Large-scale multi-quantum bit trapping ion gate

Abstract

A system (20) for quantum computing includes an array of qubits (40) and a radiation source (28) that simultaneously applies radiation to a plurality of qubits in the array that includes a set of spectral components having different respective complex amplitudes in a plurality of vibration sidebands of internal transition frequencies of the qubits. The sidebands are generated by a set of normal patterns having a minimum spacing f between respective vibration frequencies. A controller (32) initializes a multi-qubit gate comprising at least five qubits to an initial state and drives the radiation source to apply radiation to each of the qubits at a respective complex amplitude of a spectral component in the selected set so as to switch the multi-qubit gate to a target state for a gate time of less than 50 / f.

Description

Cross Reference to Related Applications

[0001] This application claims the benefit of U.S. Provisional Patent Application 63 / 506,142, filed June 5, 2023, which is incorporated by reference herein. TECHNICAL FIELD

[0002] The present invention relates generally to quantum computing, and in particular to large-scale trapped-ion gates in a quantum computer. BACKGROUND

[0003] A quantum computer applies principles of quantum physics to solve computational problems and has the potential to perform certain computations more efficiently than existing digital computers. The basic building block of a quantum computer is a qubit. A quantum computer includes qubits and gates that operate on the qubits, including single-qubit, two-qubit, and multi-qubit gates.

[0004] In a trapped-ion system, individual atomic ions serve as qubits, and trapped-ion systems hold promise as a scalable, reliable platform for quantum computing. In a trapped-ion system, individual atomic ions are trapped by electric fields in an ultrahigh vacuum and are cooled to their motional ground state. The internal electronic energy levels of the ions and the motion of the ions in the trap are controlled with high precision using laser, microwave, or radio frequency (RF) fields. To perform computations, gates are applied to the internal and motional states of the atomic ions by driving fields with the appropriate spectrum (i.e., frequency, amplitude, phase, and duration).

[0005] A popular approach to quantum computing is to decompose algorithms into cascades of single-qubit gates and two-qubit gates. However, multi-qubit gates composed of three or more qubits have also been proposed. For example, Shapira et al., in “Theory of robust multiqubit nonadiabatic gates for trapped ions,” Phys. Rev. A 101, 032330 (2020), which is incorporated by reference herein, describe gates of this type. Physical Review A 101, 032330 (2020) in an article entitled “Theory of robust multiqubit nonadiabatic gates for trapped ions,” which is incorporated by reference herein.

[0006] Multi-qubit gates will be important in the practical 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 stored directly in individual physical qubits (e.g., in individual trapped ions), but in logical qubits that are composed of multiple physical qubits. For example, Schwerdt et al., in “Fault-tolerant quantum error correction for a large number of physical qubits,” Phys. Rev. X 10, 011017 (2020), which is incorporated by reference herein, describe a QEC code that uses 15 physical qubits to encode a single logical qubit. Physical Review AA QEC scheme of this type is described in “Comparing two-qubit and multiqubit gates within the toric code” published by 105, 022612 (2022). In this article, a gate including five physical qubits is used to encode two logical qubits over the entire qubit register, and the fault tolerance threshold is significantly increased compared to the stabilizer measurements performed with a series of two-qubit physical gates.

[0007] Other applications of multi-qubit gates include significantly reducing the depth of quantum circuits by performing register-wide operations. For example, Bassler et al. in “Synthesis of and compilation with time-optimal multi-qubit gates” published in 7, 984 (2023) use multi-qubit gates to generate an N-qubit quantum Fourier transform that employs 2N entangling gates. Another example is described by Bravyi et al. in “Constant-Cost Implementations of Clifford Operations and Multiply-Controlled Gates Using Global Interactions” published in Physical Review Letters 129, 230501 (2022), which describes a quantum circuit consisting of single-qubit operations and global entangling gates generated from an Ising-type Hamiltonian. Further uses of multi-qubit gates include quantum simulation and digital simulation and quantum-classical hybrid optimization, as well as the implementation of computational components including three or more logical gates. Quantum 7, 984 (2023) published in “Synthesis of and compilation with time-optimal multi-qubit gates”. Another example is described by Bravyi et al. in “Constant-Cost Implementations of Clifford Operations and Multiply-Controlled Gates Using Global Interactions” published in Physical Review Letters 129, 230501 (2022), which describes a quantum circuit consisting of single-qubit operations and global entangling gates generated from an Ising-type Hamiltonian. Further uses of multi-qubit gates include quantum simulation and digital simulation and quantum-classical hybrid optimization, as well as the implementation of computational components including three or more logical gates. SUMMARY

[0008] Embodiments of the invention described below provide improved multi-qubit gates and methods for driving such gates.

[0009] Thus, according to embodiments of the invention, there is provided a system for quantum computing, comprising 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 qubits in the array, the normal modes having respective vibrational frequencies. A radiation source is configured to simultaneously apply to a plurality of qubits in the array radiation comprising a set of spectral components located in a plurality of vibrational sidebands of the internal transition frequency, such that the spectral components are applied to each qubit with different respective complex amplitudes. The sidebands are generated by a set of normal modes having a minimum separation between the respective vibrational frequencies of the normal modes in the set f. The controller is configured to initialize a multi-qubit gate comprising at least five qubits in the array to an initial state, and to drive the radiation source to apply the radiation to each of the qubits with the respective complex amplitudes of the spectral components in the selected set, so as to switch the multi-qubit gate to a target state in less than 50 / f of a selected gating time.

[0010] In disclosed embodiments, the respective vibrational frequencies of the normal modes in the set are distributed over a frequency range from a minimum normal mode frequency to a maximum normal mode frequency, and the controller is configured to drive the radiation source to apply radiation having a bandwidth of at least 10% of the frequency range.

[0011] In some embodiments, the system comprises an ion trap, wherein the array of qubits comprises an array of ions held in the trap, and wherein the multi-qubit gate comprises at least five ions in the array. In one embodiment, the internal transition frequency is an electronic transition frequency, and applying the radiation comprises applying laser radiation. In another embodiment, the internal transition can be a hyperfine or Zeeman frequency driven by a light source in a Raman transition configuration. In yet another embodiment, applying the radiation comprises applying radio frequency (RF) radiation. In disclosed embodiments, the array of ions is a linear array.

