computation steps according to the algorithm being implemented. 【0089】 Figure 2 is a schematic block diagram illustrating an array of trapped ions 40 configured as qubits in a quantum computer such as System 20, according to one embodiment of the present invention. A laser source 28 (Figure 1) provides several different laser beam inputs to the ion traps 24 for different purposes. An ionization laser 42 ionizes atoms output by the atomic source 22 to create ions 40 that are held in the traps. An additional cooling laser 44 cools the ions to their electronic and kinetic ground states by pumping the ions through appropriate state transitions, while detuning the laser frequency to generate mechanisms of Doppler cooling, sideband cooling, polarization gradient cooling, electrically induced transmission (EIT) cooling, and / or other cooling methods known in the art. 【0090】 The cooled ions 40 are held in a linear array along axis 38 by an electromagnetic field within trap 24. Coulomb repulsion between ions 40 and the trap field determines not only the equilibrium distance between ions but also the phonon frequencies ν of the normal vibrational modes of motion of ions 40 in the array, including both transverse and longitudinal vibrational modes. These normal vibrational modes give rise to vibrational sidebands of optical transition frequencies between the states of ions 40. Absorption of a photon at one of these sideband frequencies drives an internal transition of the absorbing ion, thus transferring energy to the normal modes of the ion array, causing excitation or deexcitation of the vibrations of the ion array due to the vibrational modes associated with the sidebands, while entanglement of the ion's internal and kinetic states by spin-dependent forces. The entanglement mechanism provided by this allows for the application of multi-qubit gates to these ions 40. Such gates may contain five or more qubits, or even more than twelve qubits. 【0091】 To operate a multi-qubit gate, the excitation laser 46 (or multiple lasers) is set to an excitation frequency ω0±ω centered around the selected internal instantaneous transition ω0 of the ion. mThe set irradiates ion 40 coherently. The beam of laser 46 has multiple sidebands ω of the internal transition frequency ω0 as defined above. m To coherently include the frequency components in the signal, they are modulated, for example, by a suitable acousto-optic modulator. 【0092】 The amplitude of the frequency component is the target entanglement phase vector with a short gate time T. 【0093】 【number】 To achieve this, the amplitude vector R of the frequency component applied to each of the ions 40 is optimized using a protocol further described below. The laser 46 is operated to irradiate each of the ions 40 with the selected frequency component at an amplitude optimal for the gate time T, in order to drive the multi-qubit gate from its initial state to the entangled target state. Although it is possible to irradiate all ions with the same set of sideband amplitudes, in this embodiment, each ion 40 is driven by its own amplitude vector R, which is typically different from the amplitude irradiated to the other ions. Examples of this type of excitation spectrum are presented below. 【0094】 After the computation cycle is complete, the readout laser 48 reads out the state of the qubit register defined by the ions 40. The readout laser 48 is tuned to one of the absorption lines of the ion states in the register. The absorption of laser radiation by the ion in the appropriate state produces fluorescence, which is measured by the photodetector 30 (Figure 1). The detector 32 measures the intensity of the fluorescence emission and thus detects the final state of the gate. 【0095】 The processor 32 typically comprises a general-purpose computer having appropriate interfaces with other components of the system 20. The processor 32 is driven by software to perform the functions and calculations described herein. The software may be stored in tangible, non-temporary computer-readable media such as optical storage media, magnetic storage media, or electronic storage media. 【0096】 Selection and optimization of excitation spectra Figure 3 is a flowchart illustrating a method for selecting parameters to drive a multi-qubit gate according to one embodiment of the present invention. The method is typically performed by a suitable computer, such as a processor 32, under the control of a suitable software code. 【0097】 The method in Figure 3 begins in register definition step 50 with the definition of a multi-qubit register within an array of trapped ions. The register defines not only the types and number N of ions 40 in the trap 24 involved in the gate, but also the internal instantaneous transition frequency ω0 and (normal mode frequency ν). j The gate definition is defined by parameters such as trap properties (which determine the target entanglement phase vector). 