Bosonic bus-mediated superconducting parallel controlled-phase gate method and system

Abstract

The application provides a Bose coding bus-mediated superconducting parallel controlled phase gate method and system, which comprises the following steps: preparing and stabilizing a two-dimensional logical coding subspace of a microwave storage mode, so that an annihilation operator projection has a non-zero diagonal dominant term with the same mode and different phases on two orthogonal logical ground states; selecting a plurality of multi-level superconducting qubits to form a target set, and selectively and effectively exchanging the auxiliary exchange doublet and the microwave storage mode, so that each target simultaneously completes conditional half exchange in a common action window; under the approximation of the projection corresponding to the dominant term, the conditional exchange terms of different targets are mutually commutable; after the effective exchange is completed, local return is performed in parallel, and the de-queuing and phase closure at the queuing time are adopted, so that each target returns to the original calculation subspace, and the product of a plurality of controlled phase gates with a quantum bus as a common control end is output.

Description

Technical Field

[0001] This invention belongs to the field of superconducting quantum computing technology, and particularly relates to a superconducting parallel controlled phase gate method and system mediated by a Bose-coded bus. Background Technology

[0002] With the development of quantum computing technology, superconducting quantum processors have become one of the important platforms for realizing quantum information processing. Among them, the lowest two energy levels of multi-level superconducting qubits... and Typically used to store a single qubit, multi-level superconducting qubits are weakly non-harmonic oscillators and also exhibit... , Higher energy levels are also possible. Through selective driving, frequency modulation, parametric sidebands, or tunable coupling networks, a specific adjacent transition can be effectively exchanged with a microwave mode. Simultaneously, a superconducting microwave resonant mode can establish capacitive, inductive, or parametrically activated coupling with multiple multi-level superconducting qubits and can serve as a shared quantum bus for transmitting quantum information.

[0003] Within a cat-state logical manifold, the annihilation operator of microwave modes has a logical Pauli projection. Exactly to the finite overlap of cat states, this projection can be written as...

[0004] exist The large amplitude limit, the dominant term is Since this term is a diagonal operator in the cat-state logic basis, it provides a physical basis for the commutation of conditional commutation terms between different multi-level superconducting qubits.

[0005] A controlled phase gate can be defined as a diagonal entanglement gate that assigns phase to a specific joint ground state of only two logic bits. CZ and CNOT can be converted to each other via local Hadamard transforms before and after the target bits. For multi-target scenarios, This represents the controlled phase gate product between the same control bit and multiple target bits.

[0006] Based on this technology, existing technologies can establish controllable coupling relationships between multiple qubits using shared resonant modes or cat-state modes, and thereby realize quantum information transfer and multi-qubit quantum gate operations. These methods can include the following implementation approaches: The first type involves connecting multiple multi-level superconducting qubits via a conventional resonator bus. This type of system typically includes multiple multi-level superconducting qubits, one or more shared resonant modes, couplers or frequency modulation ports, and control electronics. Operation may involve transferring the excitation of a single multi-level superconducting qubit to a shared resonant mode, forming a two-qubit gate using dispersion phase shifting or controlled swapping, and then returning the excitation. This type of scheme can improve the connectivity graph, but when multiple multi-level superconducting qubits simultaneously undergo resonant swapping, the conventional resonant modes still exhibit collective rather than automatically factorized dynamics.

[0007] The second type is a hybrid quantum system consisting of a stable cat state and a multi-level superconducting qubit. This type of scheme can utilize multi-level superconducting qubits to assist in the preparation, synthesis, readout, or logic gates of the cat state.

[0008] The shortcomings of existing technical solutions include: First, simultaneous coupling in a common shared harmonic oscillator leads to collective evolution. and This is not commutative. Therefore, when multiple multi-level superconducting qubits simultaneously resonate with the same ordinary mode, different target terms will collectively evolve by sharing photon degrees of freedom. To obtain multiple controlled phase gates, it is usually still necessary to select targets one by one, operate sequentially, additionally eliminate collective modes, or use different non-resonant gate mechanisms. As a result, the gate depth, calibration parameters, or residual entanglement of shared modes may increase with the number of targets.