[0012] In disclosed embodiments, the multi-qubit gate comprises more than twelve qubits in the array. Additionally or alternatively, the gating time is less than 10 / f.

[0013] In some embodiments, the multi-qubit gate is configured to implement a quantum error correction code, such as a surface code.

[0014] In disclosed embodiments, the target state of the multi-qubit gate is characterized by a target entanglement phase vector and the respective complex amplitudes of the spectral components are selected by finding an initial set of complex amplitudes that would produce a zero entanglement phase, followed by optimization of the complex amplitudes to produce the target entanglement phase vector.

[0015] In some embodiments, the target state is a highly connected entangled state. Additionally or alternatively, the target state includes multiple non-local entanglements.

[0016] According to embodiments of the invention, there is also provided a method for quantum computing, comprising providing an array of qubits having an internal transition frequency from a ground state to an excited state, and having a plurality of vibrational modes of motion between qubits in the array, the vibrational modes having respective vibrational frequencies. A multi-qubit gate comprising at least five qubits in the array is initialized to an initial state. Radiation is simultaneously applied to a plurality of qubits in the array. The radiation comprises a set of spectral components in a plurality of vibrational sidebands of the internal transition frequency, such that the spectral components are applied to each qubit with different respective complex amplitudes. The sidebands are generated by a set of vibrational modes having a minimum separation between the respective vibrational frequencies of the vibrational modes in the set f. The respective complex amplitudes of the spectral components in the set are selected so as to switch the multi-qubit gate to a target state in less than 50 / f gate time.

[0017] According to embodiments of the invention, there is also provided a method for quantum computing, the method comprising providing an array of qubits having an internal instantaneous transition frequency ω0from a ground state to an excited state. A multi-qubit gate comprising a first number N>2of qubits in the array is initialized to an initial state. A second number M>2of pairs of excitation frequencies are selected having respective frequencies ω 0± ω m and respective amplitudes r M defined by an amplitude vector R = <r1,r2, …, r m N(N-1) / 2coupling matrices A n,m are defined, where 1<n<m<N, and having a dimension MxM representing an interaction between said pairs of excitation frequencies and pairs of qubits. An initial amplitude vector r0is found satisfying the constraints for all j=1, …, N A target entanglement phase vector is selected. Parameters λ and D are calculated to find a target amplitude vector R = λR0 + D satisfying for all 1<n<m<N, where, where, . The multi-qubit gate is driven to the target state by applying radiation to the array of qubits, the radiation comprising the M pairs of excitation frequencies with amplitudes according to the target amplitude vector R.

[0018] In some embodiments, the vector needs to satisfy additional linear constraints , which is used to ensure disentanglement between qubit states and motional modes, as well as robustness against various errors and noise sources. In these cases, the vector and is found within the null space (kernel) of L.

[0019] In some embodiments, the method includes, after finding the target amplitude vector R, applying an optimization procedure to find an optimized target vector R opt that locally satisfies the constraints such that for all 1 < n < m < N, Typically, applying the optimization procedure includes reducing residual errors in the target phase Additionally or alternatively, applying the optimization procedure includes iteratively modifying the target amplitude vector in order to reduce the magnitude of the target amplitude vector while bringing the target entangling phase vector within a predefined error.

[0020] In some embodiments, the respective frequencies ω 0± ω m are selected to excite sidebands of the transition frequency due to a set of normal modes of vibrations of the qubits. In disclosed embodiments, the respective frequencies of the normal modes in the set are distributed within a frequency range from a minimum normal mode frequency to a maximum normal mode frequency, and the selected frequencies are distributed over a bandwidth of at least 10% of the frequency range. Additionally or alternatively, the set of normal modes is generated with a minimum separation f between the respective frequencies of the normal modes in the set, and wherein the target amplitude vector is computed such that the multi-qubit gate switches to the target state within a gating time of less than 50 / f.

[0021] In disclosed embodiments, finding the target amplitude vector includes computing a different respective complex amplitude for each pair of excitation frequencies.

[0022] Additionally or alternatively, the method includes defining a gating time T of the multi-qubit gate, wherein computing the target amplitude vector includes selecting the target amplitude vector such that the multi-qubit gate switches to the target state with the defined gating time.

[0023] Additionally or alternatively, the method includes defining a target infidelity of the multi-qubit gate, wherein computing the target amplitude vector includes selecting the target amplitude vector such that the multi-qubit gate switches to the target state with an infidelity that is not greater than the target infidelity.

[0024] In disclosed embodiments, the qubits include trapped ions, the internal transition frequency is an electronic transition frequency, and applying the radiation includes applying laser radiation.

[0025] In some embodiments, the multi-qubit gate includes at least five qubits, and even more than twelve qubits.

[0026] In disclosed embodiments, the multi-qubit gate is configured to implement a quantum error correction code.

[0027] Typically, finding the initial amplitude vector includes solving a set of Nth order quadratic constraints.

[0028] In some embodiments, the multi-qubit gate produces a highly connected entangled state and / or multiple non-local entanglements.

[0029] According to embodiments of the invention, there is also provided a system for quantum computing, comprising an array of qubits having an internal transient transition frequency ω0from a ground state to an excited state, and a radiation source configured to initialize a multi-qubit gate including a first number N>2 of qubits in the array to an initial state, and to drive the multi-qubit gate to a target state by applying radiation to the array of qubits. The radiation includes a second number M>2 of pairs of excitation frequencies having respective frequencies ω 0± ω m and respective amplitudes r M defined by a target amplitude vector R = <r1, r2, …, r m The target amplitude vector R is computed by defining a set of N(N-1) / 2 coupling matrices A n,m with dimension MxM representing interactions between pairs of excitation frequencies and pairs of qubits, finding an initial amplitude vector r0satisfying the constraints for all j = 1, …, N selecting a target entanglement phase vector and computing parameters and D to find a target amplitude vector R = satisfying R0 + D for all 1 < n < m < N where ).