【0098】 【number】 The gate time T will also be specified. As mentioned above, virtually any entanglement phase vector may be selected depending on the desired function of the gate. To enable the calculation to be completed quickly, the gate time T should be set to a small value, for example, T < 50 / Δf, or even T < 10 / Δf, where Δf is the respective oscillation frequency ν of the normal modes used in the gate. j This is the minimum interval between them. 【0099】 The set of excitation frequencies used to drive the multi-qubit gate is defined in frequency selection step 52. The frequency spectrum has 2M components: 【0100】 【number】 These encompass and irradiate each of the N ions with different amplitudes. The field driving the nth ion is therefore given by the following equation, where the amplitude vector r n These are the sine and cosine components. 【0101】 【number】 and 【0102】 【number】 It is broken down into. 【0103】 【number】 【0104】 For efficient gate operation, the coupling between tone and mode is inversely proportional to the frequency difference between them, so the vibration mode frequency 【0105】 【number】 Tone ω near the bandwidth m It is beneficial to choose this. The amplitude of the field should be zero before t=0 and after t=T. Therefore, a favorable choice of tone is the harmonic base. 【0106】 【number】 and h m This is the tone number. 【0107】 Amplitude vector r to drive each of the N ions n As the first step in finding the coupling matrix between the excitation frequency and the qubit, the coupling matrix between the excitation frequency and the qubit is defined in coupling definition step 54. The coupling matrix between the motions of any pair of ions m and n is given by equation 【0108】 【number】 Defined by: 【0109】 In this equation, η j is the j-th Ramdicke parameter related to the mode of motion, 【0110】 【number】 and 【0111】 【number】 is the normalized contribution of the corresponding ion in the j-th mode of motion. The elements of the matrix on the right-hand side of the equation are defined as follows (operators f and g represent sine and cosine, respectively): 【0112】 【number】 【0113】 The entanglement phase between ion n and ion m is determined by the corresponding bond matrix. 【0114】 【number】 It depends on . As explained above, the purpose of this method is to generate the desired entanglement phase within gate time T, r n The tone ω that will minimize the norm of m Amplitude vector r for a selected setn The task is to select the elements. 【0115】 Rather than attempting to directly solve the entire set of constraints inherent in the above equation, the target entanglement topology is zero: 【0116】 【number】 It is initially set to the set of non-trivial amplitude vectors r for all N ions in zero-phase solution step 56 of the problem. 【0117】 【number】 To solve this, it is subsequently derived that |r0|=1 for all j=1,···,N. As previously explained, the selection of the zero phase independently produces solutions for different entanglement phases, and thus reduces the number of constraints to the order of the number of ions N. The processor 32 finds the solution using numerical methods known in the art for solving systems of linear equations. 【0118】 The zero-phase solution found in step 56 is used in parameter optimization step 58 to determine the target phase 【0119】 【number】 This is used as a starting point to find a modified set of amplitudes that will produce the desired set. This computational and optimization process is based on the observation that if R0 solves the zero-phase problem defined above, then any linear multiple of the solution λR0 will also solve the problem. Furthermore, when λ is sufficiently large (corresponding to the high intensity of the excitation beam), the entanglement phase can be found by applying a suitable set of small deviations D to the beam intensity. 【0120】 【number】 Any set of can be substantially realized, that is, R = λR0 + D holds for all 1 < n < m < N 【0121】 【Equation】 A value of D that satisfies can be found. This principle is illustrated in Figure 4 as described below. 【0122】 Specifically, assuming that the magnitude of λR0 is much larger than the magnitude of D, 【0123】 【Equation】 The above equation for becomes a set of linear equations for D: 【0124】 【Equation】 Can be approximately reduced. The error term ∈ corresponds to the upper limit of the infidelity of the multi-qubit gate. 【0125】 Once D is found to satisfy the above equation, R = λR0 + D will define a set of beam amplitudes that will produce the target entanglement phase within the desired gate time T. This solution, however, is not optimal as it requires irradiation of the ions with a higher laser amplitude. The solution is improved in a series of optimization steps to reduce both the residual error of the target phase 【0126】 【Equation】 And the magnitude of R. Any suitable optimization technique known in the art may be used for this purpose. For example, in a linear gradient descent process, at each step s of the process, the current value R of the amplitude vector (starting from the value R = λR0 + D defined above) (n) The correction value D applied to (n+1)The following is calculated. The desired correction value at each step is given by the linear equation: 【0127】 【number】 It can be expressed by a set of Δφ. (n) teeth, 【0128】 【number】 The constraint error is given by δ, where δ represents the decrease in R, and the correction matrix M (n) The elements are, 【0129】 【number】 It is given by: At each step, a new value of R: R (s+1) =R (s) +D (s+1) This is calculated. 