Quantum computing using trapped ion arrays and optical potentials

Abstract

A quantum computing method includes defining a quantum computation that includes a sequence of computing steps in which multiple quantum operations are performed in parallel at each step. An arrangement of ions (40) in an ion trap (24) is divided into a first computational section (110) which includes groups of neighboring ions separated by a first barrier ion (112) between groups by optically confining barrier ions. An excitation field is applied to the ions in the computational section so that the groups of ions perform the quantum operations in the first step of the sequence. After the completion of the first step, the arrangement is reconfigured into a second computational section by optically confining a second barrier ion which is at least partly different from the first barrier ion, while maintaining at least some coherence from the first computational section to the second computational section.

Description

[Technical Field]

[0001] Cross-reference of related applications This application claims the interests of U.S. Provisional Patent Application No. 63 / 490,007 filed on 14 March 2023, U.S. Provisional Patent Application No. 63 / 594,976 filed on 1 November 2023, and U.S. Provisional Patent Application No. 63 / 595,349 filed on 2 November 2023. All of these related applications are incorporated herein by reference.

[0002] This invention generally relates to quantum computing, and more specifically to large-scale quantum computing using a trapped ion array. [Background technology]

[0003] Quantum computers apply the principles of quantum physics when solving computational problems and have the potential to perform certain calculations far more efficiently than existing digital computers. The basic building block of a quantum computer is the qubit. Quantum computers use qubits and gates, including single-qubit, two-qubit, and multi-qubit gates, to perform not only digital quantum computations but also analog quantum simulations. As used herein and in the claims, the terms “quantum computer” and “quantum computation” should be understood to encompass all types of quantum information processing, including both gate-based quantum computations and analog quantum simulations.

[0004] Trapped ion systems, in which individual atomic ions function as qubits, are promising as a scalable and reliable platform for quantum computing and quantum simulation. In a trapped ion system, individual atomic ions are typically trapped by an electromagnetic field in an ultra-high vacuum and cooled to a moving ground state. The internal electronic levels of the ions and the motion of the ions within the trap are controlled with high precision using laser, microwave, and / or radio frequency (RF) fields. To perform digital quantum computing, gates are applied to the internal and moving states of the atomic ions by driving fields of appropriate frequency, amplitude, phase, and duration.

[0005] In a trapped ion system, quantum entanglement gates are typically created by driving ions with an electromagnetic field that induces phonon-mediated qubit interactions. A mode of driving multi-qubit gates in a trapped ion array is described, for example, in PCT International Publication WO2023 / 105434, the disclosure of which is incorporated herein by reference.

[0006] The mainstream approach in quantum computing involves decomposing algorithms into single-qubit gates and chains of two-qubit gates. However, multi-qubit gates consisting of three or more qubits have also been proposed. For example, Shapira et al. describe this type of gate in their paper, "Theory of robust multiqubit nonadiabatic gates for trapped ions," published in Physical Review A 101, 032330 (2020), which is incorporated herein by reference.

[0007] Increasing the number of qubits in multi-qubit gates while maintaining high fidelity and fast operation is a difficult task. In particular, the design of multi-qubit quantum entanglement gates in long ion crystals consisting of hundreds of ions involves difficult optimization problems, which also make the increase in the number of qubits a conceptual challenge. Shapira et al. describe in "Fast design and scaling of multi-qubit gates in large-scale trapped-ion quantum computers" published in arXiv:2307.09566 (2023) a way to alleviate this computational challenge and thereby substantially enable polynomial-time design of fast programmable quantum entanglement gates, which is incorporated herein by reference.

Summary of the Invention

[0008] Embodiments of the invention described below provide an improved system and method for quantum computing using an array of trapped ions.

[0009] According to one embodiment of the present invention, there is provided a method of quantum computing including trapping an array of ions in an ion trap and defining a plurality of quantum computations including a sequence of computing steps including a plurality of quantum operations performed in parallel at each step. The array is partitioned into a first computational segment including respective groups of adjacent ions separated by a first barrier ion between the groups by optically confining the barrier ions. An excitation field is applied to the ions in the first computational segment to cause the quantum operation in the first step of the sequence to be performed on the groups of adjacent ions in the first computational segment. After completion of the quantum operation in the first step, the array is reconfigured as a second computational segment by optically confining at least a second barrier ion that is at least partially different from the first barrier ion while maintaining at least a portion of the coherence from the first computational segment to the second computational segment. An excitation field is applied to the ions in the second computational segment to cause the quantum operation in the second step of the sequence to be performed on the groups of adjacent ions in the second computational segment using at least a portion of the maintained coherence. To complete the quantum computation, the steps of reconfiguring the array into further computational segments and applying an excitation field to the further computational segments are repeated.

[0010] In one embodiment of the disclosure, at the completion of the quantum computation, the state of each of at least some of the ions is measured.

[0011] In some embodiments, trapping the array of ions includes forming a linear array of ions. Alternatively, trapping the array of ions includes forming a two-dimensional array of ions. As a further option, trapping the array of ions includes forming a three-dimensional array of ions.

[0012] In some embodiments, optically confining barrier ions includes applying optical tweezers to the barrier ions. In embodiments of the disclosure, applying optical tweezers includes confining barrier ions using a laser beam tuned to apply an optical attraction or repulsion to the barrier ions.

[0013] In some embodiments, the method includes performing a mid-circuit measurement by detecting the state of one or more ions in the sequence following at least a first step of the sequence. In one embodiment of the disclosure, applying an excitation field to the ions in a second computational section includes using the information contained in the detected state in the mid-circuit measurement when defining the quantum operation performed in a subsequent step. In one embodiment, the method includes applying error correction to the quantum computation based on the mid-circuit measurement. In addition to or instead of the above, performing a mid-circuit measurement includes detecting the state of one or more barrier ions in the barrier ions. Typically, the reconstruction of the sequence into a second computational section following the mid-circuit measurement is completed in a duration of less than 20 milliseconds, and possibly less than 10 milliseconds.

[0014] In embodiments of this disclosure, applying an excitation field includes directing a beam of coherent light emission to excite ion transitions in the computational region. Transitions may include internal and / or kinetic transitions of ions in the computational region.

[0015] In addition to or instead of the above, applying an excitation field includes setting the respective spectra and pulse times of the beam to drive ions to complete the quantum operation in each step. Typically, optically confining barrier ions reduces crosstalk between adjacent computational sections in the array. In some embodiments, setting the respective spectra and pulse times includes estimating the crosstalk between adjacent computational sections in the array and selecting the respective spectra and pulse times to compensate for the estimated crosstalk. In one embodiment of the disclosure, selecting the respective spectra and pulse times includes defining a desired level of crosstalk and selecting the spectra and pulse times to reduce the estimated crosstalk to below a desired level while maximizing the desired computational performance of each section.

[0016] Depending on the embodiment, the arrangement of ions within the ion trap has an inter-ion characteristic frequency ν, and optically confining barrier ions has an optical trap frequency ω otp 1.5ν, or possibly ω otp This includes irradiating the barrier ions with light radiation at an intensity sufficient to optically trap the barrier ions at >1 / 8ν. In one embodiment of the disclosure,

number

[0017] In another embodiment, the arrangement of ions in the ion trap has an inter-ion characteristic frequency ν, and the barrier ions are optically confined by each optical trap frequency ω such that the sum of their respective optical trap frequencies is greater than 2ν. opt This involves irradiating groups of barrier ions between adjacent computational regions with light radiation at an intensity sufficient to optically confine the barrier ions.

[0018] In some embodiments, optically confining barrier ions reduces the heating rate of ions within the array. Typically, the heating rate is determined not by the number of ions in the array, but primarily by the size of each computational segment.

[0019] In some embodiments, applying an excitation field includes exciting the motion modes of an array of ions having their respective motion frequencies, and optically confining barrier ions groups the motion frequencies into bands having their respective center frequencies and bandwidths such that the bandwidth of each band is less than the difference between the center frequencies of adjacent bands. In embodiments of the disclosure, optically confining barrier ions reduces the bandwidth to less than 20% of the difference between the intermediate frequencies of adjacent bands. In other embodiments, optically confining barrier ions reduces the bandwidth to less than 10% of the difference between the intermediate frequencies of adjacent bands, or even less than 5% of the difference between the intermediate frequencies of adjacent bands. In embodiments of the disclosure, applying an excitation field includes performing a multi-qubit gate operation in at least part of the computation interval.

[0020] In some embodiments, at least a portion of the computational divisions obtained by partitioning the sequence each contains at least 10 ions from the ions, or further, at least 20 ions from the ions.

[0021] In addition to or instead of the above, applying an excitation field includes performing at least a portion of quantum operations across a gate containing at least four or more ions, or across a gate containing twelve or more ions.

[0022] In some embodiments, reconfiguring the array into a second computational division while maintaining at least some coherence includes entangling the ions in the second computational division with the ions in the first computational division. In one embodiment of the disclosure, the array contains n ions, and entangling the ions in the second computational division includes controllingly entangling at least 70% of the ions in the computational divisions within the array over a number of reconfiguration steps s such that s < 0.2 * n.

[0023] Depending on the embodiment, the reconfiguration of the sequence into a second computational segment is completed in a duration of less than 10 milliseconds, or in some cases less than 1 millisecond, or less than 100 microseconds, or less than 10 microseconds, or even less than 1 microsecond.

[0024] In one embodiment, defining a quantum computation includes applying a quantum error correction code over a sequence of computing steps. In another embodiment, defining a quantum computation includes performing a quantum simulation over a sequence of computing steps.

[0025] According to one embodiment of the present invention, a method of quantum computing is also provided, which includes trapping an array of ions in an ion trap and dividing the array into computational compartments, each containing a group of neighboring ions separated by barrier ions between the groups, by optically confining barrier ions. A quantum computation is defined, comprising a plurality of quantum operations performed in parallel across the computational compartments. The quantum operations define a target quantum entanglement phase between ions in each compartment. Crosstalk between neighboring computational compartments in the array is estimated. The spectra of each excitation field are computed to drive the ions to the target quantum entanglement phase while compensating for the estimated crosstalk. The excitation fields, each having a different spectrum, are applied to the ions in the computational compartment to perform the quantum computation.

[0026] In some embodiments, compensating for estimated crosstalk reduces the fidelity of the quantum operation to less than 0.1, or in some cases less than 0.01, less than 0.001, or even less than 0.0001.

[0027] In some embodiments, partitioning the array generates motion modes within a computational segment, each having a vibration frequency grouped within a frequency band by a minimum interval Δf between frequency bands, and applying an excitation field drives the ions to the target quantum entanglement phase within a time of less than 50 / Δf.

[0028] In embodiments of the disclosure, optically confining barrier ions reduces crosstalk between adjacent computational segments within the array so as to result in residual crosstalk, and compensating for estimated crosstalk compensates for residual crosstalk.

[0029] In some embodiments, applying an excitation field involves directing a beam of coherent light emission to excite transitions of ions within a computational region. In one embodiment of the disclosure, computing each spectrum involves determining an initial spectrum and pulse time that will result in a zero-entanglement phase between ions, and applying an optimization process starting from the initial spectrum and pulse time to determine a target vector of complex amplitude that will result in a target-entanglement phase. Typically, applying the optimization process involves reducing estimated crosstalk as part of the optimization process, thereby increasing the fidelity of the quantum computation.

[0030] According to one embodiment of the present invention, a quantum computing method is further provided which includes trapping an array of ions in an ion trap configured such that the array of ions has an inter-ion characteristic frequency ν. otp>1.5 optically confines the barrier ions with sufficient intensity to optically trap them, thereby dividing the data into computational units containing each group of neighboring ions separated by the barrier ions between groups. A quantum computation is defined that includes multiple quantum operations performed in parallel across the computational units. An excitation field is applied to the ions within the computational units so that the groups of neighboring ions perform the quantum operations.