[0030] The present invention will be more fully understood from the following detailed description of the embodiments thereof, taken together with the drawings in which: BRIEF DESCRIPTION OF DRAWINGS Figure 1 is a block diagram schematically illustrating a quantum computing system according to embodiments of the invention; Figure 2 is a block diagram schematically illustrating a trapped ion array configured as a qubit in a quantum computer according to embodiments of the invention; Figure 3 is a flowchart schematically illustrating a method for selecting parameters to drive a multi-qubit gate according to an embodiment of the application; Figure 4 is a plot schematically illustrating a simplified example of the selection of amplitudes of spectral components used in driving a multi-qubit gate using a method according to an embodiment of the application; Figure 3 Figure 5A and Figure 5B are plots showing the physical and logical arrangement of a trapped ion array implementing a surface code for quantum error correction according to embodiments of the application, respectively; Figure 6 is a plot schematically illustrating the driving amplitudes of ions in a physical array of Figure 5A according to an embodiment of the application; Figure 7 is a plot schematically illustrating the amplitudes of spectral components of radiation used to drive a physical array of Figure 5A according to an embodiment of the application; and Figure 8 is a plot schematically illustrating the amplitudes of vibrational motion of ions in a physical array of Figure 5A over time according to an embodiment of the application. DETAILED DESCRIPTION

[0031] SUMMARY In trapped ion systems, entangling gates are typically generated by driving the ions with electromagnetic fields that produce phonon-mediated qubit-qubit interactions. This driving scheme uses vibrational sidebands of the internal transition frequencies of the ions. In small multi-qubit gates, the trapped ions have only a few normal vibrational modes, so it is relatively easy to select a set of excitation frequencies and amplitudes that will result in the desired target entanglement phase and gate time (i.e., the time required to drive the gate from its initial state to the target entangled state).

[0032] However, as the number of qubits increases, the number and complexity of the normal vibrational modes grows rapidly. Selecting a set of sideband frequencies and amplitudes to robustly (i.e., with high fidelity) and quickly (with low gate time) drive the transitions of a multi-qubit gate is a difficult optimization problem with quadratic constraints. Even for gates containing as few as four qubits, it is difficult to find a set of optimal driving frequencies and amplitudes.

[0033] Some embodiments of the application described herein address this difficulty by providing a systematic method for selecting driving frequencies and amplitudes for gates of arrays comprising N qubits, where N > 2. In these embodiments, there are N 2 ​The hard optimization problem of the order constraint is reduced to a special instance with polynomial complexity, where only quadratic constraints of order N are solved to find a solution for some instance of a two-part multi-qubit gate (i.e., a gate where an entangling phase is defined for each pair of qubits, and the qubits are driven in parallel with the target entangling phase). This special solution can then be converted to an optimized general solution using linear transformations and local optimization. Thus, an optimized set of drive frequencies and amplitudes can be quickly derived that will be able to drive a multi-qubit gate to perform the desired two-part entanglement operation in a short gating time, including gates with more than twelve qubits.

[0034] To implement this solution, in some embodiments of the invention, a number M > 2 of pairs of excitation frequencies are chosen, with corresponding frequencies ω M 0± m and corresponding amplitudes r m . (Here, ω0is the instantaneous internal transition frequency of a qubit from the ground state to the excited state.) While the same amplitude vector can be applied to all qubits, embodiments of the invention relate to the more general case where a respective different amplitude vector r n is applied to each qubit independently, so that the complete set of amplitudes can be represented by a matrix r of dimension N x M (where the case of all ions being driven by the same global beam or by beams overlapping with several ions is a special case of independent driving described herein).

[0035] Based on the normal modes of motion of the qubits, a set of N(N-1) / 2 coupling matrices A n,m is defined of dimension M x M to represent the interaction between a pair of excitation frequencies and qubits n and m in the array. In particular, O is a matrix of so that is the participation of the n th ion in the j th mode of motion. A j represents the interaction between a pair of excitation frequencies and the j th mode of motion. The matrix is constructed as a linear combination of A j matrices.

[0036] The target entangling phase vector is achieved by applying the amplitude vector to all qubits. For all 1 < n < m < N, this amplitude vector satisfies ​​​However, as described above, finding the vector is a difficult problem.

[0037] By considering the vector , a useful representation of the problem was constructed, namely, the vector composed of all amplitude vectors driving various ions. We also defined as matrix, which is composed of blocks of size , and these blocks are zero except for the and and blocks with values. Using this formula, for all 1 < n < m < N, the form of the optimization problem is .

[0038] Therefore, in some embodiments, the solution process starts from finding an initial non-trivial amplitude vector R0, which satisfies the constraint of for all 1 < n < m < N, that is, for all pairs of qubits, the entanglement phase .

[0039] As described above, solving this zero-phase instance involves only a number of quadratic constraints of the order of N. By solving the zero-phase instance for all interaction matrices A j and all N qubits and setting , the reduction from N 2 order quadratic constraints to order quadratic constraints is achieved.

[0040] Once this initial solution is found, the parameters and D can be calculated through a linear solution process to find the nearby amplitude vector R = R0 + D that satisfies for all 1 < n < m < N. (The vector R is "nearby" in the multi-dimensional solution space defined by the vector elements of R, in the sense that the magnitude D of the vector is less than the magnitude of R0.) Then, for example, optimize the solution space in the gradient descent process to find the optimized target vector R opt , which locally satisfies the constraint argmin |R <00​​​​​​​a set of spectral components in the corresponding sideband representing the instantaneous internal transition frequency ω0, and indicating the corresponding complex amplitudes (including magnitude and phase) to be applied to each qubit. Applying these spectral components simultaneously to the qubits in the array excites selected normal modes and switches the multi-qubit gate from the initial state to the target state with the target entanglement phase vector The operation implements the unitary evolution operator (in the local qubit rotation range) where is the relative XX rotation of the nth and mth qubits.

[0042] The gating time of the multi-qubit gate is determined by the smallest separation f between the corresponding vibration frequencies of the set of normal modes excited by the applied radiation. In the adiabatic limit, the gating time , the coupling matrix A j becomes diagonal and the amplitude vector R satisfying the constraints can be easily found; but in this case the long gating time makes the multi-qubit gate impractical for real quantum computations. Therefore, in some embodiments of the invention, the coupling matrix is chosen to support a faster gating time, for example , or even The coupling matrix in this case is usually full rank, but the above method can be applied to find the optimal amplitude vector R that implements the required fast gating time. Constraints on maximum infidelity and on error and noise robustness can also be added in the solving process to ensure that the resulting amplitude vector will drive a multi-qubit gate with high fidelity and robustness.