[0009] Secondly, executable multi-level superconducting qubit gates require a defined energy level closure chain, including operations for calculating energy levels, assisted transitions, returning to computation space after the gate, and phase closure conditions. This also applies to the brief occupation of multi-level superconducting qubits within the gate. The process also needs to consider Error model corresponding to decay branch and final leakage.

[0010] Furthermore, writing a native block error as n independent two-bit errors results in the loss of physical structure. The single-photon loss of a cat-state is the loss of the entire native block. Block sharing The event, and the multi-level superconducting quantum bit Contributions are summed according to the target. If the gate is split into n independent two-bit channels, the shared cat-state event will be incorrectly counted n times, and one event will be lost. The cat-state mode generated by the jump event is a joint component with the target qubit. Summary of the Invention

[0011] This invention provides a superconducting parallel controlled phase gate method and system mediated by a Bose-coded bus, which solves the technical problem in the prior art that it is difficult to use a single stable Bose-coded mode as a common degree of freedom to directly perform one-to-many controlled phase operations on multiple multi-level superconducting qubits with two-dimensional computational space and auxiliary exchange dual states within the same physical action window, and to make all multi-level superconducting qubits return to their respective computational subspaces after the gate.

[0012] To solve the above problems, the technical solution of the present invention is: a superconducting parallel controlled phase gate method mediated by a Bose-coded bus, comprising: A two-dimensional logical encoding subspace is prepared and stabilized for use as a microwave storage mode under a stable Bose-encoded quantum bus; wherein the projection of the annihilation operator of the microwave storage mode into the encoding subspace has a non-zero diagonal dominant term, the dominant term having the same modulus and phase difference on two orthogonal logical ground states. By using encoding parameters and stability control, corrections deviating from the dominant term and leakage outside the encoding subspace are suppressed; Select one or more multi-level superconducting qubits to form a target set, each target having a two-dimensional computational subspace and an auxiliary exchanged dual state containing at least one energy level outside the computational subspace; make the computational state participating in the controlled phase directly as the first state of the auxiliary exchanged dual state, or map it to the first state through a temporary storage operation; The effective exchange between the auxiliary exchange dual state and the microwave storage mode, involving the annihilation operator and its Hermitian conjugate operator, is selectively activated, while the exchange of non-target transitions and unselected multi-level superconducting qubits is suppressed; the conditional half-exchange of each target is completed simultaneously within the common action window; under the projection approximation corresponding to the dominant term, the conditional exchange terms of different targets commutate with each other; The effective exchange ends, and the local return of each target, the release of temporary storage when temporary storage is used, and the phase closure are executed in parallel, so that each target returns to its original computational subspace. The computational states that did not participate in the controlled phase remain unchanged or only have compensable phases. The controlled phase is output with the quantum bus as the common control terminal and the selected target as the target terminal. The product of phase gates.

[0013] In one or more embodiments, the coding subspace is a two-component cat-state coding subspace, or a compressed cat-state coding subspace obtained by applying the same compression transformation to the two-component cat-state coding subspace; the effective amplitude and phase of the non-zero diagonal dominant term are determined based on the cat-state amplitude and the compression parameters when the compression transformation is applied, and the conditional half-exchange and return control are calibrated accordingly.

[0014] In one or more embodiments, the same effective coupling envelope and the same exchange axis phase are applied to each target in the target set; or, the control channels of each target are pre-calibrated so that each target obtains the same effective rotation angle and rotation axis to complete the conditional half-exchange within the common action window.

[0015] In one or more embodiments, each target is , Energy levels are used as computational states, with , The energy levels constitute the auxiliary exchange dual state; State components enter through conditional half-exchange The state, after the effective exchange ends, returns via local access. Pulse return The phase closure is achieved through pulse phase setting or virtual Z-correction. The state does not participate in the condition exchange.