[0031] Depending on the embodiment, applying an excitation field may result in the fundamental trap frequency ω of the ion trap. trap This involves exciting the motion modes of the ion array by an oscillation frequency centered on ω. In one embodiment of the disclosure, barrier ions are optically confined such that the sum of their respective trap frequencies is ω trap Each optical trap frequency ω that becomes larger opt This involves irradiating a group of barrier ions between adjacent computational regions with light radiation at an intensity sufficient to optically trap the barrier ions.

[0032] According to one embodiment of the present invention, a system for quantum computing is further provided, comprising an ion trap configured to hold an array of ions at their respective positions along the array axis. A radiation source is configured to apply an optical field to partition the array into a plurality of computational partitions, each comprising a group of neighboring ions separated by barrier ions between groups by optically confining barrier ions, and is further configured to apply an excitation field to the ions in the computational partitions to cause the groups of neighboring ions in the computational partitions to perform quantum operations. A controller is configured to receive a definition of a quantum computation, comprising a sequence of computing steps comprising a plurality of quantum operations, each step of which is performed in parallel.

[0033] The controller is configured to control the radiation source to partition the array into a first computational section by optically confining a first barrier ion, and to apply an excitation field to the ions in the first computational section so that the group of neighboring ions in the first computational section can perform the quantum computation in the first step of the sequence. After the completion of the quantum computation in the first step, the array is reconfigured into a second computational section by optically confining a second barrier ion, which is at least partially different from the first barrier ion, while maintaining at least some coherence from the first to the second computational section. An excitation field is applied to the ions in the second computational section so that the group of neighboring ions in the second computational section can perform the quantum computation in the second step of the sequence using at least some of the maintained coherence. The controller is configured to repeat the steps of reconfiguring the array into further computational sections and applying an excitation field to further computational sections in order to complete the quantum computation.

[0034] According to one embodiment of the present invention, a system for quantum computing is further provided, comprising an ion trap configured to hold an array of ions at their respective positions along the array axis. A radiation source is configured to apply an optical field to divide the array into a plurality of computational segments, each containing a group of neighboring ions separated by barrier ions between groups by optically confining barrier ions, and is further configured to apply an excitation field to the ions within the computational segments so that the groups of neighboring ions within the computational segments perform quantum operations. A controller is configured to receive a definition of a quantum computation comprising a plurality of quantum operations performed in parallel across the computational segments. The quantum computation defines a target quantum entanglement phase between ions within each segment, the definition including the respective spectra of the excitation fields for driving the ions to the target quantum entanglement phase while compensating for estimated crosstalk between neighboring computational segments in the array. The controller is configured to drive the radiation source to apply excitation fields having their respective spectra to the ions within the computational segments to perform the quantum operations.

[0035] According to one embodiment of the present invention, a system for quantum computing is further provided, comprising an ion trap configured to hold an ion arrangement such that the ion arrangement has an inter-ion characteristic frequency ν. The radiation source has an optical trap frequency ω otp The system is configured to apply an optical field to partition the array into multiple computational units, each containing a group of neighboring ions separated by barrier ions between groups, by optically confining the barrier ions with an intensity sufficient to optically trap them at >1.5ν, and further configured to apply an excitation field to the ions within the computational units so that the groups of neighboring ions in the computational units perform quantum operations. The controller is configured to receive a definition of a quantum computation involving multiple quantum operations performed in parallel across the computational units, and to drive a radiation source to apply an excitation field to the ions within the computational units so that the groups of neighboring ions perform quantum operations. As a final computing step, state detection can be performed.

[0036] The present invention will be better understood by reading the following detailed description of embodiments of the invention together with the drawings. [Brief explanation of the drawing]

[0037] [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 schematic block diagram showing the arrangement of trap ions configured as qubits in a quantum computer according to one embodiment of the present invention. [Figure 3] This is a schematic side view showing a multi-beam optical confinement and excitation subsystem used in a quantum computing system according to one embodiment of the present invention. [Figure 4] This is a schematic detail diagram showing a multibeam generation and modulation module according to one embodiment of the present invention. [Figure 5]This is a schematic block diagram illustrating the sequence of quantum computing steps performed using a trap ion array according to one embodiment of the present invention. [Figure 6A] This flowchart schematically illustrates a method for mid-circuit measurement within a sequence of quantum computing steps according to one embodiment of the present invention. [Figure 6B] Figure 6A is a schematic atomic-level (not to exact scale) diagram showing the details of the energy levels used in the mid-circuit measurement. [Figure 7] This plot schematically shows the change in the axial mode frequency of the trap ion array as a function of the optical trap potential applied in array partitioning according to one embodiment of the present invention. [Figure 8] This is a plot schematically showing the radial mode frequencies in a partitioned arrangement of trap ions according to one embodiment of the present invention. [Figure 9] This flowchart schematically illustrates a method for selecting parameters to drive a multi-qubit gate in a partitioned array of trap ions according to one embodiment of the present invention. [Figure 10] This plot schematically shows the fidelity of the partitioned arrangement of trap ions, with and without compensation for residual crosstalk, as a function of the optical trap potential applied in the partitioning of the arrangement, according to one embodiment of the present invention. [Figure 11A] This is a schematic front view showing a compartmentalized two-dimensional arrangement of trap ions according to one embodiment of the present invention. [Figure 11B] This is a schematic front view showing a compartmentalized two-dimensional arrangement of trap ions according to one embodiment of the present invention. [Figure 11C] This is a schematic front view showing a compartmentalized two-dimensional arrangement of trap ions according to one embodiment of the present invention. [Figure 11D] This is a schematic front view showing a compartmentalized three-dimensional arrangement of trap ions according to one embodiment of the present invention. [Modes for carrying out the invention]

[0038] overview Trapped ions possess ideal properties for use as qubits in quantum computing. Specifically, they feature long coherence times, efficient state preparation and detection techniques, and high connectivity. For example, an array of equally spaced ions (also called an "ionic crystal") in a linear RF pole trap can be used to form a quantum register consisting of thousands of qubits.

[0039] However, there are practical problems associated with large ionic crystals that have hindered progress in this direction. One problem is that as the number of ions N in the crystal increases, the heating of the ion motion modes due to electric field noise increases. The resulting heating rate can degrade the fidelity of qubit operations and destabilize the ionic crystal. Another problem with large ionic crystals is spectral density. That is, as the crystal size increases, the frequency difference between adjacent motion modes decreases. In the case of large ionic crystals with high-density mode spectra, it becomes increasingly difficult to handle individual modes and therefore achieve desired qubit coupling with high fidelity. Furthermore, there is strong evidence that the minimum feasible gate time is limited by the minimum frequency spacing between motion modes, and this spacing shrinks as N increases as described above, making quantum computation extremely slow in large ionic crystals.

[0040] In response to these challenges, embodiments of the present invention described herein provide a scalable architecture for quantum computing based on trapped ion qubits that maintains the advantages of long ionic crystals while avoiding the problems described above. In embodiments of the present disclosure, an ionic crystal of arbitrary length is partitioned into computational segments by the dynamic application of an optical potential. These embodiments use a high-intensity light beam to confine the movement of selected barrier ions between computational segments. (For example, a “optical tweezers” can be applied to confine the barrier ions by using a laser beam tuned to apply an optical attraction or repulsion to the barrier ions.) In this way, the motion mode structure of the ionic crystal is modified such that the heating rate reflects only the segment size and not N. Using this technique, programmable, high-fidelity multi-qubit entanglement gates can be independently implemented simultaneously within all segments.

[0041] This dynamic optical partitioning method also facilitates multi-step quantum computations, where the selection of barrier ions and computational partitions can change step by step. Switching between array partitioning configurations is performed while maintaining the coherence already accumulated within each partition, and is fast enough to maintain the coherence of at least some of the qubit states, allowing for handover from partition to partition in consecutive computing steps. The configuration itself does not introduce any additional incoherence.

[0042] In some embodiments, mid-circuit measurements are incorporated into the reconstruction of computational segments between steps. These mid-circuit measurements can be used, for example, to support quantum error correction (QEC) techniques. In addition to or instead of this, the multi-step computational schemes described herein can be applied in quantum simulations together with the reconstruction of computational segments.

[0043] The embodiments described below primarily relate to linear arrangements of trapped ions, i.e., one-dimensional ionic crystals, but the principles of the present invention can also be applied to two-dimensional and three-dimensional trapped ion arrangements with necessary modifications. Furthermore, this method for quantum computing using partitioned ionic crystals can also be incorporated into other multi-trap techniques known in the art for expanding quantum computing, such as photonic interconnections between ion chains, quantum charge-coupled device architectures (including various ion shuttle schemes), and two-dimensional arrangements of traps using dipole interactions for quantum entanglement. All such alternative configurations and embodiments are considered to fall within the scope of the present invention.

[0044] Embodiments of the present invention, described below, provide a method of quantum computing using an arrangement of ions in an ion trap. A quantum computation is defined that includes a sequence of computing steps, each step comprising multiple quantum operations performed in parallel. In each step, the arrangement is divided into computational sections, each containing a group of neighboring ions, by optically confining barrier ions between groups. An excitation field is applied to the ions in the computational section so that the group of ions in the computational section performs the quantum operation in the current step of the sequence.

[0045] After the completion of the quantum operation in each such step, the sequence is reconfigured into different computational divisions for the next step by optically confining a new set of barrier ions, which may be at least partially different from the barrier ions in the previous step. The new computational divisions defined by the new barrier ions retain at least some of the coherence from the previous computational divisions. An excitation field is applied to the ions in the new computational divisions so that they perform the quantum operation in the next step of the sequence using at least some of the coherence maintained in the group of ions in these computational divisions.

[0046] These steps of reconstructing the array into a new computational segment and applying an excitation field to the ions within the new computational segment are repeated until the quantum calculation is completed. Typically, upon completion of the quantum calculation, the state of each of at least some of the ions is measured to read out the result of the quantum calculation.

[0047] To achieve high computational fidelity, in this type of segmented calculation method, it is important that the barrier ions are strongly trapped such that the crosstalk between adjacent segments due to the vibrations transmitted through the barrier ions is reduced to an acceptable level and the vibrational modes within each segment are sufficiently separated. Typically, the array of trapped ions will have a fundamental inter-ion interaction frequency ν that is determined by the properties of the selected ion species and the distance between the ions. For example, this frequency can be expressed as

Equation

[0048] Therefore, in some embodiments, to achieve a clear separation of vibrational modes and low residual crosstalk, the parameters of the ion trap and the optical confinement beam are selected such that ω otp > 1.5ν. Desirably, the light intensity is even greater, for example ω otp > 1.8ν or more, and ω otp = 2ν is optimal. Optically confining the barrier ions in this way also reduces the rate of heating of the ions in the array such that the rate of heating is determined primarily by the size of each computational segment rather than by the total number of ions in the array.

[0049] Strong optical confinement of barrier ions sufficiently reduces crosstalk between adjacent computational units, such that residual crosstalk is typically less than a few percent. However, this residual crosstalk may still be too high to achieve the desired fidelity in quantum computations performed on ion arrays. In some embodiments of the present invention, to compensate for this residual crosstalk, the excitation field spectrum and, optionally, the pulse time are adjusted to compensate for the effects of residual crosstalk. (The term "spectrum" is used herein and in the claims to mean the frequency, magnitude, and phase of the excitation field applied to ions in a computational unit. Generally, each ion can be excited by its own respective spectrum, which may differ from the spectrum used to excite other ions.)