[0043] The corresponding vibration frequencies of the normal modes used in the multi-qubit gate are distributed in a certain frequency range from the minimum normal mode frequency to the maximum normal mode frequency. To achieve fast switching (where ), the bandwidth of the radiation used to drive the gate is at least 10% of this frequency range, and can cover the entire frequency range.

[0044] Although the solution given above uses frequency domain analysis and optimization, the principles of the invention can alternatively be implemented in the time domain. In this case, for example, the waveforms used to excite the qubits in the array can be defined in terms of time bins, where the optimal amplitudes are computed for each bin. Computing initial waveforms of this type to achieve zero entanglement phase, followed by an optimization process to reach the target phase while satisfying constraints on gating time, fidelity and other parameters.

[0045] Multi-qubit gates driven according to the present approach can be used for a variety of computational tasks. The principles of the present invention can be applied to create multi-qubit gates for universal quantum computation and / or to implement a portion of a computational task or circuit along with other gates (which can include one, two, or more qubits). As described above, the present approach implements many two-part entanglement phases in parallel within a multi-qubit gate. Many N-qubit operations can be implemented using this two-part parallel operation. Additionally, some N-qubit operations that cannot be performed in a single step using a multi-qubit gate can be implemented as part of a computational circuit (e.g., 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 universal quantum computation schemes with reduced quantum circuit depth (fewer circuit layers needed for a given global operation) relative to schemes known in the art. Smaller quantum circuit depth enables faster circuits with potentially better overall fidelity.

[0046] Multi-qubit gates according to embodiments of the present invention can be used to implement a universal set of quantum computation gates with high efficiency (because fewer circuit layers are needed for a given global operation) because any unitary operation can be sufficiently approximated using a circuit that includes single-qubit gates and multi-qubit gates as described herein). The universal set of gates can be used for algorithmic tasks, including, for example, fault-tolerant circuits, surface and toric codes, Ising spin models, prime factorization, and database searching.

[0047] Furthermore, using multi-qubit gates according to embodiments of the present invention, fewer quantum gates are needed to implement a given algorithmic task, and the resulting circuit is executed correspondingly faster. Such implementations provide enhanced coherence for circuit time and overall better fidelity.

[0048] In addition to implementing parallel gate operations using two-part multi-qubit gate operations, the present approach also facilitates creating gates that produce highly connected entangled states, i.e., states in which many ions have substantial entanglement phases with two or more other ions The entanglement phases are "substantial," i.e., their respective amplitudes are at least 50% of the amplitude of the maximum entanglement phase. For example, at least 10% (or possibly greater than 20%) of the ions can have substantial entanglement phases with two or more other ions, or possibly with three or more ions.

[0049] Additionally or alternatively, the present approach can be used to create gates that produce multiple non-local entanglements (i.e., entanglements between non-adjacent qubits) in parallel. Specifically, there are multiple pairs of non-adjacent qubits (n, m) in which n - m is substantial (e.g., ) with substantial entanglement phases as defined above .

[0050] In some embodiments, such a gate is configured to implement a quantum error correction scheme, such as a surface code. Examples of such implementations are described below. In alternative embodiments, the present approach can be applied to drive quantum simulations.

[0051] In the presented description, for the sake of clarity and concreteness, it is assumed that the transition frequency ω is the instantaneous frequency of a suitable electronic transition in a trapped ion system, which is excited using laser radiation. Alternatively, the principles of the present invention can be applied, mutatis mutandis, to quantum gates based on other trapped ion transitions (e.g. transitions between spin states of a Zeeman-split manifold, or between states in a hyperfine-split manifold), as well as to other types of quantum gates, in which case microwave or radiofrequency excitations, as well as Raman couplings, can be used.

[0052] Furthermore, although the embodiments described herein specifically relate to trapped ion quantum computing systems, the principles of the present invention can be applied, mutatis mutandis, to other types of arrays of qubits, such as superconducting (SC) qubits or arrays of neutral atoms trapped inside optical cavities. In a trapped ion system, the qubits exploit internal electronic degrees of freedom of the trapped ions (e.g. electronic spins), while the interactions between the qubits are mediated by bosons based on harmonic phonon modes. For example, SC qubits exploit transmons, and their interactions are mediated by bosons excited by photons based on a waveguide resonator to which all the SC qubits are coupled. In alternative embodiments of the present invention, a set of frequency components can be similarly used to drive multi-qubit gates in SC, which is selected using the optimization method described herein.

[0053] System description Figure 1 is a block diagram schematically showing a quantum computing system 20 according to an 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 the source 22. (In the present example, it is assumed that the system 20 is based on electronic transitions, as described above, and that the radiation source 28 includes a laser emitting a coherent beam of radiation; however, for example, non-coherent beams can be alternatively used to perform ionization.) The resulting atomic ions are trapped in an ion trap 24 (such as a Paul trap) that uses RF fields to confine the ions along a specified line within the vacuum chamber 26. A magnetic field can also be applied to the ion trap 24 to separate different spin components of the electronic states of the ions into Zeeman energy levels.

[0054] The electronic qubit control and computing processor 32 drives the radiation source 28 to direct additional beams at the trapped ions in order to perform quantum computation operations and then to read out the computation results. Typically, the results are read out by tuning a laser beam to an absorption line of one qubit state and then measuring the resulting fluorescence emission using the optical detector 30. The processor 32 receives the results of the computation and drives the laser source 28 to perform additional computation steps according to the algorithm being implemented.

[0055] Figure 2 is a block diagram schematically illustrating an array of trapped ions 40 configured as qubits in a quantum computer, for example in the system 20, according to an embodiment of the present application. The laser source 28 Figure 1 provides several different laser beam inputs to the ion trap 24 for different purposes. An ionization laser 42 ionizes atoms output by the atomic source 22 to produce ions 40, which are held in the trap. Additional cooling lasers 44 cool the ions to their electronic ground state and motional ground state by pumping appropriate state transitions of the ions while the laser frequency is detuned to produce mechanisms of Doppler cooling, sideband cooling, polarization gradient cooling, cooling through electrical induced transparency (EIT), and / or other cooling methods known in the art.