【0130】 This process is performed within the specified fidelity limit. 【0131】 【number】 The condition argmin |R opt An optimized solution R that locally satisfies | opt This process continues until a solution is found. This solution is one of many possible solutions for the initial set of constraints. Therefore, in some embodiments, steps 56 and 58 are repeated multiple times to find multiple zero-phase solutions and then optimize each of them. The solution that gives the best performance with respect to parameters including gate time, fidelity, robustness, and drive strength is selected. 【0132】 Once the optimal solution is found, the N ions in the multi-qubit gate, in gate drive step 60, each have an amplitude R relative to each ion. opt M frequencies defined by 【0133】 【number】 It is driven in the spectrum. Therefore, the processor 32 can perform quantum computation using N qubit gates. 【0134】 Figure 4 is a schematic graph illustrating the selection of spectral component amplitudes used when driving a multi-qubit gate by the method described above, according to one embodiment of the present invention. In this simplified example, the ion is driven by two tones having amplitudes r1 and r2, respectively. The coupling matrix is ​​A1=diag(1,-2), and the entanglement phase is 【0135】 【number】 That is the case. 【0136】 In Figure 4, the zero-phase solution lies along axis 62, while contour lines 64 are (in integer increments) 【0137】 【number】 This shows the solutions for larger and smaller values ​​of λ. Arrow 66 is the multiplied zero-phase solution λ r0 This represents . Arrow 70 is r T A n The initial solution λ represented by arrow 72 satisfies r=2. r0 This represents the correction value d that generates +d. This solution lies on contour line 68. The value of r is the optimal solution r represented by arrow 74. opt Until it is found, it will be optimized step by step along contour line 68. 【0138】 Examples - Surface Reference Numerals Figures 5A and 5B show the physical and logical arrangements 80 and 84, respectively, of the array of trapped ions 82 that perform the entanglement gate required for a surface code for use in quantum error correction according to one embodiment of the present invention. This code is shown here as an example of a multi-qubit operation that can actually be performed using the techniques described above. 【0139】 The logical arrangement of surface codes 84 is the σ of auxiliary qubits 88 for detecting and correcting errors during quantum computation. X It consists of four "plackets" 86 that can be used to evaluate parity. Each placket 86 consists of five ions, including a central auxiliary qubit 88 and four edge qubits 90, which are coupled to the auxiliary qubits by a pairwise link 94. The link 94 is created by setting appropriate coupling phases between the auxiliary qubits 88 and the corresponding edge qubits 90 in the trapped ion array and then selecting excitation frequency spectra using the method described herein to implement these coupling phases. Ions 92 that are not involved in surface sign do not participate in entanglement operation and are not connected by the link 94. 【0140】 In this example, the physical arrangement 80 is arranged at equal intervals with an inter-ion distance of 5 μm. 40 Ca + It includes chains of ions. (Alternatively, the technique presented here may be applicable to other types of ion chains that include non-equally spaced arrangements.) The qubit has a ground state Zeeman 5S. 1 / 2 Mapped to a manifold and driven by a 400 nm laser field using Raman transitions, the laser field couples ions using transverse vibration modes at frequencies in the range of 1–2 MHz. Coupling matrix A m,n It is constructed in response to the entanglement required by link 94, and each amplitude vector r n This is calculated and optimized for each of the 82 ions using the technique described above. The gate time is, for example, T=2.5T. min The value is set to T minThis is the reciprocal of the minimum angular frequency difference Δf between the normal mode vibration frequencies used when performing the gate. 【0141】 Figure 6 is a graph schematically illustrating the drive amplitude applied to ions 82 in a physical array 80 according to one embodiment of the present invention. The vertical bars in this figure represent the total amplitude of the laser frequencies applied to each of the ions |r| j The auxiliary qubits 88 (ions #6, 8, 16, and 18) are driven most strongly because they each have four links 94, while the edge qubits are driven with lower amplitudes. The unbonded ion 92 is not driven at all. 