[0050] To achieve these desirable spectral qualities, some embodiments provide a method for selecting spectra to be used in performing multi-partition quantum computation, i.e., computations in which multiple quantum operations are performed in parallel across computational divisions of an array of trapped ions separated by barrier ions. Each quantum operation defines a target quantum entanglement phase between ions within each division. Crosstalk between adjacent computational divisions in the array is estimated, and the spectra of the excitation fields used to drive the ions into the target quantum entanglement phase in each division are calculated, while compensating for the estimated crosstalk. These excitation fields, each with its respective spectrum, are applied to the ions in the computational division to perform the quantum operations.

[0051] Estimated crosstalk compensation typically reduces the non-fidelity of the quantum operation to less than 0.1. Depending on the embodiment, an optimization process is applied when selecting the excitation field spectrum to mitigate residual crosstalk. With proper optimization of the spectrum over a sufficient number of computing steps, the non-fidelity can be reduced to less than 0.01, or even less than 0.001, and potentially less than 0.0001 with sufficient compensation efforts and careful control of excitation parameters.

[0052] In some embodiments, the spectrum applied to an ion is calculated by determining an initial non-trivial spectrum and pulse time that will produce a zero-entanglement phase between the ions. Next, an optimization process is applied, starting from the initial spectrum, to determine a target set of spectral components and amplitudes and phases that will produce the desired target-entanglement phase. This optimization process includes mitigating estimated crosstalk as part of the process, thereby increasing the fidelity of the quantum computation.

[0053] System Description Figure 1 is a schematic block diagram showing a quantum computing system 20 according to one embodiment of the present invention. System 20 is presented as a non-limiting example of an application environment in which an array of excitation and confinement beams can be used. The embodiments described below relate to a linear array of trapped ions, but the principle of this embodiment can be similarly applied to two-dimensional and three-dimensional arrays with necessary modifications.

[0054] In this exemplary embodiment, an atomic source 22 injects a stream of natural atoms, such as calcium atoms, into a vacuum chamber 26 with an ultra-high vacuum. A radiation source 28 directs multiple beams of radiation into the vacuum chamber 26, including a beam tuned to ionize the atoms injected by the atomic source 22. (In this embodiment, the system 20 is assumed to be based on electronic transitions as described above, and the radiation source 28 is assumed to include a laser emitting a beam of coherent radiation; however, ionization detection and tweezers beam may be performed instead using, for example, an incoherent 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 predetermined axis within the vacuum chamber 26, under the control of a trap controller 25. An electric field is also applied to the ion trap 24 to separate the spin components of the ions' electronic states into Zeeman levels.

[0055] To perform a quantum computation and then read out the computation result, the electronic qubit control and computation processor 32 drives the radiation source 28 to tune and direct an additional beam towards the trapped ions. Typically, the result is read out by tuning the laser beam to an absorption line with one of the qubit states and then measuring the resulting fluorescence emission using the optical detector 30. Each step in this embodiment may involve using a single gate or multiple gates in parallel, defined by appropriate program code, to redefine a group of ions that constitute a register on which the gates act in each step. Alternatively, a sequence of operations on a group of ions may be defined and applied to perform a quantum simulation.

[0056] Figure 2 is a schematic block diagram showing 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 radiation source 28 (Figure 1) supplies several different laser beam inputs to ion traps 24 for different purposes. An ionization laser 42 ionizes atoms output by the atomic source 22 to form ions 40 that are held by the traps. An additional cooling laser 44 cools the ions to their electronic and kinematic ground states by pumping the ions through appropriate state transitions, while detuning the laser frequency to produce mechanisms of Doppler cooling, sideband cooling, polarization gradient cooling, electromagnetically induced clearing (EIT) and / or other cooling methods known in the art.

[0057] The cooled ions 40 are held in a linear arrangement along axis 38 by an electromagnetic field within the trap 24. The Coulomb repulsion between the ions 40 and the trap field applied by the trap 24 determine the equilibrium distance between the ions and the phonon frequency {ν} of the normal mode of vibration of the motion of the ions 40 in the arrangement, which includes both the transverse and longitudinal modes of vibration. nThis determines the normal vibrational modes. These normal vibrational modes give rise to vibrational sidebands of the optical transition frequencies between the states of ion 40 used in quantum computation.

[0058] To define and operate multi-qubit gates (containing two, three, or more qubits) and single-qubit gates, the radiation source 28 (Figure 1) includes an excitation source 46 containing one or more lasers that direct beams of radiation of multiple different frequencies to strike ions 40 from various spatial directions. All beams may be generated by the same laser with appropriate amplitude, frequency, and phase modulation, or by multiple different lasers. Among these beams are a Raman beam 48 and a tweezers beam 50. The tweezers beam 50 is tuned to confine selected ions 40, referred to herein as barrier ions, using a high-intensity optical field. Thus, the application of the tweezers beam defines a computational partition, also called a multi-qubit register, between the confined ions. The wavelength of the tweezers beam 50 can be selected and tuned to confine the barrier ions by applying an optical attraction or repulsion to them. The Raman beam 48, also known as the excitation beam, is tuned to coherently excite and manipulate the internal and kinetic transitions of ions 40 within these multi-qubit registers to drive gate operations to perform quantum computations.

[0059] Finally, the readout beam 52 is tuned to excite an internal transition of ion 40 to read out the gate state. The readout beam 52 causes ion 40 to emit fluorescence of an intensity dependent on the state of the corresponding qubit. This resulting fluorescence emission is measured using the optical detector 30, and the calculation results are received by the qubit control and computation processor 32 (Figure 1). As part of this scheme, an operation sequence of optical pulses may also be used to optically shift, shelv, and store the data qubit and protect it from errors caused by photon scattering during the measurement sequence. These features will be described later with reference to Figures 5 and 6A / 6B.

[0060] In embodiments of the present invention, various coherent manipulation techniques can be used to manipulate multiple qubit gates, such as quadrupole optical transitions used for optical qubits, or Raman transitions used for hyperfine or Zeeman qubits. In addition to or instead of the above, other methods for encoding quanta and manipulating quantum information may be used, such as dimensional generalizations of qubits and metastable qubits (called qudits). In this embodiment, the Raman beam 48 is excited to each group of ions 40 at an excitation frequency ω0±ω centered on a selected internal instantaneous transition frequency ω0 of the ion. m A set of (or any other suitable type of transition and excitation spectra known in the art) is coherently irradiated. (Alternatively, any other suitable type of transition and excitation spectra known in the art may be used.) Beam 48 has multiple sidebands ω of the internal transition frequency ω0 m To coherently include the frequency components in the beam, it is modulated by, for example, a suitable multi-channel acousto-optic modulator (mcAOM), as described later. Alternatively, other forms of modulation such as an electro-optic modulator (EOM) or a Mach-Zehnder modulator (MZM) may be used. For example, beam 48, output by a laser operating at approximately 400 nm, contains calcium ions. 1 / 2 The Zeeman splitting transition sideband frequency is modulated by the mcAOM to drive the ion in the Raman transition. The internal qubit transition frequency ω0 is determined by the externally applied magnetic field B.

[0061] The Raman beam 48 individually irradiates at least a portion of the ions 40 with selected frequency components in a locally optimal spectrum over gate time T to drive each of the multiple qubit gates from the initial state of its qubit to the target state, and thereby complete the quantum computation at each step. In one embodiment of the present invention, individual modulation of the Raman beam 48 allows each ion 40 to be driven with its own spectrum, which is typically different from the spectrum applied to other ions. In other embodiments, a global Raman beam or a semi-global Raman beam may also be used (within each section), or similar spectra may be utilized for each section to manipulate the required quantum entanglement gate within each register section, or the global beam may be used in local operations by individually manipulated optical shifts.

[0062] After the computation cycle is complete, the readout beam 52 can be directed towards the ions 40 to read out the state of the computational segment, i.e., the state of the multi-qubit register defined by the tweezers beam 50. The readout beam 52 is tuned to the absorption line of one of the ion states in the register. As described above, the absorption of laser radiation by the ion in the appropriate state produces fluorescence, which is measured by the optical detector 30 (Figure 1). The detector 30 measures the intensity of the fluorescence emission, thereby detecting the final state of the qubits, and therefore the final state of the operation. Alternatively, other detection methods known in the art may be used to read out the state of the gate.

[0063] The processor 32 typically includes a general-purpose computer having appropriate interfaces to 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 a tangible, non-temporary computer-readable medium, such as an optical, magnetic, or electronic storage medium.

[0064] Figure 3 is a schematic side view of a multi-beam optical trap and excitation subsystem 71 used in system 20 (Figure 1) according to one embodiment of the present invention. The subsystem 71 forms beams 48 and 50 (Figure 2), and optionally beam 52, which propagate from the excitation source 46 to the ion trap 24. Further details of subsystem 71 are described in U.S. Provisional Patent Application No. 63 / 595,349 above.

[0065] The optical subsystem 71 includes a splitter 72 that splits the coherent radiation output by one or more lasers in the excitation source 46 into multiple beams. The splitter 72 may include, for example, a diffractive optical element (DOE), a spatial light modulator (SLM), or a multi-channel deflector such as an acousto-optic deflector (AOD) or a micromirror array, or multiple single-channel deflectors. The splitter 72 drives the coherent radiation into multiple beams of different frequencies, angles, amplitudes, and phases. Depending on the type of splitter, the beams may have equal (or nearly equal) intensity, or the beams may have substantially different intensity depending on whether they function as a Raman beam or a tweezers beam during a given time interval.

[0066] Following the splitter 72, the lens 74 directs the beam array to a multi-channel acousto-optic modulator (mcAOM) 76, which modulates the amplitude, frequency, and phase of each beam. Specifically, the mcAOM 76 applies different frequencies and phases to the different beams so as to drive the Raman transitions of each ion into which the beams are incident. The lens 74 can be advantageously configured as a Fourier transform lens, with the splitter 72 at its front focal plane and the mcAOM 76 at its rear focal plane. Thus, the lens 74 forms a spatial Fourier transform of the beams, where the deflection angle of each beam output by the splitter 72 is converted to its lateral position on the mcAOM 76 in an array of equally or unequally spaced collimated beams.

[0067] In the embodiment shown in Figure 3, the same laser in the excitation source 46 generates both the Raman beam and the tweezers beam, and the mcAOM 76 modulates the amplitudes of both the Raman beam and the tweezers beam. Alternatively, in other embodiments, different lasers may be used to generate the Raman beam and the tweezers beam. If the splitter 72 includes a DOE or a multi-channel polarizer, all beams split by the splitter may have sufficient intensity to function as tweezers beams. In this case, the mcAOM 76 is controlled to apply a substantial attenuation to the high-intensity beam from the splitter 72 that will function as a Raman beam, to one-tenth or even one-hundredth or less. Alternatively, if the splitter 72 includes a multi-channel acousto-optic deflector (AOD), the controller 32 (Figure 1) may generate drive signals to adjust the intensity of each of the individual beams output by the AOD. This technique allows for rapid switching between different configurations of tweezers beams and Raman beams. In other embodiments in which the splitter 72 includes an SLM, the SLM may be driven to modulate the beam intensity such that the beam intended to function as a tweezers beam has a higher intensity than the beam intended to function as a Raman beam in each computational cycle.