[0056] The cooled ions 40 are held in a linear array by electromagnetic fields within the trap 24 along the axis 38. The Coulomb repulsion between the ions 40 and the trapping fields determines the equilibrium distance between the ions and the phonon frequencies of the normal modes of motion of the ions 40 in the array, including both transverse and longitudinal vibration modes These normal modes of motion produce vibrational sidebands of the optical transition frequencies between the states of the ions 40. Absorbing a photon at one of these sideband frequencies causes excitation or de-excitation of the vibrational modes of the ion array associated with the sideband, while driving an internal transition of the absorbing ion, thereby transferring energy to the normal modes of the ion array and entangling the internal and motional states of the ions through spin-dependent forces. The entangling mechanisms it provides enable multi-qubit gates to be applied to these ions 40. Such gates can include five or more qubits, even greater than twelve qubits.

[0057] To operate the multi-qubit gates, an excitation laser 46 (or multiple lasers) coherently illuminates the ions 40 with a set of excitation frequencies centered on selected internal instantaneous transitions of the ions . The beams of the laser 46 are modulated, for example by suitable acousto-optic modulators, to coherently include frequency components in multiple sidebands of the internal transition frequencies as defined above. .

[0058] The amplitudes of the frequency components are selected using a scheme described further below, so as to optimize the amplitude vector R of the frequency components, which is to reach the target entangled phase vector The laser 46 is operated to irradiate each ion 40 with the selected frequency components at the optimal amplitudes for the duration of the gating time T, to drive the multi-qubit gate from its initial state to the target entangled state. While the same set of sideband amplitudes can be applied to all ions, in the present embodiment each ion 40 is driven with its own amplitude vector R, which is generally different from the amplitudes applied to the other ions. An example of such an excitation spectrum is shown below.

[0059] After the computation cycle is completed, the readout laser 48 reads the state of the qubit register defined by the ions 40. The readout laser 48 is tuned to an absorption line of one of the states of the ions in the register. Absorption of the laser radiation by an ion in the appropriate state produces fluorescence, which is measured by the optical detector 30 Figure 1 The detector 32 measures the intensity of the fluorescence emission, thereby detecting the final state of the gate.

[0060] The processor 32 generally comprises a general purpose computer having appropriate interfaces to the other components of the system 20. The processor 32 is driven by software to perform the functions and calculations described herein. The software can be stored on a tangible, non-transitory computer readable medium, such as an optical, magnetic or electronic storage medium.

[0061] Selection and optimization of excitation spectrum Figure 3 is a flowchart schematically showing a method for selecting parameters to drive a multi-qubit gate according to an embodiment of the present application. The method is generally performed by a suitable computer, such as the processor 32, under control of suitable software code.

[0062] Figure 3 The method of begins with defining a multi-qubit register in the trapped ion array at a register definition step 50. The register is defined by the type and number N of ions 40 in the trap 24 that are to participate in the gate, as well as parameters such as the internal transient transition frequencies and the trap characteristics, which determine the normal mode frequencies j The corresponding gate definition will also specify the target entangled phase vector and the gating time T. As described above, substantially any entangled phase vector can be selected, depending on the desired function of the gate. In order for the computation to be completed quickly, the gating time T should be set to a small value, for example , even where is the individual vibrational frequencies of the normal modes used in the gate j The minimum spacing between them.

[0063] In frequency selection step 52, the set of excitation frequencies to be used to drive the multi-qubit gate is defined. The spectrum contains 2M components: It is applied to each of the N ions with different amplitudes. Therefore, the driving force of the first ion is given by the following equation. n The field of ions, where the amplitude vector r n Decomposed into sinusoidal components Sum and cosine components : .

[0064] To efficiently drive the gate, the vibration modal frequency band is selected. Nearby frequency components (tone) This is beneficial because the coupling between frequency components and modes is inversely proportional to the frequency difference between them. The field amplitude should disappear before t=0 and after t=T. Therefore, a convenient option for frequency components is the harmonic basis. ,in h m It is a frequency component.

[0065] As a means of finding the amplitude vector r used to drive each of the N ions. n The first step, defined in step 54 of the coupling definition, is to define the coupling matrix between the excitation frequency and the qubit. Any pair of ions is defined by the following equation. m and n The coupling matrix between motions:

[0066] In this equation, j Is with the first j Lamb-Dicke parameters associated with each motion pattern, and and It is in the j The normalized participation degree of the corresponding ion under each motion mode. The matrix elements on the right side of the equation are defined as follows (where appropriate, the operators f and g represent sine and cosine): .

[0067] In ions n and ions m The entanglement phase between them depends on the corresponding coupling matrix:

[0068] As stated above, the purpose of this method is to target selected frequency components. The set, choose the amplitude vector r n The elements that will produce the desired entangled phase within the gating time T and minimize r n The norm of .

[0069] The target entanglement phase is initially set to zero: Instead of attempting to directly solve the entire set of constraints inherent in the above equations, the set of nontrivial amplitude vectors r for all N ions is then derived in the zero-phase solution step 56 to solve the problem. Where for all j=1, ...,N, As explained earlier, the choice of zero phase makes the solution independent of different entanglement phases, thereby reducing the number of constraints to the order of the number of ions N. The processor 32 typically uses numerical methods known in the art for solving systems of simultaneous equations to find the solution.

[0070] The zero-phase solution found in step 56 is used as the starting point for finding the modified amplitude set, which will produce the desired target phase in parameter optimization step 58. The set. The calculation and optimization process is based on the observation that if R0 solves the zero-phase problem as defined above, then the solution of any linear multiple is... R0 will also solve this problem. Furthermore, when A sufficiently large value (corresponding to a high intensity of the excitation beam) allows for the near realization of entangled phase by applying an appropriate set of small deviations D to the beam intensity. Any set of , i.e., finding the value of D such that for all 1s <n<m<N, satisfy As described below, this principle is... Figure 4 It is shown graphically in the middle.

[0071] Specifically, assuming If the amplitude of R0 is much larger than the amplitude of D, then The above expression can be approximately simplified to a set of linear equations for D:

[0072] Error term This corresponds to the upper limit of the fidelity of multi-qubit gates.