【0142】 Figure 7 is a graph schematically illustrating the amplitude of the spectral components used to drive ions 82 in array 80 using an optimal amplitude vector, according to one embodiment of the present invention. Curve 100 shows the average amplitude of the driving tone as a function of frequency, superimposed on vertical bars 102 representing the normal vibrational modes of array 80. The spectrum of curve 100 is concentrated at frequencies near the vibrational mode frequencies and is dominated by the low-end frequencies of the spectrum, which are more effective in distinguishing between entanglements of adjacent ions. 【0143】 Figure 8 is a graph schematically illustrating the amplitude of the oscillation motion of ions 82 in array 80 over time according to one embodiment of the present invention. The motion begins at time t=0 when laser radiation is irradiated according to an optimal amplitude vector and ends at gate time t=T. 【0144】 Curve 110 represents the mean motion over time of the bound ions (including edge qubit 90), while curve 112 represents the mean motion over time of the unbound ions 92. The upper curve 114 represents the motion of ion #6 (one of the auxiliary qubits 88), while the lower curve 116 represents the unbound ion #12 in the center of array 82. The curves show that the unbound ions 92 are not driven by the laser beam, but they are involved in the vibrational modes of array 80. Different optimized amplitude vectors r j The ability to apply this to different ions, however, minimizes the energy wasted for these unbonded ions, enabling current 25-qubit gates to achieve high fidelity within fast gate times. 【0145】 The examples presented above, for the sake of specificity and clarity, relate to linear arrays of qubits (and specifically, linear arrays of trapped ions), but the principles of the present invention may be applied to other types of qubit arrays, including two-dimensional and three-dimensional arrays, as needed. Furthermore, the present methods for quantum computing may be applied when implementing multi-qubit gates within segments of a segmented qubit array, as described, for example, in PCT patent application PCT / IB2024 / 052100, filed March 5, 2024, whose disclosure is incorporated herein by reference. These methods may also be integrated with other multi-trap techniques known in the art for scaling up quantum computing, such as two-dimensional trap arrays using photon interconnections between ion chains, quantum charge-coupled device architectures (including various ion-shutting schemes), and dipole-dipole interactions for entanglement. All such alternative configurations and implementations are considered to be within the scope of the present invention. 【0146】 The embodiments described above are illustrative, and the present invention is not limited to those specifically shown and described above. Rather, the scope of the present invention includes not only combinations and subcombinations of the various features described above, but also variations and modifications thereof not disclosed in the prior art, which a person skilled in the art would conceive upon reading the above description.

Claims

[Claim 1] A system for quantum computing, An array of qubits having internal transition frequencies from a ground state to an excited state, and having a plurality of normal modes of oscillatory motion between the qubits in the array, each of which has an oscillatory frequency; A radiation source configured to simultaneously irradiate a plurality of qubits in an array with radiation including a set of spectral components in a plurality of vibration sidebands of the internal transition frequency, such that each of the qubits is irradiated with spectral components by different complex amplitudes, wherein the sidebands are generated by the group of normal modes having a minimum interval Δf between the respective vibration frequencies of the normal modes in the group, A controller configured to initialize a multi-qubit gate containing at least five of the qubits in the array to an initial state, and to drive the radiation source to irradiate each of the qubits with the radiation by the complex amplitude of each of the spectral components in the set selected to switch the multi-qubit gate to a target state within a gate time of less than 50 / Δf, A system that includes these features. [Claim 2] The system according to claim 1, wherein the respective vibration frequencies of the normal modes within the group extend over a frequency range from the minimum normal mode frequency to the maximum normal mode frequency, and the controller is configured to drive the radiation source to irradiate the radiation with a bandwidth of at least 10% of the frequency range. [Claim 3] The system according to claim 1, comprising an ion trap, wherein the array of qubits includes an array of ions held within the trap, and the