[0068] In some embodiments, the splitter 72 includes a high-speed actuator, such as a rotating mirror or AOD, which rapidly switches the tweezers beam 50 between computing steps performed by the array 40. This rapid switching allows the computational divisions of the array 40 to be rapidly reconfigured step by step for efficient execution of sequences of quantum operations with high fidelity. In this case, the reconfiguration of the computational divisions can be completed in less than 10 milliseconds. With proper system design, the reconfiguration time can be reduced to less than 1 millisecond, or less than 100 microseconds, or less than 10 microseconds, or in some cases even less than 1 microsecond.

[0069] Following the AOM76, the telescope 78 directs the modulated beam towards the ion trap 24. The telescope 78 also allows for adjustment of the beam spacing to precisely match the spacing between ions 40 in the trap. In addition to, or instead of, a drive signal applied to the mcAOM76 or AOD may be adjusted to compensate for deviations in the position, shape, and focus of the beam 62 on each ion 40. Following the telescope 78, the beam passes, for example, through a dichroic beam splitter 80 and is then focused into the ion trap 24 by the objective optical system 82. The objective optical system 82 reduces the spot size of the beam 62 incident on the ions 40 to near the diffraction limit, i.e., less than about 1 μm, and reduces the spacing between beams to the separation distance between ions 40 along axis 38, typically a few μm.

[0070] To read out the intermediate and final states of register 68, an excitation source 46 and a tunable readout beam 52 are directed to the qubit of interest in the register. Alternatively, the readout beam may be introduced through a different optical channel. Absorption of photons in the readout beam causes ions 40 to emit fluorescence radiation representing each state of the quantum gate. The objective optical system 82 collects the fluorescence radiation emitted by ions 40 in the ion trap 24 and directs the emitted radiation to a dichroic beam splitter 80, which reflects the emitted radiation to a detector array 84. The detector array 84 measures the resulting fluorescence emission intensity and reads the results to the controller 32.

[0071] Figure 4 is a schematic detail diagram of a multi-beam generation and modulation module 87 in an optical subsystem 71 according to one embodiment of the present invention. An excitation source 46 outputs a source beam 88, which is then split into multiple input beams 90 by a splitter 72. A Fourier transform lens 74 directs the beams 90 into an acousto-optic crystal 86 in an mcAOM 76. As the input beams 90 pass through the acousto-optic crystal 86, they are diffracted by sound waves within the crystal, resulting in a change in the direction of the diffracted beams. These diffracted beams form an array of output beams 92. This diffraction process modulates the output beams 92 so that each beam has its own intensity, frequency, and phase.

[0072] Computational architecture including mid-circuit measurements Figure 5 is a schematic block diagram showing a sequence of quantum computing steps 102, 104, 106, 108, ... performed using an array 100 of trapped ions 40 according to one embodiment of the present invention. The state of the array 100 is indicated by the corresponding rows of ions 40 before and after each step. The illustrated embodiment shows a portion of the array 100 containing about 50 ions, but the principle of this embodiment can be extended in a simple manner to many more arrays.

[0073] The array 100 is divided into computational sections 110 by dynamically applying an optical trapping potential to the barrier ions 112. In the illustrated embodiment, the computational sections are separated by pairs of adjacent barrier ions 112. Alternatively, the sections may be separated by a single barrier ion or by three or more barrier ions. In this embodiment, each section 100 contains 10 ions 40. Alternatively, the computational sections may contain more than 10 ions, or even more than 20 ions. Also, although all computational sections 110 are shown to be of equal size in Figure 5, in another embodiment the size of the sections may vary depending on the computational requirements and may vary from one computing step to the next.

[0074] The Raman beam 48 (Figure 2) applies an excitation field to the ions 40 in each computation section 110 so that each quantum operation 114 is performed in parallel in each successive computing step 102, 104, 106, 108, ... The quantum operation 114 typically includes multi-qubit gate operations and single-qubit gate operations in some or all of the section 110. For example, a multi-qubit gate may include four or more ions 40. In another embodiment having a larger computation section (not shown), a multi-qubit gate may include even more ions, for example, a gate may include 12 or more ions.

[0075] Following each computing step 102, 104, 106, ..., a section 110 within array 100 is reconfigured by selecting a different set of barrier ions 112. (In the illustrated embodiment, each step also includes a mid-circuit measurement, as described later, although the mid-circuit measurement may be omitted as an alternative.) For reconfiguration, the tweezers beam 50 (Figure 2) is switched to a new barrier ion 112 to be used in the next computing step, and then the barrier ions 112 that were confined in the previous computing step are switched off. In the illustrated embodiment, array 100 is thus alternately switched between two configurations labeled "A" and "B". In configuration A, the computing section is subjected to quantum computing.

number

number

number

[0076] Alternatively, other partitioning schemes can be used that, without the regular alternation shown in Figure 5, may include partitions of different sizes and / or confine some or all of the same barrier ions across two or more consecutive computing steps. The system configurations shown in Figures 1 to 4 and described above allow for the implementation of substantially any desired computing configuration of barrier ions and computing partitions within array 100, and enable the dynamic and rapid modification of the configuration for each computing step.

[0077] The coherence time of the ions 40 involved in each computing step is long enough so that at least some coherence is maintained from the computing section 110 of configuration A to the new computing section 110 of configuration B, and similarly from configuration B to configuration A in subsequent steps. Thus, the quantum operations in each subsequent computing step of the sequence use a portion of this maintained coherence. In this way, in each computing step 104, 106, 108, ..., the ions in the new computing section can become quantum entangled with some or all of the ions from the previous computing section. The number of computing steps s required to quantum entangle all (or at least a substantial proportion) of the ions in the array 100 in this way depends on the size of the computing sections 110 and the degree of overlap between steps. Typically, s is substantially less than the number of ions N. For example, in the configuration shown in Figure 5 without mid-circuit measurements, the number of steps s required to quantum entangle at least 70% of the ions 40 in the computing section 110 is less than 0.2*N.

[0078] The computational configuration shown in Figure 5 also facilitates mid-circuit measurements 116, such as between consecutive computing steps 102 and 104, and then between steps 104 and 106. The results of the mid-circuit measurements 116 are used in subsequent computing steps to provide classical feedback used to define quantum operations 114, for example, for quantum error correction. In the illustrated embodiment, the mid-circuit measurements 116 are applied to an intermediate ion 118, which is then optically confined to function as a barrier ion 112 in the next computing step. The process of performing these mid-circuit measurements, then reading out the intermediate ion 118, and then cooling to reconstruct the array 100 into a new computational section 110 can typically be completed within a duration of less than 20 milliseconds, and in some cases less than 10 milliseconds.

[0079] Next, we refer to Figures 6A and 6B, which schematically illustrate a method for mid-circuit measurement within a sequence of quantum computing steps according to one embodiment of the present invention. This method is applicable to array 100 when performing mid-circuit measurement 116 as described above. Figure 6A is a flowchart showing the steps of the measurement process, and Figure 6B is used in the mid-circuit measurement of Figure 6A. 40 Ca + This is an atomic-level diagram schematically showing the details of the energy levels of an ion. These specific energy levels are shown here as examples, and the principle of the method in Figure 6A is similarly applicable with other suitable ions and other sets of energy levels.

[0080] The method in Figure 6A uses three types of ions taken from Figure 5: a computation ion 40 (labeled C), an intermediate ion 118 (labeled B), and a current barrier ion 112 (labeled A). For example, as a result of the previous quantum operation 114 in step 102, data is encoded on computation ion C and intermediate ion B. In the shelving step 120, one of the qubit states of ion B is "shelved" to a non-fluorescent state using local control. Next, an intermediate optical partitioning configuration is applied by applying an optical confinement field to both ion A and ion B, thereby separating their motion from computation qubit 40. In step detection 122, the state of the barrier ion is measured and then reset in preparation step 124. Finally, in preparation for the next computing step 104, the optical partitioning configuration is switched so that ion B becomes the barrier ion and ion A is released to function as the intermediate or computation ion.

[0081] Figure 6B shows 4S 1 / 2 Ground state manifold 130 and metastable 4D 5 / 2 Manifold 132 and short-lived 4P 1 / 2 Includes manifold 134 40 Ca + The relevant atomic level (not to exact scale) is shown for performing the method in Figure 6A using the arrangement of ions. Manifolds 130 and 134 on the left side of Figure 6B represent the interaction between S and P states without optical confinement (as used in the computational operation), while manifolds 130' and 134' represent the states of optically confined barrier ions. The shelving field 136 at 729 nm couples the S and D levels, while the Raman field 138 at 400 nm couples the Raman transition and 4P 1 / 2 S via off-resonant coupling to manifold 134 1 / 2 This induces an optical shift between qubit states in manifold 130. An additional field 140 at 397 nm is used for cooling, state preparation, and detection.

[0082] The Raman field 138 is used for local control that acts independently on all computational ions 40 to produce single-qubit rotations and multi-qubit programmable gates. However, the Raman field 138 is also used to localize a global control field using optical shifts. Specifically, the shelving step 120 can be performed by applying fields 136 and 138 together, thereby shelving one of the qubit states of ion 118 (ion B in Figure 6A) into manifold 132.

[0083] After shelving ion 118, the partitioned configuration of array 100 is changed to an intermediate setting in which all barrier ions 112 and 118 are illuminated. The purpose of optically confining the ions is to prepare them for measurement by separating the motion of the ions from the motion of the computational qubits and to optically shift their SⁿⁿP transitions. State detection in step 122 is performed using the optically shifted field 140 at a 397 nm field, and then in step 124, the qubits are reset and prepared to cool the ions using combinations of field 140 and field 138 at 397 nm and 400 nm, respectively.

[0084] After preparation step 124, the partitioned configuration of array 100 is changed, and the roles of computational ions and barrier ions are swapped. The cooled ions then cool the bulk vibrational modes of the array by co-cooling.

[0085] Optical trapping requirements As mentioned above, the partitioning of the ion array 100 (Figure 5) maintains the stability of the ionic crystal and allows programmable multi-qubit quantum gates to operate simultaneously and independently within different computational partitions. The confinement of barrier ions 112 irradiated by the tweezers beam 50 (Figure 2) can be represented using an optical trap potential that induces the following optical trap frequency.

[0086]

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[0087] The effect of the optical trap potential can be compared to the fundamental trap frequency of ion trap 24, which is the interion characteristic frequency associated with the Coulomb interaction between adjacent ions, as follows.

[0088]

number

[0089] Figure 7 is a plot schematically showing the changes in the axial mode frequency bands 150, 152, 154, ... of the trapped ion array as a function of the optical trapping potential applied to the partitioning of the array, according to one embodiment of the present invention. The lowest frequency band 150 corresponds to the center of mass band. The relative intensity of the optical trapping potential is given by the ratio ω otp It is expressed using / ν. The frequencies in this figure are calculated for an arrangement of N=231 ions, which are divided into six computational sections, each consisting of 35 ions, separated by three barrier ions between adjacent sections.

[0090] As shown in this figure, in the case of a weak optical trap field, the computational segments are vibrationally coupled to each other, thereby giving rise to a diffuse band structure. ω otpAs / ν increases beyond approximately 1.5, the structure of frequency bands 150, 152, 154, ... becomes clear, allowing us to handle different vibrational modes in different computational units. Above this level of optical trapping potential, the optical confinement of barrier ions groups the ion motion frequencies into bands 150, 152, 154, ... such that the bandwidth of each band is less than the difference in the center frequencies of adjacent bands.