[0073] Once it has been found that D satisfies the above equation... A set of amplitudes of the light beams will be defined that will produce the target entanglement phase within the desired gating time T. However, this solution is not optimal as it requires high laser amplitudes to irradiate the ions. The solution is improved by a series of optimization steps to reduce the residual in the target phase and the amplitude of R. Any suitable optimization technique known in the art can be used for this purpose. For example, in a linear gradient descent process, at each step s in the process, a correction is calculated to apply to the current value of the amplitude vector (starting from the values defined above). The correction required at each step can be represented by a set of linear equations:

[0074] In this equation, is the constraint error, given by , represents the reduction of R, and is given by The elements of the correction matrix M (n) are given by At each step, the new value of R is calculated as: .

[0075] This process continues until an optimized solution R opt is found that locally satisfies the condition such that i.e. within the specified fidelity limit. 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, which are then optimized each. The solution that provides the best performance in terms of parameters including gating time, fidelity, robustness, and driving strength can then be selected.

[0076] At gate driving step 60, once the optimal solution is found, the N ions in the multi-qubit gate are driven on a spectrum of M frequencies , where the respective amplitudes are defined by R opt for each ion. The processor 32 is thus able to perform a quantum computation using the N-qubit gate.

[0077] Figure 4 is a graph schematically illustrating the selection of amplitudes of spectral components used in driving a multi-qubit gate according to the method described above, according to an embodiment of the application. In this simplified example, the ions are driven by two frequency components with respective amplitudes r1 and r2. The coupling matrix is A1 = diag(1,-2), and the entanglement phase is .

[0078] InFigure 4 In the diagram, the zero-phase solution is along axis 62, while profile 64 represents the solution for both larger and smaller phases. The solution (in integer increments). Arrow 66 indicates the zero-phase solution after multiplication. Arrow 70 indicates the correction d, which produces the initial solution. (Indicated by arrow 72), to satisfy The solution lies on contour 68. The value of r is optimized incrementally along contour 68 until the optimal solution r, represented by arrow 74, is found. opt .

[0079] Implementation Example - Surface Code Figure 5A and Figure 5B These are diagrams illustrating the physical arrangement 80 and logical arrangement 84 of an array of trapped ions 82 for quantum error correction, required for implementing surface codes, according to an embodiment of the present invention. The code is shown herein as an example of multi-qubit operations that can be practically implemented using the techniques described above.

[0080] The logical arrangement 84 of the surface code consists of four "lattice points" 86, which can be used to evaluate the auxiliary qubits 88. Parity is used to detect and correct errors in quantum computing. Each lattice point 86 consists of five ions, including a central auxiliary qubit 88 and four edge qubits 90, which are coupled to the auxiliary qubits via paired links 94. Links 94 are created by setting appropriate coupling phases between the auxiliary qubits 88 and their corresponding edge qubits 90 in the trapped ion array, and then selecting the excitation spectrum using the method described herein to achieve these coupling phases. Ions 92 that do not participate in the surface code do not participate in entanglement operations and are not connected via links 94.

[0081] In this example, the physical arrangement 80 includes equidistant... Ion chains are formed with an inter-ion spacing of 5 μm (or, the technique proposed in this paper can be applied to other types of ion chains, including non-equidistant arrangements). The qubits are mapped to the ground-state Zeeman 5S... 1 / 2 Energy levels, driven by a 400 nm laser field using Raman transitions, are coupled to ions using transverse vibrational modes with frequencies in the 1-2 MHz range. Coupling matrix. The entanglement required for link 94 is constructed accordingly, and for each of ions 82, the corresponding amplitude vector r is calculated and optimized using the above-described technique. n The gating time is set, for example, to a value of T=2.5T. min T min It is the minimum angular frequency difference between the vibration frequencies of the normal modes used in implementing the gate. The reciprocal of.

[0082] Figure 6 is a plot schematically illustrating drive amplitudes applied to ions 82 in physical array 80 according to an embodiment of the application. The vertical bars in the plot show the total amplitude of the laser frequency applied to each ion, found according to the method using Figure 3 Auxiliary qubits 88 (ions #6, 8, 16 and 18) are driven most strongly, since each has four links 94, while the edge qubits are driven at lower amplitudes. Decoupled ions 92 are not driven at all.

[0083] Figure 7 is a plot schematically illustrating amplitudes of spectral components used to drive ions 82 in array 80 according to an embodiment of the application using the optimal amplitude vector. Curve 100 shows the average amplitude of the drive frequency components as a function of frequency, overlaid on vertical bars 102 marking the normal modes of vibration of array 80. The spectrum of curve 100 is concentrated at frequencies near the vibration mode frequencies, and dominated by frequencies at the low frequency end of the spectrum, which are more effective in distinguishing entanglement of adjacent ions.

[0084] Figure 8 is a plot schematically illustrating amplitudes of vibrational motion of ions 82 in array 80 over time according to an embodiment of the application. The motion begins at time t = 0, when laser radiation is applied according to the optimal amplitude vector, and ends at a gating time t = T.

[0085] Curve 110 represents the average motion of coupled ions, including edge qubits 90, over time, while curve 112 represents the average motion of decoupled ions 92 over time. Upper curve 114 represents the motion of ion #6, one of auxiliary qubits 88, while lower curve 116 represents decoupled ion #12 at the center of array 82. The curves show that, although decoupled ions 92 are not driven by the laser beam, they still participate in the vibration modes of array 80. However, the ability to apply different optimal amplitude vectors r j to different ions minimizes the energy wasted on these decoupled ions, and enables the 25-qubit gate of the present application to achieve high fidelity in a fast gating time.

[0086] ​While the examples given above refer to linear arrays of qubits (and specifically to linear arrays of trapped ions) for concreteness and clarity, the principles of the present invention can be applied to other types of qubit arrays, including two- and three-dimensional arrays, mutatis mutandis. Moreover, the present methods for quantum computing can be applied to implementing multi-qubit gates within segments of segmented qubit arrays, e.g., as described in PCT Patent Application PCT / IB2024 / 052100, filed March 5, 2024, the disclosure of which is incorporated by reference herein. These methods can also be integrated with other multi-well techniques known in the art for performing quantum computations, such as photonic interconnections between ion chains; quantum charge-coupled device architectures (including various ion shuttling schemes); and two-dimensional well arrays for entanglement using dipole-dipole interactions. All such alternative configurations and implementations are considered to be within the scope of the present invention.