multi-qubit gate includes at least five of the ions within the array. [Claim 4] The system according to claim 3, wherein the internal transition frequency is an electronic transition frequency, and the irradiation of the radiation includes irradiation with laser radiation. [Claim 5] The system according to claim 3, wherein the internal transition frequency is the Raman transition frequency. [Claim 6] The system according to claim 3, wherein the irradiation of the aforementioned radiation includes the irradiation of radio frequency (RF) radiation. [Claim 7] The system according to claim 3, wherein the array of ions is a linear array. [Claim 8] The system according to any one of claims 1 to 7, wherein the multi-qubit gate includes more than 12 qubits in the array. [Claim 9] The system according to any one of claims 1 to 7, wherein the gate time is less than 10 / Δf. [Claim 10] The system according to any one of claims 1 to 7, wherein the multi-qubit gate is configured to implement a quantum error correction code. [Claim 11] The system according to claim 10, wherein the quantum error correction code includes a surface code. [Claim 12] The target state of the multi-qubit gate is the target entanglement phase vector [Math 1] The system according to any one of claims 1 to 7, characterized by the fact that the respective complex amplitudes of the spectral components are selected by optimizing the complex amplitudes to generate the target entanglement phase vector, following the discovery of an initial set of the complex amplitudes that will produce a zero entanglement phase. [Claim 13] The system according to any one of claims 1 to 7, wherein the target state is a highly connected entangled state. [Claim 14] The system according to any one of claims 1 to 7, wherein the target state includes a plurality of nonlocal entanglements. [Claim 15] A method for quantum computing, To provide an array of qubits, each having an internal transition frequency from a ground state to an excited state, and each qubit having multiple normal modes of oscillatory motion, wherein each normal mode has its own oscillatory frequency. Initializing a multi-qubit gate containing at least five of the qubits within the array to its initial state, Irradiating multiple qubits in the array with radiation simultaneously, wherein the radiation comprises a set of spectral components in multiple vibration sidebands of the internal transition frequency, such that each of the qubits is irradiated with spectral components by different complex amplitudes, and the sidebands are generated by the group of normal modes having a minimum interval Δf between the respective vibration frequencies of the normal modes within the group. Selecting the respective complex amplitudes of the spectral components in the set such that the multi-qubit gate is switched to the target state within a gate time of less than 50 / Δf, Methods that include... [Claim 16] The method according to claim 15, wherein the respective vibration frequencies of the normal modes within the group extend over a frequency range from the minimum normal mode frequency to the maximum normal mode frequency, and the radiation is irradiated with a bandwidth of at least 10% of the frequency range. [Claim 17] The method according to claim 15, wherein preparing the array includes trapping ions in an ion trap, and the multi-qubit gate includes at least five of the ions in the array. [Claim 18] The method according to claim 17, wherein the internal transition frequency is an electronic transition frequency, and the irradiation of the radiation includes irradiation with laser radiation. [Claim 19] The method according to claim 17, wherein the internal transition frequency is the Raman transition frequency. [Claim 20] The method according to claim 17, wherein the irradiation of the aforementioned radiation includes irradiation of radio frequency (RF) radiation. [Claim 21] The method according to claim 17, wherein the array of ions is a linear array. [Claim 22] The method according to any one of claims 15 to 21, wherein the multi-qubit gate includes more than 12 qubits in the array. [Claim 23] The method according to any one of claims 15 to 21, wherein the gate time is less than 10 / Δf. [Claim 24] The method according to any one of claims 15 to 21, wherein the multi-qubit gate implements a quantum error correction code. [Claim 25] The method according to claim 24, wherein the quantum error correction code includes a surface code. [Claim 26] The target state of the multi-qubit gate is the target entanglement phase vector [Math 2] The method according to any one of claims 15 to 21, characterized by, the selection of each of the complex amplitudes, comprising finding an initial set of the complex amplitudes that will produce a zero-entanglement phase, followed by optimizing the complex amplitudes to generate the target entanglement phase vector. [Claim 27] The method according to any one of claims 15 to 21, wherein the multi-qubit gate