[0016] In one or more embodiments, each target is , Energy levels are used as computational states, with , The energy levels constitute the auxiliary exchange dual state; before the conditional exchange, parallel processing is performed. Temporarily store state components to state, then through and Conditional half-swap, local return and to The temporary storage is released and the system returns to the original computational subspace. The phase of each pulse is set to close the control path consisting of the temporary storage, conditional half-exchange, local return, and temporary storage release.

[0017] In one or more embodiments, the coding subspace employs uncompressed two-component cat-state coding; based on the single-photon loss rate of the acquired or calibrated microwave storage mode, the effective coupling strength of the auxiliary transition corresponding to the auxiliary exchange dual state, the relaxation rate of the relevant energy level, and the local pulse duration, the error budget during conditional exchange and local control is evaluated, the cat-state amplitude operating point is determined, and the bus preparation, stabilization control, and exchange pulse parameters are set accordingly to execute the controlled phase gate.

[0018] In one or more embodiments, the controlled phase gate, with the quantum bus as the control terminal, is used to construct a star-shaped controlled phase gate between superconducting qubits, including: Another multi-level superconducting qubit that does not belong to the target set is selected as the control qubit, and the quantum bus is prepared as a superposition of two logic ground states with equal amplitude and in phase. The controlled phase gate is executed once with the control qubit as a single target, and a logical Hadamard transform is applied to the quantum bus; With the multi-level superconducting qubit in the target set as the target, the parallel controlled phase gate is executed within the common action window. Then, a logical Hadamard transform is applied to the quantum bus again, and the controlled phase gate is executed again with the control qubit as the single target. The quantum bus is de-entangled with the control qubits and the target set, returning to the equal-amplitude, in-phase superposition state. The output is a controlled system with the control qubits as the common control endpoint and the multi-level superconducting qubits in the target set as the target endpoints. The product of phase gates.

[0019] Based on the same concept, the present invention also provides a superconducting parallel controlled phase gate system mediated by a Bose-coded bus, comprising: a resonant structure providing a microwave storage mode, multiple multi-level superconducting qubits, a selectable coupling channel connecting the microwave storage mode and each qubit to assist in the exchange of dual states, and a controller connected to the resonant structure, the coupling channel and the local control port of each qubit. The controller is used to prepare and stabilize a two-dimensional logic encoding subspace of the microwave storage mode, such that the projection of the annihilation operator of the microwave storage mode into the encoding subspace has the same mode and phase difference on two orthogonal logic ground states. The non-zero diagonal dominant term is used, and projection correction and external leakage of the coding subspace are suppressed by encoding parameters and stability control; Each of the multi-level superconducting qubits has a two-dimensional computational subspace and an auxiliary exchanged dual state containing at least one energy level outside the computational subspace. The computational state participating in the controlled phase is directly located in the first state of the auxiliary exchanged dual state or mapped to the first state through a temporary storage operation. The controller is also used to select multi-level superconducting qubits to form a target set, suppress non-target transitions and exchanges of unselected multi-level superconducting qubits, and activate effective exchanges involving annihilation operators and their Hermitian conjugate operators through the coupling channel, so that each target can simultaneously complete conditional half-exchanges within the common action window; under the projection approximation corresponding to the dominant term, the conditional exchange terms of each target commutate with each other; the controller then ends the effective exchange, and performs return, necessary release of temporary storage and phase closure in parallel through the local control port, so that each target returns to its original computational subspace, the computational states that did not participate in the controlled phase remain unchanged or only have compensable phases, and outputs the controlled phase with the quantum bus as the common control terminal and the selected target as the target terminal. The product of phase gates.

[0020] In one or more embodiments, the controller is configured to apply the same effective coupling envelope and the same exchange axis phase to each target in the target set; or to precalibrate the control channels of each target to give each target the same effective rotation angle and rotation axis to complete the conditional half-exchange within the common action window.