[0087] The embodiments described above are set forth by way of example and are not meant as limitations on the present invention. More specifically, the present invention encompasses all variations, modifications and alternatives of the various features set forth herein, and equivalents thereof, as would be appreciated by one of ordinary skill in the art having the benefit of this disclosure, in addition to those already described.

Claims

1. A system for quantum computing, comprising: 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 qubits in the array, the normal modes having respective vibrational frequencies; a radiation source configured to simultaneously apply radiation to a plurality of qubits in the array, the radiation comprising a set of spectral components located in a plurality of vibrational sidebands of the internal transition frequency, such that the spectral components are applied to each of the qubits with different respective complex amplitudes, wherein the sidebands are generated by a set of normal modes having a minimum separation between respective vibrational frequencies of the normal modes in the set f; and a controller configured to initialize a multi-qubit gate comprising at least five qubits in the array to an initial state, and to drive the radiation source to apply the radiation to each of the qubits with a respective complex amplitude of a spectral component in the selected set so as to switch the multi-qubit gate to a target state in less than 50 the gating time of f.

2. The system of claim 1, wherein, the respective vibrational frequencies of the normal modes in the set are distributed over a range of frequencies from a minimum normal mode frequency to a maximum normal mode frequency, and wherein the controller is configured to drive the radiation source to apply radiation having a bandwidth of at least 10% of the range of frequencies.

3. The system of claim 1, further comprising an ion trap, wherein the array of qubits comprises an array of ions held in the trap, and wherein the multi-qubit gate comprises at least five ions in the array.

4. The system of claim 3, wherein, the internal transition frequency is an electronic transition frequency, and wherein applying the radiation comprises applying laser radiation.

5. The system of claim 3, wherein, the internal transition frequency is a Raman transition frequency.

6. The system of claim 3, wherein, applying the radiation comprises applying radio frequency (RF) radiation.

7. The system of claim 3, wherein, the array of ions is a linear array.

8. The system of any one of claims 1-7, wherein, the multi-qubit gate comprises more than twelve qubits in the array.

9. The system of any one of claims 1-7, wherein, the gate time is less than 10 f.

10. The system of any one of claims 1-7, wherein, the multi-qubit gate is configured to implement a quantum error correcting code.

11. The system of claim 10, wherein, the quantum error correcting code comprises a surface code.

12. The system of any one of claims 1-7, wherein, the target state of the multi-qubit gate is generated by a target entangling phase vector characterized, and wherein respective complex amplitudes of the spectral components are selected by finding an initial set of complex amplitudes that would produce a zero entangling phase, followed by optimization of the complex amplitudes to produce the target entangling phase vector.

13. The system of any one of claims 1-7, wherein, the target state is a highly connected entangled state.

14. The system of any one of claims 1-7, wherein, the target state comprises a plurality of non-local entanglements.

15. A method for quantum computing, comprising: providing 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 qubits in the array, the normal modes having respective vibrational frequencies; initializing a multi-qubit gate comprising at least five qubits in the array to an initial state; applying radiation to a plurality of qubits in the array simultaneously, the radiation comprising a set of spectral components located in a plurality of vibrational sidebands of the internal transition frequency, such that the spectral components are applied to each of the qubits with different respective complex amplitudes, wherein the sidebands are generated by a set of normal modes having a minimum separation between respective vibrational frequencies of the normal modes in the set f; and selecting respective complex amplitudes of the spectral components in the set so as to switch the multi-qubit gate to a target state in less than 50 gated time of f.

16. The method of claim 15, wherein, the respective vibrational frequencies of the normal modes in the set are distributed over a range of frequencies from a minimum normal mode frequency to a maximum normal mode frequency, and wherein the radiation is applied with a bandwidth of at least 10% of the range of frequencies.

17. The method of claim 15, wherein, providing the array comprises trapping ions in an ion trap, and wherein the multi-qubit gate comprises at least five ions in the array.

18. The method of claim 17, wherein, the internal transition frequency is an electronic transition frequency, and wherein applying the radiation comprises applying laser radiation.

19. The method of claim 17, wherein, the internal transition frequency is a Raman transition frequency.

20. The method of claim 17, wherein, applying the radiation comprises applying radio frequency (RF) radiation.

21. The method of claim 17, wherein, the array of ions is a linear array.

22. The method of any one of claims 15-21, wherein, the multi-qubit gate comprises more than twelve qubits in the array.

23. The method of any one of claims 15-21, wherein, the gate time is less than 10 f.

24. The method of any one of claims 15-21, wherein, the multi-qubit gate implements a quantum error correcting code.

25. The method of claim 24, wherein, the quantum error correcting code comprises a surface code.

26. The method of any one of claims 15-21, wherein, the target state of the multi-qubit gate is represented by a target entangling phase vector characterized, and wherein selecting the respective complex amplitudes comprises finding an initial set of complex amplitudes that would produce a zero entangling phase, and subsequently optimizing the complex amplitudes to produce the target entangling phase vector.

27. The method of any one of claims 15-21, wherein, the multi-qubit gate produces a highly connected entangled state.

28. The method of any one of claims 15-21, wherein, the multi-qubit gate produces a plurality of non-local entanglements.

29. A method for quantum computing, comprising: providing an array of qubits having an internal instantaneous transition frequency ω0 from a ground state to an excited state; initializing a multi-qubit gate comprising a first number N > 2 of qubits in the array to an initial state; a second number M > 2 of excitation frequency pairs with corresponding frequencies ω 0± ω m and corresponding amplitudes r M defined by the amplitude vector R = <r1, r2, …, r m M define a set of N(N-1) / 2 coupling matrices A n,m with dimension MxM representing the interaction between the excitation frequency pairs and the pairs of qubits, where 1 < n < m < N finding an initial amplitude vector r0 that satisfies the constraints such that for all j = 1,..., N the initial amplitude vector r0 Selecting a target entanglement phase vector ; The parameters λ and D are computed to find the target amplitude vector R = λR0 + D that satisfies for all 1 < n < m < N, where where ; and driving the multi-qubit gate to a target state by applying radiation to the array of qubits, the radiation comprising M pairs of excitation frequencies having amplitudes according to a target amplitude vector R.