generates a highly connected entanglement state. [Claim 28] The method according to any one of claims 15 to 21, wherein the multi-qubit gate generates a plurality of nonlocal entanglements. [Claim 29] A method for quantum computing, Internal instantaneous transition frequency ω from ground state to excited state 0 To prepare an array of qubits having, Initializing a multi-qubit gate containing a first number N > 2 of the qubits in the array to its initial state, Each frequency ω 0 ±ω m And the amplitude vector R = < r 1 ,r 2 , ..., r M Each amplitude r defined by > m Selecting a second number M > 2 excitation frequency pairs having, N(N-1) / 2 bond matrices A having dimension M × M representing the interaction between the excitation frequency pair and the qubit pair, with 1 < n < m < N. n,m Defining a set, For all j = 1, ..., N [Math 3] constraint |r 0 such that the initial amplitude vector r satisfies |r| = 1 0 find, and Target entanglement phase vector [Math 4] Choosing and For all 1 < n < m < N [Math 5] The target amplitude vector R = λR that satisfies this condition. 0 To find +D, we calculate the parameters λ and D, [Math 6] And, [Number 7] That is, the act of calculating, The method for driving a multi-qubit gate to a target state by irradiating the array of qubits with radiation, wherein the radiation comprises M excitation frequency pairs having amplitudes according to the target amplitude vector R. Methods that include... [Claim 30] After finding the target amplitude vector R, for all 1 < n < m < N [Number 8] The constraint argmin | R is such that opt An optimized target vector R that locally satisfies | opt The method according to claim 29, comprising applying an optimization process to find. [Claim 31] Applying the aforementioned optimization process to the target phase [Number 9] The method according to claim 30, comprising reducing the residual error in the following. [Claim 32] The method according to claim 30, wherein applying the optimization process includes iteratively modifying the target amplitude vector to reduce the magnitude of the target amplitude vector while bringing the target entanglement phase vector within a predetermined error. [Claim 33] The respective frequencies ω 0 ±ω m The method according to claim 29, wherein is selected to excite sidebands of the transition frequency resulting from a group of normal modes of the vibration of the qubit. [Claim 34] The method according to claim 33, wherein the respective vibration frequencies of the normal modes within the group extend over a frequency range from the minimum normal mode frequency to the maximum normal mode frequency, and the selected frequencies extend over a bandwidth of at least 10% of the frequency range. [Claim 35] The method according to claim 33, wherein the sidebands are generated by the group of normal modes having a minimum interval Δf between the respective vibration frequencies of the normal modes within the group, and the target amplitude vector is calculated such that the multi-qubit gate switches to the target state within a gate time of less than 50 / Δf. [Claim 36] The method according to claim 29, wherein finding the target amplitude vector includes calculating the different complex amplitudes of the excitation frequency pair for each of the qubits. [Claim 37] The method of claim 29, comprising defining a gate time T for the multi-qubit gate, and calculating the target amplitude vector, comprising selecting the target amplitude vector such that the multi-qubit gate switches to the target state at the defined gate time. [Claim 38] The method of claim 29, comprising defining a target unfaithfulness for the multi-qubit gate, wherein calculating the target amplitude vector includes selecting the target amplitude vector such that the multi-qubit gate switches to the target state with an unfaithfulness less than or equal to the target unfaithfulness. [Claim 39] The method according to any one of claims 29 to 38, wherein the qubit includes a trapped ion. [Claim 40] The method according to claim 39, wherein the internal transition frequency is an electronic transition frequency, and the irradiation of the radiation includes irradiation with laser radiation. [Claim 41] The method according to any one of claims 29 to 38, wherein the multi-qubit gate includes at least five qubits. [Claim 42] The method according to claim 41, wherein the multi-qubit gate includes more than 12 qubits. [Claim 43] The method according to any one of claims 29 to 38, wherein the multi-qubit gate is configured to implement a quantum error correction code. [Claim 44] The method according to any one of claims 29 to 38, wherein finding the initial amplitude vector comprises solving a set of quadratic constraints of order N. [Claim 45] The method according to any one of claims 29 to 38, wherein the multi-qubit gate generates a highly connected entanglement state. [Claim 46] The method according to any one of claims 29 to 38, wherein the multi-qubit gate generates