[0091] ω otp When / ν > 1.8, the bandwidths of bands 150, 152, 154, ... are less than 20% of the difference in center frequencies, and as the optical trapping potential increases, the bandwidths shrink to 10% of the difference in center frequencies, and even to less than 5%. otp When = 2ν, the narrow-band structure approaches that of an independent arrangement of 35 ions, i.e., the motion modes in different computational partitions are separated from each other (although a small amount of crosstalk remains, as will be further explained below). This separation of motion modes makes it possible to perform the parallel multiple quantum gate operations of the type described above using these separated motion modes. The separation of computational partitions is enhanced when adjacent computational partitions are separated by groups of two or more barrier ions. In this case, each optical trap frequency ω such that the sum of their respective trap frequencies is greater than 2ν otp Sufficient separation can be achieved by applying a tweezers beam of sufficient intensity to optically trap the barrier ions.

[0092] Another advantage of the strong optical trapping potential applied during barrier ion confinement in this embodiment is that it reduces the rate of heating of ions within the array. High ω as shown in Figure 7 otp The separation of vibrational modes in adjacent computational regions means that the rate of ion heating is determined not by the total number of ions in the array, but primarily by the size of each computational region.

[0093] Figure 8 is a schematic plot showing the radial mode frequencies 160, 162, 164, ..., 166, 168, 170, 172 in a segmented array of trap ions according to one embodiment of the present invention. These radial mode frequencies are ω otp Assuming = 2.1ν, the axial spectra were calculated for the same segmented arrangement of N=231 ions shown in Figure 7. In addition to the 174 additional high-frequency modes associated with the barrier ions, there are 35 radial bands, each containing 6 modes, corresponding to 35 ions in each calculation segment.

[0094] As shown in the inset in Figure 8, the modes are sufficiently frequency-separated and each has a bandwidth BW that is much smaller than the band separation Δω. The crosstalk in the quantum entanglement operation between adjacent computational segments is given by approximately ε = BW / 2Δω, which in this embodiment is estimated to be about 2.5%.

[0095] Reducing residual crosstalk Figure 9 is a schematic flowchart illustrating a method for selecting parameters to drive a multi-qubit gate in a segmented array of trapped ions according to one embodiment of the present invention. This method is based on the technique for calculating the excitation field frequency and complex amplitude for a multi-qubit gate described in U.S. Provisional Patent Application No. 63 / 506,142, filed June 5, 2023, whose disclosure is incorporated herein by reference. This method extends these techniques to compensate for crosstalk between computational segments within a segmented array, such as array 100 (Figure 5). This method suppresses the effects of residual crosstalk that remains despite barrier confinement, thereby enhancing the fidelity of quantum operations performed using the array.

[0096] The method in Figure 9 begins in register definition step 180 by defining a set of multi-qubit registers in the array of trapped ions. For example, the registers may correspond to computational sections 110 defined by barrier ions 112 in array 100 in each computing step 102, 104, 106, and 108, as shown in Figure 5. In frequency selection step 182, a number of excitation frequency pairs M>2 is selected to excite the vibrational modes in section 110. The frequency pairs are each with frequency ω 0± ω m And the amplitude vector r = <r1,r2,...,r M Each amplitude r defined by > m (where ω0 is the internal instantaneous 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 assign a different amplitude vector r to each qubit so that the complete set of amplitudes can be represented by a matrix r of dimension N×M. n These are applied independently, where N is the number of qubits in each section.

[0097] To calculate the respective excitation spectra applied to ion 40, in matrix definition step 184, set of N(N-1) / 2 bond matrices A n,m A matrix of dimension M×M is defined to represent the interaction between the excitation frequency pair and the qubits n and m in each section of the array, based on the reference mode of the qubit's vibration. Specifically,

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[0098] The target quantum entanglement phase vector for each computational unit is

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[0099] In order to enable fast and efficient calculation of solutions, in the zero-phase step 186, for each computational segment, an initial non-trivial excitation spectrum is calculated to put each of the multi-qubit gates of the zero entanglement phase into an entangled state. This step involves constraints

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[0100] the parameters λ and D can be calculated by a linear solution process to obtain a proximity amplitude vector R = λR0 + D that satisfies [[ID= 37]]

Number

[0101] Next, for all 1 < n < m < N

number

[0102] In addition to the constraints between qubits within each computational segment in this optimization process, crosstalk reduction constraints are calculated in crosstalk reduction step 190 to be applied to the optimization process to compensate for the estimated residual crosstalk between segments. For this purpose, residual crosstalk between adjacent computational segments is estimated. This residual crosstalk was estimated to be approximately 2.5% above, based on the bandwidth of the vibrational bands, for example, as shown in Figure 7. A more accurate estimate of the residual crosstalk is given by the coupling matrix A described above, which represents the coupling between ions within adjacent computational segments. n,m This can be derived by constructing a matrix similar to the one shown. Next, the level of residual crosstalk can be calculated as the ratio of the magnitude of ion bonds in different sections to the magnitude of ion bonds in a single section. The result is similar to a simpler bandwidth-based estimate.

[0103] In crosstalk optimization step 192, the final optimal vector R compensates for the effects of crosstalk to achieve the desired fidelity target. opt To derive this, the amplitude vector R is iteratively optimized for each computational segment using the estimated residual crosstalk. Following each iteration i, the phase deviation of the qubits within each segment is calculated relative to their respective target phases at the end of gate time.

number

[0104] The formal definition of the phase deviation due to residual crosstalk and an algorithm for optimizing the excitation spectrum to minimize non-fidelity in the presence of residual crosstalk are presented in the following appendix.

[0105] Based on the calculated phase deviation, a new set of corrected amplitudes R is calculated to reduce the phase deviation and thereby improve the fidelity of the quantum computation. This process reaches the desired goal and the final optimal vector R opt The process is repeated iteratively until the desired result is obtained, and as a result, the fidelity is reduced in each iteration.

[0106] After the optimal solution is found, in gate drive step 194, R is applied to each ion. opt Each amplitude defined by the calculation results in N ions in each of the calculation sections 110 having M frequencies

number

[0107] The gate time for each of the multi-qubit gates defined in array 100 is determined by the minimum interval Δf between the vibrational frequencies of each group of reference modes excited by the applied radiation. In the adiabatic limit, the gate time T >> 1 / Δf determines the coupling matrix A n While the resulting matrix is ​​diagonal, and the amplitude vector r satisfying the constraints can be easily found, in this case, the long gate times make multi-qubit gates impractical for actual quantum computation. Therefore, in some embodiments of the present invention, the coupling matrix is ​​selected to support faster gate times, for example, T < 50Δf or even T < 10 / Δf. In such cases, the coupling matrix is ​​generally dense, but the method described above can be applied to find the optimal amplitude vector r that will enable the desired fast gate times. Constraints on maximum non-fidelity and resilience to errors, noise, and residual crosstalk can also be added to the solution process to ensure that the resulting amplitude vector drives multiple multi-qubit gates in parallel with high fidelity and robustness.

[0108] In a multi-qubit gate, the oscillation frequencies of each reference mode span a specific frequency range from the minimum reference mode frequency to the maximum reference 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.

[0109] Figure 10 is a plot schematically showing the nonfictionality of a partitioned array of trap ions, such as array 100 (Figure 5), according to one embodiment of the present invention, as a function of the optical trap potential applied to the barrier ions 112 in the partitioning of the array. The nonfictionality is expressed using the error per calculation partition 110, based on the phase deviation of the qubits within each partition at the end of the gate time relative to each target phase, as defined above. The upper curve 200 shows the residual crosstalk before optimization of the excitation spectrum, and the lower curve 202 shows the residual crosstalk achieved by compensating for the residual crosstalk using the method shown in Figure 9. Both curves 200 and 202 are ω otp It descends sharply when the value is >1.8ν.

[0110] As shown by the difference between curves 200 and 202 in Figure 10, the spectral optimization techniques described above can be used to compensate for residual crosstalk and reduce errors caused by residual crosstalk by more than two orders of magnitude. As a result, the fidelity of quantum operations performed using arrays can be reduced to less than 0.1. By increasing the computational complexity applied to the methods described below, the fidelity can be reduced to less than 0.01, less than 0.001, or even less than 0.0001.

[0111] Two-dimensional and three-dimensional trap ion arrays As described above, the embodiments described above relate to a linear arrangement of trap ions 40, but the principle of the present invention is similarly applicable to two-dimensional and three-dimensional trap ion arrangements with necessary modifications. Ion traps capable of forming two-dimensional or three-dimensional ion arrangements are known in the art. In such arrangements, layers of barrier ions can be formed by confining selected ions using an optical trapping potential applied by a suitable laser beam. These layers of barrier ions define two-dimensional and three-dimensional computational regions, which can then be driven by excitation fields to perform complex quantum operations. After each operation, the arrangement can be reconstructed by selecting and confining a new set of barrier ions, as in the case of the linear arrangement described above.

[0112] Figure 11A is a schematic front view of a partitioned two-dimensional array 220 of trapped ions 40 according to one embodiment of the present invention. This array geometry is based on the trapping scheme described by Kiesenhofer et al. in "Controlling Two-Dimensional Coulomb Crystals of More Than 100 Ions in Monolithic Radio-Frequency Trap," published in PRX QUANTUM 4, 020317 (2023). Barrier ions 112 are optically confined around the outer periphery of the array 220 and along the lateral partitioning boundary, thereby partitioning the array into two-dimensional computational compartments 222.

[0113] Figure 11B is a schematic front view of a partitioned two-dimensional array 230 of trap ions 40 according to another embodiment of the present invention. The array 230 has a rectangular shape, and rows of barrier ions 112 partition the array 230 into a plurality of parallel two-dimensional calculation sections 232.

[0114] Figure 11C is a schematic front view of a partitioned two-dimensional array 240 of trap ions 40 according to yet another embodiment of the present invention. In this embodiment as well, the array 240 is rectangular and partitioned into a matrix of calculation sections 242 by rows and columns of barrier ions 112.

[0115] Figure 11D is a schematic front view of a compartmentalized three-dimensional array 250 of trap ions according to another embodiment of the present invention. An optical trapping potential is applied to the barrier ions 112 so as to define a computational compartment 252 consisting of parallel three-dimensional "slices" of ions 40. Alternatively, multiple different configurations of barrier ions can be used to form different corresponding two-dimensional and three-dimensional computational compartment topologies, as in the two-dimensional case.

[0116] 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 both combinations and subcombinations of the various features described above, as well as modifications and alterations not disclosed in the prior art, which would be conceivable to those skilled in the art by reading the above description.

[0117] Appendix - Crosstalk Reduction Algorithm As described above, the final optimal vector R opt When calculating the value of, following each iteration i, the phase deviation of the qubits within each segment relative to the respective target phase is calculated at the end of the gate time.

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[0118]

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[0119]

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[0121] For adjacent segments s and s+1, the correction coefficients for compensating for errors and crosstalk are given by the following formula.

[0122]

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[0123] Deviation from target phase

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[0124]

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Claims

1. A method of quantum computing, Trapping an ion sequence within an ion trap, Defining quantum computation involves a sequence of computing steps, where each step includes multiple quantum operations performed in parallel. The arrangement is divided into a first computational division, which includes each of the groups of adjacent ions separated by a first barrier ion between the groups, by optically confining the barrier ion. An excitation field is applied to the ions in the first calculation section so that the group of adjacent ions in the first calculation section performs the quantum operation in the first step of the sequence, After the completion of the quantum operation in the first step, the arrangement is reconstructed into the second calculation section by optically confining a second barrier ion, which is at least partially different from the first barrier ion, while maintaining at least some coherence from the first calculation section to the second calculation section. Applying the excitation field to the ions in the second calculation section such that the group of adjacent ions in the second calculation section performs the quantum operation in the second step of the sequence using at least a portion of the maintained coherence, A method for completing the quantum computation, comprising repeating the steps of: reconfiguring the array into further computational segments; and applying the excitation field to the further computational segments.