30. The method of claim 29, further comprising, after finding the target amplitude vector R, applying an optimization procedure to find an optimized target vector R opt the optimized target vector R opt locally satisfies the constraint argmin |R opt | such that for all 1 < n < m < N, .

31. The method of claim 30, wherein, Applying the optimization process includes reducing residual errors in the target phase .

32. The method of claim 30, wherein, Applying the optimization procedure includes iteratively modifying the target amplitude vector so as to reduce the magnitude of the target amplitude vector while bringing the target entanglement phase vector to within a predefined error.

33. The method of claim 29, wherein, the corresponding frequency ω 0± ω m sidebands selected to excite the transition frequency due to a set of normal modes of vibration of the qubit.

34. The method of claim 33, wherein, The respective vibrational frequencies of the normal modes in the group are distributed over a frequency range from a minimum normal mode frequency to a maximum normal mode frequency, and wherein the selected frequency is distributed over a bandwidth that is at least 10% of the frequency range.

35. The method of claim 33, wherein, The sideband is generated from a set of normal modes having a minimum separation between the respective vibration frequencies of the normal modes in the set f, and wherein the target amplitude vector is calculated such that the multi-qubit gate switches to the target state in less than 50 f gate time.

36. The method of claim 29, wherein, Finding the target amplitude vector includes, for each of the qubits, calculating a different respective complex amplitude of the pair of excitation frequencies.

37. The method of claim 29, further comprising defining a gating time T of the multi-qubit gate, wherein calculating the target amplitude vector includes selecting the target amplitude vector so that the multi-qubit gate switches to the target state with the defined gating time.

38. The method of claim 29, further comprising defining a target infidelity of the multi-qubit gate, wherein calculating the target amplitude vector includes selecting the target amplitude vector so that the multi-qubit gate switches to the target state with an infidelity that is not greater than the target infidelity.

39. The method of any one of claims 29-38, wherein, The qubits include trapped ions.

40. The method of claim 39, wherein, The internal transition frequencies are electron transition frequencies, and wherein applying the radiation includes applying laser radiation.

41. The method of any one of claims 29-38, wherein, The multi-qubit gate includes at least five qubits.

42. The method of claim 41, wherein, The multi-qubit gate includes more than twelve qubits.

43. The method of any one of claims 29-38, wherein, The multi-qubit gate is configured to implement a quantum error correction code.

44. The method of any one of claims 29-38, wherein, Finding the initial amplitude vector includes solving a set of Nth order quadratic constraints.

45. The method of any one of claims 29-38, wherein, The multi-qubit gate produces a highly connected entangled state.

46. The method of any one of claims 29-38, wherein, The multi-qubit gate produces a plurality of non-local entanglements.

47. A system for quantum computing, comprising: an array of qubits having internal transient transition frequencies ω0 from a ground state to an excited state; and a source of radiation configured to initialize a multi-qubit gate including a first number N > 2 of qubits in the array to an initial state, and to drive the multi-qubit gate to a target state by applying radiation to the array of qubits, wherein the radiation comprises a second number M > 2 of pairs of excitation frequencies, the pairs of excitation frequencies having respective frequencies ω 0± ω m and respective amplitudes r M > defined by a target amplitude vector R = <r1, r2, …, r m , wherein the target amplitude vector R is calculated by: define a set of N(N-1) / 2 coupling matrices A n,m with dimension MxM representing the interaction between the excitation frequency pairs and the pairs of qubits, where 1 < n < m < N; finding a vector r that satisfies the constraints such that for all j = 1,..., N an initial amplitude vector r0; Selecting a target entanglement phase vector ; and The parameters λ and D are computed to find the target amplitude vector R = λR0 + D that satisfies for all 1 < n < m < N, where where .

48. The system of claim 47, wherein, The target amplitude vector R is computed by the following steps: after finding the target amplitude vector R, an optimization procedure is applied to find an optimized target vector R opt The optimized target vector R opt Locally satisfies constraints So that for all 1 < n < m < N .

49. The system of claim 48, wherein, Applying the optimization process includes reducing residual errors in the target phase .

50. The system of claim 48, wherein, Applying the optimization procedure includes iteratively modifying the target amplitude vector so as to reduce the magnitude of the target amplitude vector while bringing the target entanglement phase vector to within a predefined error.

51. The system of claim 47, wherein, the corresponding frequency ω 0± ω m sidebands of the transition frequency are selected to be excited due to a set of normal modes of vibrations of the qubit.

52. The system of claim 51, wherein, The respective vibrational frequencies of the normal modes in the group are distributed over a frequency range from a minimum normal mode frequency to a maximum normal mode frequency, and wherein the selected frequency is distributed over a bandwidth that is at least 10% of the frequency range.

53. The system of claim 51, wherein, The sideband is generated from a set of normal modes having a minimum separation between the respective vibration frequencies of the normal modes in the set f, and wherein the target amplitude vector is calculated such that the multi-qubit gate switches to the target state in less than 50 f gate time.

54. The system of claim 47, wherein, Finding the target amplitude vector includes, for each of the qubits, calculating a different respective complex amplitude of the pair of excitation frequencies.

55. The system of claim 47, wherein, The target amplitude vector is calculated by defining a gating time T of the multi-qubit gate and selecting the target amplitude vector so that the multi-qubit gate switches to the target state with the defined gating time.

56. The system of claim 47, wherein, The target amplitude vector is computed by defining a target infidelity for the multi-qubit gate and selecting the target amplitude vector such that the multi-qubit gate switches to the target state with an infidelity no greater than the target infidelity.

57. The system of any one of claims 47-56, wherein, The qubits include trapped ions.

58. The system of claim 57, wherein, The internal transition frequency is an electronic transition frequency, and wherein applying the radiation includes applying laser radiation.

59. The system of any one of claims 47-56, wherein, The multi-qubit gate includes at least five qubits.

60. The system of claim 59, wherein, The multi-qubit gate includes more than twelve qubits.

61. The system of any one of claims 47-56, wherein, The multi-qubit gate is configured to implement a quantum error correction code.

62. The system of any one of claims 47-56, wherein, Finding the initial amplitude vector includes solving a set of N second order constraints.

63. The system of any one of claims 47-56, wherein, The multi-qubit gate produces a highly connected entangled state.

64. The system of any one of claims 47-56, wherein, The multi-qubit gate produces multiple non-local entanglements.

Images