a plurality of nonlocal entanglements. [Claim 47] A system for quantum computing, Internal instantaneous transition frequency ω from ground state to excited state 0 An array of qubits having, A radiation source configured to initialize a multi-qubit gate containing a first number N > 2 qubits in the array to an initial state, and to drive the multi-qubit gate to a target state by irradiating the array of qubits with radiation, Equipped with, The aforementioned radiation has a frequency ω 0 ±ω m And the target amplitude vector R = < r 1 ,r 2 , ..., r M Each amplitude r defined by > m A second number M > 2 excitation frequency pairs having The aforementioned target amplitude vector R is, N(N-1) / 2 bond matrices A having dimension M × M representing the interaction between the excitation frequency pair and the qubit pair, with 1 < n < m < N. n,m Defining a set, For all j = 1, ..., N [Number 10] Constrained to be such as |r 0 Initial amplitude vector r that satisfies |=1 0 Finding, Target entanglement phase vector [Math 11] Choosing and For all 1 < n < m < N [Math 12] The target amplitude vector R = λR that satisfies this condition. 0 The process involves calculating the parameters λ and D in order to find +D, [Number 13] And, [Number 14] That is, the act of calculating, A system calculated by [this method]. [Claim 48] The target amplitude vector R is determined after finding the target amplitude vector R, for all 1 < n < m < N [Number 15] The constraint argmin | R is such that opt An optimized target vector R that locally satisfies | opt The system according to claim 47, which is calculated by applying an optimization process to find. [Claim 49] Applying the aforementioned optimization process to the target phase [Number 16] The system according to claim 48, comprising reducing residual errors in the following: [Claim 50] The system according to claim 48, wherein applying the optimization process includes iteratively modifying the target amplitude vector to reduce the magnitude of the target amplitude vector while bringing the target entanglement phase vector within a predetermined error. [Claim 51] The respective frequencies ω 0 ±ω m The system according to claim 47, wherein is selected to excite sidebands of the transition frequency resulting from a group of normal modes of the vibration of the qubit. [Claim 52] The system according to claim 51, wherein the respective vibration frequencies of the normal modes within the group extend over a frequency range from the minimum normal mode frequency to the maximum normal mode frequency, and the selected frequencies extend over a bandwidth of at least 10% of the frequency range. [Claim 53] The system according to claim 51, wherein the sidebands are generated by the group of normal modes having a minimum interval Δf between the respective vibration frequencies of the normal modes within the group, and the target amplitude vector is calculated such that the multi-qubit gate switches to the target state within a gate time of less than 50 / Δf. [Claim 54] The system according to claim 47, wherein finding the target amplitude vector includes calculating the different complex amplitudes of the excitation frequency pair for each of the qubits. [Claim 55] The system according to claim 47, wherein the target amplitude vector is calculated by defining a gate time T for the multi-qubit gate and selecting the target amplitude vector such that the multi-qubit gate switches to the target state at the defined gate time. [Claim 56] The system according to claim 47, wherein the target amplitude vector is calculated by defining a target fidelity of the multi-qubit gate and selecting the target amplitude vector such that the multi-qubit gate switches to the target state with a fidelity of less than or equal to the target fidelity. [Claim 57] The system according to any one of claims 47 to 56, wherein the qubit includes a trapped ion. [Claim 58] The system according to claim 57, wherein the internal transition frequency is an electronic transition frequency, and the irradiation of radiation includes irradiation with laser radiation. [Claim 59] The system according to any one of claims 47 to 56, wherein the multi-qubit gate includes at least five qubits. [Claim 60] The system according to claim 59, wherein the multi-qubit gate includes more than 12 qubits. [Claim 61] The system according to any one of claims 47 to 56, wherein the multi-qubit gate is configured to implement a quantum error correction code. [Claim 62] The system according to any one of claims 47 to 56, wherein finding the initial amplitude vector includes solving a set of quadratic constraints of order N. [Claim 63] The system according to any one of claims 47 to 56, wherein the multi-qubit gate generates a highly connected entanglement state. [Claim 64] The system according to any one of claims 47 to 56, wherein the multi-qubit gate generates a plurality of nonlocal entanglements.

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