2. The method according to claim 1, comprising measuring the respective states of at least some of the ions upon completion of the quantum computation.

3. The method according to claim 1, wherein trapping the arrangement of ions is to form a linear arrangement of ions.

4. The method according to claim 1, wherein trapping the arrangement of ions is to form a two-dimensional arrangement of ions.

5. The method according to claim 1, wherein trapping the arrangement of ions is to form a three-dimensional arrangement of ions.

6. The method according to claim 1, wherein optically confining the barrier ion includes applying optical tweezers to the barrier ion.

7. The method according to claim 6, wherein the application of the optical tweezers includes confining the barrier ions using a laser beam tuned to exert an optical attraction or repulsion on the barrier ions.

8. The method according to claim 1, comprising performing a mid-circuit measurement by detecting the state of one or more of the ions following at least the first step of the sequence.

9. The method according to claim 8, wherein applying the excitation field to the ion in the second calculation segment includes using information contained in the detected state in the mid-circuit measurement when defining the quantum operation to be performed in a subsequent step.

10. The method according to claim 8, comprising applying error correction to the quantum computation based on the mid-circuit measurement.

11. The method according to claim 8, wherein performing the mid-circuit measurement includes detecting the state of one or more of the barrier ions.

12. The method according to claim 8, wherein the reconstruction of the sequence into the second calculation segment following the mid-circuit measurement is completed in a duration of less than 20 milliseconds.

13. The method according to claim 12, wherein the duration for completing the reconstruction of the sequence into the second calculation segment following the mid-circuit measurement is less than 10 milliseconds.

14. The method according to any one of claims 1 to 13, wherein applying the excitation field includes directing a beam of coherent light emission to excite the transition of the ions in the calculation section.

15. The method according to claim 14, wherein the transition includes an internal transition of the ion within the calculation section.

16. The method according to claim 14, wherein the transition includes the motion transition of the ion within the calculation section.

17. The method according to claim 14, wherein applying the excitation field includes setting the respective spectra and pulse times of the beam to drive the ions in order to complete the quantum operation in each step.

18. The method according to claim 17, wherein optically confining the barrier ions reduces crosstalk between adjacent computational regions within the array.

19. The method according to claim 18, wherein setting each of the spectra and pulse times includes estimating the crosstalk between adjacent calculation segments in the array and selecting each of the spectra and pulse times to compensate for the estimated crosstalk.

20. The method according to claim 19, wherein selecting each of the spectra and pulse times includes defining a desired level of crosstalk and selecting the spectra and pulse times to reduce the estimated crosstalk below the desired level.

21. The arrangement of ions within the ion trap has an inter-ion characteristic frequency ν, and optically confining the barrier ions results in an optical trap frequency ω otp The method according to any one of claims 1 to 13, comprising irradiating the barrier ions with light radiation at an intensity sufficient to optically trap the barrier ions by 1.5ν.

22. ω otp The method according to claim 21, wherein the value is >1.8ν. 【Request Item 23】 【Number 1】 Here, e is the electron charge, and ε 0 The method according to claim 21, wherein is the permittivity of vacuum, m is the mass of each ion, and d is the inter-ion distance in the arrangement.

24. The arrangement of ions within the ion trap has an inter-ion characteristic frequency ν, and the barrier ions are optically confined such that the sum of the respective optical trap frequencies is greater than 2ν. otp The method according to any one of claims 1 to 13, comprising irradiating a group of barrier ions between adjacent computational regions with light radiation at an intensity sufficient to optically confine the barrier ions.

25. The method according to any one of claims 1 to 13, wherein optically confining the barrier ions reduces the rate of heating of the ions in the array.

26. The method according to claim 25, wherein the heating rate is determined not by the number of ions in the arrangement, but primarily by the size of each of the calculation segments.

27. The method according to any one of claims 1 to 13, wherein applying the excitation field includes exciting the motion modes of the arrangement of ions having their respective motion frequencies, and optically confining the barrier ions involves grouping the motion frequencies into bands having their respective center frequencies and bandwidths such that the bandwidth of each band is less than the difference between the center frequencies of adjacent bands.

28. The method according to claim 27, wherein optically confining the barrier ions reduces the bandwidth to 20% or less of the difference between the center frequencies of adjacent bands.

29. The method according to claim 28, wherein optically confining the barrier ions reduces the bandwidth to 10% or less of the difference between the center frequencies of adjacent bands.

30. The method according to claim 29, wherein optically confining the barrier ions reduces the bandwidth to 5% or less of the difference between the center frequencies of adjacent bands.

31. The method according to claim 27, wherein applying the excitation field includes performing a plurality of qubit gate operations in at least a portion of the calculation section.

32. The method according to any one of claims 1 to 13, wherein at least a portion of the calculation divisions formed by dividing the sequence each contains at least 10 ions from the ions.

33. The method according to claim 32, wherein at least a portion of the calculation divisions formed by dividing the sequence each contains at least 20 ions from the ions.

34. The method according to any one of claims 1 to 13, wherein applying the excitation field includes performing at least a portion of the quantum operations across a gate containing four or more of the ions.

35. The method according to claim 34, wherein applying the excitation field includes performing at least a portion of the quantum operations across a gate containing 12 or more of the ions.

36. The method according to any one of claims 1 to 13, wherein reconstructing the sequence into the second calculation section while maintaining at least a portion of the coherence includes causing the ions in the second calculation section to be quantum entangled with the ions in the first calculation section.

37. The method according to claim 36, wherein the array comprises n ions, and the number of reconstruction steps s such that s < 0.2 * n of the ions in the second calculation segment are quantum entangled, the number of reconstruction steps s such that s < 0.2 * n, wherein at least 70% of the ions in the calculation segment of the array are quantum entangled.

38. The method according to any one of claims 1 to 13, wherein the reconfiguration of the sequence into the second calculation unit is completed in a duration of less than 10 milliseconds.

39. The method according to claim 38, wherein the reconfiguration of the sequence into the second calculation unit is completed in a duration of less than 1 millisecond.

40. The method according to claim 39, wherein the reconstruction of the sequence into the second calculation unit is completed in a duration of less than 100 microseconds.

41. The method according to claim 40, wherein the reconstruction of the sequence into the second calculation unit is completed in a duration of less than 10 microseconds.

42. The method according to claim 41, wherein the reconstruction of the sequence into the second calculation unit is completed within a duration of less than one microsecond.

43. The method according to any one of claims 1 to 13, wherein defining the quantum computation includes applying a quantum error correction code over the sequence of computing steps.

44. The method according to any one of claims 1 to 13, wherein defining the quantum computation includes performing a quantum simulation over the sequence of computing steps.

45. A method of quantum computing, Trapping an ion sequence within an ion trap, By optically confining barrier ions, the arrangement is divided into computational divisions that include each of the groups of adjacent ions separated by the barrier ions between the groups, Defining a quantum computation that includes multiple quantum operations performed in parallel across the aforementioned computational divisions, wherein the quantum operations define a target quantum entanglement phase between the ions within each division, To estimate crosstalk between adjacent calculation segments within the aforementioned array, Calculating the respective spectra of the excitation fields for driving the ions into the target quantum entanglement phase while compensating for the estimated crosstalk, A method comprising applying the excitation field having the respective spectra to the ions in the calculation section in order to perform the quantum operation.

46. The method according to claim 45, wherein trapping the arrangement of ions is to form a linear arrangement of ions.

47. The method according to claim 45, wherein trapping the arrangement of ions is to form a two-dimensional arrangement of ions.

48. The method according to claim 45, wherein trapping the arrangement of ions is to form a three-dimensional arrangement of ions.

49. The method according to claim 45, wherein compensating for the estimated crosstalk reduces the non-fidelity of the quantum operation to less than 0.

1.

50. The method according to claim 49, wherein compensating for the estimated crosstalk reduces the non-fidelity of the quantum operation to less than 0.

01.

51. The method according to claim 50, wherein compensating for the estimated crosstalk reduces the non-fidelity of the quantum operation to less than 0.

001.

52. The method according to claim 51, wherein compensating for the estimated crosstalk reduces the non-fidelity of the quantum operation to less than 0.0001.

53. The method according to claim 45, wherein partitioning the array generates motion modes within the calculation partitions, each having an oscillation frequency grouped into the frequency bands at a minimum interval Δf between frequency bands, and applying the excitation field drives the ions to the target quantum entanglement phase in a time less than 50 / Δf.

54. The method of claim 45, wherein optically confining the barrier ions reduces crosstalk between adjacent computational segments within the sequence such that it results in residual crosstalk, and compensating for the estimated crosstalk is equivalent to compensating for the residual crosstalk.

55. The method according to claim 45, wherein optically confining the barrier ion includes applying optical tweezers to the barrier ion.

56. The method according to claim 55, wherein the application of the optical tweezers includes confining the barrier ions using a laser beam tuned to exert an optical attraction or repulsion on the barrier ions.

57. The method according to any one of claims 45 to 56, wherein applying the excitation field includes directing a beam of coherent light emission to excite the transition of the ions in the calculation section.

58. The method according to claim 57, wherein the transition includes an internal transition of the ion within the calculation section.

59. The method according to claim 57, wherein the transition includes the motion transition of the ion within the calculation section.

60. The method according to claim 57, wherein calculating each of the aforementioned spectra includes determining an initial spectrum and pulse time that will result in a zero-quantum entanglement phase between the ions, and applying an optimization process starting from the initial spectrum and pulse time to determine a target vector of the complex amplitude that will result in the target quantum entanglement phase.

61. The method according to claim 60, wherein applying the optimization process includes, as part of the optimization process, reducing the estimated crosstalk and thereby increasing the fidelity of the quantum computation.

62. The arrangement of ions within the ion trap has an inter-ion characteristic frequency ν, and optically confining the barrier ions results in an optical trap frequency ω otp The method according to any one of claims 45 to 56, comprising irradiating the barrier ions with light radiation at an intensity sufficient to optically trap the barrier ions by 1.5ν.

63. ω otp The method according to claim 62, wherein the value is 1.8ν. [Request Item 64] [Number 2] Here, e is the electron charge, and ε 0 The method according to claim 62, wherein m is the permittivity of vacuum, m is the mass of each ion, and d is the inter-ion distance in the arrangement.

65. The arrangement of ions within the ion trap has an inter-ion characteristic frequency ν, and the barrier ions are optically confined such that the sum of the respective optical trap frequencies is greater than 2ν. otp The method according to any one of claims 45 to 56, comprising irradiating a group of barrier ions between adjacent computational regions with light radiation at an intensity sufficient to optically confine the barrier ions.

66. The method according to any one of claims 45 to 56, wherein optically confining the barrier ions reduces the rate of heating of the ions in the array.

67. The method according to claim 66, wherein the heating rate is determined not by the number of ions in the arrangement, but primarily by the size of each of the calculation segments.

68. The method according to any one of claims 45 to 56, wherein applying the excitation field includes exciting the motion modes of the arrangement of ions having their respective motion frequencies, and optically confining the barrier ions involves grouping the motion frequencies into bands having their respective center frequencies and bandwidths such that the bandwidth of each band is less than the difference between the center frequencies of adjacent bands.

69. The method according to claim 68, wherein optically confining the barrier ions reduces the bandwidth to 20% or less of the difference between the center frequencies of adjacent bands.

70. The method according to claim 69, wherein optically confining the barrier ions reduces the bandwidth to 10% or less of the difference between the center frequencies of adjacent bands.

71. The method according to claim 69, wherein optically confining the barrier ions reduces the bandwidth to 5% or less of the difference between the center frequencies of adjacent bands.

72. The method according to claim 68, wherein applying the excitation field includes performing a plurality of qubit gate operations in at least a portion of the computational section using the motion mode.

73. The method according to any one of claims 45 to 56, wherein at least a portion of the calculation divisions formed by dividing the sequence each contains at least 10 ions from the ions.

74. The method according to claim 73, wherein at least a portion of the calculation divisions formed by dividing the sequence each contains at least 20 ions from the ions.

75. The method according to any one of claims 45 to 56, wherein applying the excitation field includes performing at least a portion of the quantum operations across a gate containing four or more of the ions.

76. The method according to claim 75, wherein applying the excitation field includes performing at least a portion of the quantum operations across a gate containing 12 or more of the ions.

77. A method of quantum computing, Trapping the ion arrangement in an ion trap configured such that the ion arrangement has an inter-ion characteristic frequency ν, Optical trap frequency ω otp By optically confining the barrier ions with sufficient intensity to optically trap the barrier ions by > 1.5ν, the array is partitioned into computational segments each including one of the groups of adjacent ions separated by the barrier ions between the groups, and Defining a quantum computation that includes multiple quantum operations performed in parallel across the aforementioned computational divisions, A method comprising applying an excitation field to the ions in the calculation section so that the group of adjacent ions performs the quantum calculation.

78. The method according to claim 77, wherein trapping the arrangement of ions is to form a linear arrangement of ions.

79. The method according to claim 77, wherein trapping the arrangement of ions is to form a two-dimensional arrangement of ions.

80. The method according to claim 77, wherein trapping the arrangement of ions is to form a three-dimensional arrangement of ions.

81. The method according to claim 77, wherein optically confining the barrier ion includes applying optical tweezers to the barrier ion.

82. The method according to claim 81, wherein the application of the optical tweezers includes confining the barrier ions using a laser beam tuned to exert an optical attraction or repulsion on the barrier ions.

83. The method according to claim 77, wherein applying the excitation field includes directing a beam of coherent light emission to excite the transition of the ions in the calculation section.

84. The method according to claim 83, wherein the transition includes an internal transition of the ion within the calculation section.

85. The method according to claim 83, wherein the transition includes the motion transition of the ion within the calculation section.

86. Applying the excitation field brings the fundamental trap frequency ω of the ion trap to trap The method according to any one of claims 77 to 85, comprising exciting the motion mode of the ion arrangement at an oscillation frequency centered on .

87. Optically confining the aforementioned barrier ions results in the sum of their respective optical trap frequencies being ω trap Each of the optical trap frequencies ω that becomes larger otp The method according to claim 86, comprising irradiating a group of barrier ions between adjacent computational units with light radiation at an intensity sufficient to optically trap the barrier ions.

88. ω otp The method according to any one of claims 77 to 85, wherein the coefficient is 1.8ν. [Request Item 89] [Number 3] Here, e is the electron charge, and ε 0 The method according to any one of claims 77 to 85, wherein is the permittivity of vacuum, m is the mass of each ion, and d is the inter-ion distance in the arrangement.

90. The method according to any one of claims 77 to 85, wherein optically confining the barrier ions reduces the rate of heating of the ions in the array.

91. The method according to claim 90, wherein the heating rate is determined not by the number of ions in the arrangement, but primarily by the size of each of the calculation segments.

92. The method according to any one of claims 77 to 85, wherein applying the excitation field includes exciting the motion modes of the arrangement of ions having their respective motion frequencies, and optically confining the barrier ions involves grouping the motion frequencies into bands having their respective center frequencies and bandwidths such that the bandwidth of each band is less than the difference between the center frequencies of adjacent bands.

93. The method according to claim 92, wherein optically confining the barrier ions reduces the bandwidth to 20% or less of the difference between the center frequencies of adjacent bands.

94. The method according to claim 93, wherein optically confining the barrier ions reduces the bandwidth to 10% or less of the difference between the center frequencies of adjacent bands.

95. The method according to claim 94, wherein optically confining the barrier ions reduces the bandwidth to 5% or less of the difference between the center frequencies of adjacent bands.

96. The method according to claim 93, wherein applying the excitation field includes performing a plurality of qubit gate operations in at least a portion of the computational section using the motion mode.

97. The method according to any one of claims 77 to 85, wherein at least a portion of the calculation divisions formed by dividing the sequence each contains at least 10 ions from the ions.

98. The method according to claim 97, wherein at least a portion of the calculation divisions formed by dividing the sequence each contains at least 20 ions from the ions.

99. The method according to any one of claims 77 to 85, wherein applying the excitation field includes performing at least a portion of the quantum operations across a gate containing four or more of the ions.

100. The method according to claim 99, wherein applying the excitation field includes performing at least a portion of the quantum operations across a gate containing 12 or more of the ions.

101. A system for quantum computing, An ion trap configured to hold an arrangement of ions at each position along the arrangement axis, A radiation source configured to apply a light field to divide the array into a plurality of computational divisions, each containing a group of neighboring ions separated by the barrier ions between the groups, by optically confining barrier ions, and further configured to apply an excitation field to the ions within the computational divisions so that the groups of neighboring ions within the computational divisions perform quantum operations, A controller configured to receive a definition of a quantum computation including a sequence of computing steps, each step including multiple quantum operations performed in parallel, wherein the radiation source is The aforementioned arrangement is divided into a first computational section by optically confining the first barrier ion, Applying the excitation field to the ions in the first calculation section so that the group of adjacent ions in the first calculation section performs the quantum operation in the first step of the sequence, After the completion of the quantum operation in the first step, the arrangement is reconstructed into the second calculation section by optically confining a second barrier ion, which is at least partially different from the first barrier ion, while maintaining at least some coherence from the first calculation section to the second calculation section. Applying the excitation field to the ions in the second calculation section such that the group of adjacent ions in the second calculation section performs the quantum operation in the second step of the sequence using at least a portion of the maintained coherence, A system including a controller configured to control the following steps in order to complete the quantum computation: repeating the steps of reconfiguring the array into further computational units and applying the excitation field to the further computational units.

102. The system according to claim 101, further comprising an array of detectors, wherein the controller is configured to apply the radiation source and the detectors to measure the state of each of at least some of the ions upon completion of the quantum computation.

103. The system according to claim 101, wherein the arrangement of ions includes a linear arrangement of ions.

104. The system according to claim 101, wherein the arrangement of ions includes a two-dimensional arrangement of ions.

105. The system according to claim 101, wherein the arrangement of ions includes a three-dimensional arrangement of ions.

106. The system according to claim 101, wherein optically confining the barrier ions includes applying optical tweezers to the barrier ions.

107. The system according to claim 106, wherein the application of the optical tweezers includes confining the barrier ions using a laser beam tuned to exert an optical attraction or repulsion on the barrier ions.

108. The system according to claim 101, further comprising an array of detectors, wherein the controller is configured to perform a mid-circuit measurement by applying the radiation source and the detectors to detect the state of one or more of the ions, following at least the first step of the sequence.

109. The system according to claim 108, wherein the controller is configured to use information contained in the state detected in the mid-circuit measurement when defining the quantum operation to be performed in a subsequent step.

110. The system according to claim 108, wherein the controller is configured to apply error correction to the quantum computation based on the mid-circuit measurement.

111. The system according to claim 108, wherein performing the mid-circuit measurement includes detecting the state of one or more of the barrier ions.

112. The system according to claim 108, wherein the controller is configured to reconstruct the sequence into the second calculation segment with a duration of less than 20 milliseconds following the mid-circuit measurement.

113. The system according to claim 112, wherein the duration for completing the reconstruction of the sequence into the second calculation segment following the mid-circuit measurement is less than 10 milliseconds.

114. The system according to any one of claims 101 to 113, wherein applying the excitation field includes directing a beam of coherent light emission to excite the transition of the ions in the calculation section.

115. The system according to claim 114, wherein the transition includes an internal transition of the ion within the calculation section.

116. The system according to claim 114, wherein the transition includes the motion transition of the ion within the calculation section.

117. The system according to claim 114, wherein the controller is configured to set the respective spectra and pulse times of the beam in order to drive the ions to complete the quantum operation in each step.

118. The system according to claim 117, wherein optically confining the barrier ions reduces crosstalk between adjacent computational regions within the array.

119. The system according to claim 118, wherein each of the spectra and pulse times is selected to compensate for estimated crosstalk between adjacent computational segments in the array.

120. The system according to claim 119, wherein each of the spectra and pulse times is selected by defining a desired level of crosstalk and selecting the spectra and pulse times to reduce the estimated crosstalk below the desired level.

121. The arrangement of ions within the ion trap has an inter-ion characteristic frequency ν, and the barrier ion has an optical trap frequency ω otp The system according to any one of claims 101 to 113, wherein the barrier ions are optically confined by irradiating them with light radiation at an intensity sufficient to optically trap them by 1.5ν.

122. ω otp The method according to claim 121, wherein the value is >1.8ν. The system according to claim 121. [Request Item 123] [Number 4] Here, e is the electron charge, and ε 0 The system according to claim 121, wherein is the permittivity of vacuum, m is the mass of each ion, and d is the inter-ion distance in the arrangement.

124. The arrangement of ions in the ion trap has an inter-ion characteristic frequency ν, and the barrier ions have optical trap frequencies such that the sum of their respective optical trap frequencies is greater than 2ν ω otp The system according to any one of claims 101 to 113, wherein the barrier ions are optically confined by irradiating a group of barrier ions between adjacent computational units with light radiation at an intensity sufficient to optically confine the barrier ions.

125. The system according to any one of claims 101 to 113, wherein optically confining the barrier ions reduces the rate of heating of the ions in the array.

126. The system according to claim 125, wherein the heating rate is determined not by the number of ions in the arrangement, but primarily by the size of each of the calculation segments.

127. The system according to any one of claims 101 to 113, wherein the excitation field excites the motion modes of the arrangement of ions having their respective motion frequencies, and optically confines the barrier ions, and the motion frequencies are grouped into bands having their respective center frequencies and bandwidths such that the bandwidth of each band is smaller than the difference between the center frequencies of adjacent bands.

128. The system according to claim 127, wherein optically confining the barrier ions reduces the bandwidth to 20% or less of the difference between the center frequencies of adjacent bands.

129. The system according to claim 128, wherein optically confining the barrier ions reduces the bandwidth to 10% or less of the difference between the center frequencies of adjacent bands.

130. The system according to claim 129, wherein optically confining the barrier ions reduces the bandwidth to 5% or less of the difference between the center frequencies of adjacent bands.

131. The system according to claim 127, wherein the controller is configured to apply the excitation field to the radiation source such that it performs a plurality of qubit gate operations in at least a portion of the calculation section.

132. The system according to any one of claims 101 to 113, wherein at least a portion of the calculation divisions formed by dividing the sequence each contains at least 10 ions from the ions.

133. The system according to claim 132, wherein at least a portion of the calculation divisions formed by dividing the sequence each contains at least 20 ions from the ions.

134. The system according to any one of claims 101 to 113, wherein the controller is configured to cause the emission source to apply the excitation field to perform at least a portion of the quantum operations across a gate containing four or more of the ions.

135. The system according to claim 134, wherein at least a portion of the quantum operation is performed across a gate containing 12 or more ions from among the ions.

136. The system according to any one of claims 101 to 113, wherein reconstructing the sequence into the second calculation unit while maintaining at least some of the coherence includes causing the ions in the second calculation unit to become quantum entangled with the ions in the first calculation unit.

137. The system according to claim 136, wherein the array comprises n ions, and the number of reconstruction steps s such that s < 0.2 * n of the ions in the second calculation segment are quantum entangled, the number of reconstruction steps s such that s < 0.2 * n, and the number of reconstruction steps s such that the number of reconstruction steps s is quantum entangled, and the number of reconstruction steps s such that the number of reconstruction steps s is quantum entangled, is quantum entangled, and the number of reconstruction steps s has been quantum entangled, and the number of reconstruction steps s has been quantum entangled, and the number of reconstruction steps s has been quantum entangled, and the number of reconstruction steps s has been quantum entangled, and the number of reconstruction steps s has been quantum entangled, is

138. The system according to any one of claims 101 to 113, wherein the reconfiguration of the sequence into the second calculation unit is completed in a duration of less than 10 milliseconds.

139. The system according to claim 138, wherein the reconfiguration of the sequence into the second calculation unit is completed in a duration of less than 1 millisecond.

140. The system according to claim 139, wherein the reconstruction of the sequence into the second calculation unit is completed in a duration of less than 100 microseconds.

141. The system according to claim 140, wherein the reconstruction of the sequence into the second calculation unit is completed in a duration of less than 10 microseconds.

142. The system according to claim 141, wherein the reconstruction of the sequence into the second calculation unit is completed in a duration of less than one microsecond.

143. The system according to any one of claims 101 to 113, wherein the quantum computation includes the application of a quantum error correction code over the sequence of computing steps.

144. The system according to any one of claims 101 to 113, wherein the quantum computation includes a quantum simulation performed over the sequence of computing steps.

145. A system for quantum computing, An ion trap configured to hold an arrangement of ions at each position along the arrangement axis, A radiation source configured to apply a light field to divide the array into a plurality of computational divisions, each containing a group of neighboring ions separated by the barrier ions between the groups, by optically confining barrier ions, and further configured to apply an excitation field to the ions within the computational divisions so that the groups of neighboring ions within the computational divisions perform quantum operations, A controller configured to receive definitions of quantum computations comprising a plurality of quantum operations performed in parallel across the computational divisions, wherein the quantum operations define a target quantum entanglement phase between the ions in each division, the definitions comprising the respective spectra of excitation fields for driving the ions into the target quantum entanglement phase while compensating for estimated crosstalk between adjacent computational divisions in the array, and the controller is further configured to drive the radiation source to apply the excitation fields having the respective spectra to the ions in the computational divisions in order to perform the quantum computations.

146. The system according to claim 145, wherein the arrangement of ions includes a linear arrangement of ions.

147. The system according to claim 145, wherein the arrangement of ions includes a two-dimensional arrangement of ions.

148. The system according to claim 145, wherein the arrangement of ions includes a three-dimensional arrangement of ions.

149. The system according to claim 145, wherein compensating for the estimated crosstalk reduces the fidelity of the quantum operation to less than 0.

1.

150. The system according to claim 149, wherein compensating for the estimated crosstalk reduces the non-fidelity of the quantum operation to less than 0.

01.

151. The system according to claim 150, wherein compensating for the estimated crosstalk reduces the non-fidelity of the quantum operation to less than 0.

001.

152. The system according to claim 151, wherein compensating for the estimated crosstalk reduces the non-fidelity of the quantum operation to less than 0.0001.

153. The system according to claim 145, wherein partitioning the array generates motion modes in the calculation partition having respective vibrational frequencies grouped into the previous frequency bands by a minimum interval Δf between frequency bands, and the controller is configured to drive the radiation source to apply the excitation field to drive the ions into the target quantum entanglement phase in a time of less than 50 / Δf.

154. The system according to claim 145, wherein optically confining the barrier ions reduces crosstalk between adjacent computational segments within the sequence such that it results in residual crosstalk, and compensating for the estimated crosstalk results in compensating for the residual crosstalk.

155. The system according to claim 145, wherein optically confining the barrier ion includes applying optical tweezers to the barrier ion.

156. The system according to claim 155, wherein the application of the optical tweezers includes confining the barrier ions using a laser beam tuned to exert an optical attraction or repulsion on the barrier ions.

157. The system according to any one of claims 145 to 156, wherein applying the excitation field includes directing a beam of coherent light emission to excite the transition of the ions in the calculation section.

158. The system according to claim 157, wherein the transition includes an internal transition of the ion within the calculation section.

159. The system according to claim 157, wherein the transition includes the motion transition of the ion within the calculation section.

160. The system according to claim 157, wherein the controller is configured to drive the radiation source to apply the excitation field according to a complex amplitude target vector, the target vector being calculated by determining an initial spectrum and pulse time that will produce a zero-entanglement phase between the ions, and by applying an optimization process that starts from the initial spectrum and pulse time to determine the complex amplitude target vector that will produce the target-entanglement phase.

161. The system according to claim 160, wherein the optimization process reduces the estimated crosstalk, thereby increasing the fidelity of the quantum computation.

162. The arrangement of ions within the ion trap has an inter-ion characteristic frequency ν, and the barrier ion has an optical trap frequency ω otp The system according to any one of claims 145 to 156, wherein the barrier ions are optically confined by irradiating them with light radiation at an intensity sufficient to optically trap them by 1.5ν.

163. ω otp The system according to claim 162, wherein the coefficient is 1.8ν. [Request Item 164] [Number 5] Here, e is the electron charge, and ε 0 The system according to claim 162, wherein is the permittivity of vacuum, m is the mass of each ion, and d is the inter-ion distance in the arrangement.

165. The arrangement of ions in the ion trap has an inter-ion characteristic frequency ν, and the barrier ions have optical trap frequencies such that the sum of their respective optical trap frequencies is greater than 2ν ω otp The system according to any one of claims 145 to 156, wherein the barrier ions are optically confined by irradiating a group of barrier ions between adjacent computational regions with light radiation of sufficient intensity to optically confine them.

166. The system according to any one of claims 145 to 156, wherein optically confining the barrier ions reduces the rate of heating of the ions in the array.

167. The system according to claim 166, wherein the heating rate is determined not by the number of ions in the arrangement, but primarily by the size of each of the calculation segments.

168. The system according to any one of claims 145 to 156, wherein the excitation field excites the motion modes of the arrangement of ions having their respective motion frequencies, and optically confines the barrier ions, and the motion frequencies are grouped into bands having their respective center frequencies and bandwidths such that the bandwidth of each band is smaller than the difference between the center frequencies of adjacent bands.

169. The system according to claim 168, wherein optically confining the barrier ions reduces the bandwidth to 20% or less of the difference between the center frequencies of adjacent bands.

170. The system according to claim 169, wherein optically confining the barrier ions reduces the bandwidth to 10% or less of the difference between the center frequencies of adjacent bands.

171. The system according to claim 169, wherein optically confining the barrier ions reduces the bandwidth to 5% or less of the difference between the center frequencies of adjacent bands.

172. The system according to claim 168, wherein the controller is configured to apply the excitation field to the radiation source such that it performs a plurality of qubit gate operations in at least a portion of the calculation section.

173. The system according to any one of claims 145 to 156, wherein at least a portion of the calculation divisions formed by dividing the sequence each contains at least 10 ions from the ions.

174. The system according to claim 173, wherein at least a portion of the calculation divisions formed by dividing the sequence each contains at least 20 ions from the ions.

175. The system according to any one of claims 145 to 156, wherein the controller is configured to cause the emission source to apply the excitation field to perform at least a portion of the quantum operation across a gate containing four or more of the ions.

176. The system according to claim 175, wherein at least a portion of the quantum operation is applied across a gate containing 12 or more of the ions.

177. A system for quantum computing, An ion trap configured to hold the arrangement of ions such that the arrangement of ions has an inter-ion characteristic frequency ν, A radiation source configured to apply a light field to divide the array into a plurality of computational divisions, each containing a group of neighboring ions separated by the barrier ions between groups, by optically confining the barrier ions with sufficient intensity to optically trap them at an optical trap frequency ωotop > 1.5ν, and further configured to apply an excitation field to the ions within the computational divisions so that the groups of neighboring ions within the computational divisions perform quantum operations, A system comprising: a controller configured to receive a definition of a quantum computation including a plurality of quantum operations performed in parallel across the computational divisions; and a controller configured to drive the radiation source to apply an excitation field to the ions in the computational division so that the group of adjacent ions performs the quantum computation.

178. The system according to claim 177, wherein the arrangement of ions includes a linear arrangement of ions.

179. The system according to claim 177, wherein the arrangement of ions includes a two-dimensional arrangement of ions.

180. The system according to claim 177, wherein the arrangement of ions includes a three-dimensional arrangement of ions.

181. The system according to claim 177, wherein optically confining the barrier ion includes applying optical tweezers to the barrier ion.

182. The system according to claim 181, wherein the application of the optical tweezers includes confining the barrier ions using a laser beam tuned to exert an optical attraction or repulsion on the barrier ions.

183. The system according to claim 177, wherein applying the excitation field includes directing a beam of coherent light emission to excite the transition of the ions in the calculation section.

184. The system according to claim 183, wherein the transition includes an internal transition of the ion within the calculation section.

185. The system according to claim 183, wherein the transition includes the motion transition of the ion within the calculation section.

186. Applying the excitation field brings the fundamental trap frequency ω of the ion trap to trap The system according to any one of claims 177 to 185, comprising exciting the motion mode of the ion arrangement at an oscillation frequency centered on .

187. Optically confining the aforementioned barrier ions results in the sum of their respective optical trap frequencies being ω trap Each of the optical trap frequencies ω that becomes larger otp The system according to claim 186, comprising irradiating a group of barrier ions between adjacent computational units with light radiation at an intensity sufficient to optically trap the barrier ions.

188. ω otp The system according to any one of claims 177 to 185, wherein the coefficient is 1.8ν. [Request Item 189] [Number 6] Here, e is the electron charge, and ε 0 The system according to any one of claims 177 to 185, wherein m is the permittivity of vacuum, m is the mass of each ion, and d is the inter-ion distance in the arrangement.

190. The system according to any one of claims 177 to 185, wherein optically confining the barrier ions reduces the rate of heating of the ions in the array.

191. The system according to claim 190, wherein the heating rate is determined not by the number of ions in the arrangement, but primarily by the size of each of the calculation segments.

192. The system according to any one of claims 177 to 185, wherein the excitation field excites the motion modes of the arrangement of ions having their respective motion frequencies, and optically confines the barrier ions, and the motion frequencies are grouped into bands having their respective center frequencies and bandwidths such that the bandwidth of each band is smaller than the difference between the center frequencies of adjacent bands.

193. The system according to claim 192, wherein optically confining the barrier ions reduces the bandwidth to 20% or less of the difference between the center frequencies of adjacent bands.

194. The system according to claim 193, wherein optically confining the barrier ions reduces the bandwidth to 10% or less of the difference between the center frequencies of adjacent bands.

195. The system according to claim 194, wherein optically confining the barrier ions reduces the bandwidth to 5% or less of the difference between the center frequencies of adjacent bands.

196. The system according to claim 193, wherein the controller is configured to cause the excitation field to be applied to the reflection source so as to perform a plurality of qubit gate operations in at least a portion of the computational section using the motion mode.

197. The system according to any one of claims 177 to 185, wherein at least a portion of the calculation divisions formed by dividing the sequence each contains at least 10 ions from the ions.

198. The system according to claim 197, wherein at least a portion of the calculation divisions formed by dividing the sequence each contains at least 20 ions from the ions.

199. The system according to any one of claims 177 to 185, wherein the controller is configured to cause the emission source to apply the excitation field to perform at least a portion of the quantum operations across a gate containing four or more of the ions.

200. The system according to claim 199, wherein at least a portion of the quantum operations is applied across a gate containing 12 or more ions from the ions.

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