[0021] In one or more embodiments, the controller is further configured to select a multi-level superconducting quantum bit that does not belong to the target set as the control quantum bit, and control the bus logic basis transformation port to sequentially execute the controlled phase gate between the control quantum bit and the quantum bus, the bus logic Hadamard transformation, the parallel controlled phase gate between the quantum bus and the target set, the bus logic Hadamard transformation, and the controlled phase gate between the control quantum bit and the quantum bus, so that the quantum bus, which is initially in a superposition state of equal amplitude and in phase of two logic ground states, returns to the initial state and is unentangled, forming a star-shaped controlled phase gate between superconducting quantum bits with the control quantum bit as the common control terminal.

[0022] Because the present invention adopts the above technical solution, it has the following advantages and positive effects compared with the prior art: (1) In this invention, for a fixed cat-state amplitude With effective coupling envelope The ideal interaction duration is determined by the common pulse area and does not increase linearly with the increase of the number of targets n; at the same time, the return pulses of all selected targets can be completed in parallel. Therefore, this invention can avoid splitting the controlled phase operation corresponding to multiple targets into ordinary two-bit gates executed sequentially, which is beneficial to reducing the time depth of multi-target gate operation and improving the efficiency of multi-target parallel control.

[0023] (2) In the case of finite overlap parameters Under ideal conditions, the commutative terms corresponding to each objective are all expressed as The form, and for any different objectives j and k, they commute with each other, that is, for any satisfy Therefore, in this invention, co-evolution can be strictly decomposed into multiple conditional rotation products with the same cat-state control, enabling multiple targets to achieve mutually compatible parallel evolution within the same co-action window, thereby providing a dynamic basis for the direct realization of native multi-target controlled phase gates.

[0024] (3) In the three-level implementation, the target qubit occupies only a brief position during gate execution. Energy levels, and after the conditional exchange is completed, the corresponding quantum state components are returned via a parallel return operation. Energy levels. Therefore, in this invention, the auxiliary energy level only participates temporarily during the gate operation, and all targets return to their original positions after the gate operation is completed. In the computational space, long-term quantum information will continue to be used. The calculation encodes the energy levels to form a complete closed energy level chain.

[0025] (4) When the finite overlap parameter u is not zero, a first-order coherent error generator will be introduced; starting from the number of targets n=2, correlation amplitudes dependent on the states of other targets may appear, and the process fidelity will decrease from... The order begins to appear. Therefore, this invention can describe the coherent correction and multi-objective correlation effects caused by finite cat-state overlap in a clear analytical form, providing a basis for the analysis, calibration, and subsequent selection of control parameters for correlation errors.

[0026] (5) The cat-state single-photon loss corresponds to the shared operation block of a native parallel gate. In this event, under the conditions of strong stability projection approximation and the independent environments of each multi-level superconducting qubit, the first-order error contribution is mainly manifested as the sum of the local terms corresponding to the cat-state mode and a single target, and the first-order error does not generate random cross terms that simultaneously connect two different targets. Therefore, this invention avoids repeatedly including the loss of a single shared cat state in the errors of multiple independent two-bit gates, making the error structure and error budget of the native parallel gate more consistent with its actual physical process.

[0027] (6) Given parameters such as the single-photon loss rate, effective coupling strength, and energy level lifetime of the cat state, the amplitude of the cat state can be selected by analytical formula or one-dimensional equation. , to balance The cat-state loss increases with increasing 1 / This invention reduces the residence error of multi-level superconducting qubits. Therefore, it allows the determination of a suitable cat-state amplitude operating point based on actual device parameters, and further refines the corresponding fabrication, stabilization, and switching control parameters accordingly, improving the calibrability of gate parameter selection. Attached Figure Description

[0028] Figure 1 A schematic flowchart of the superconducting parallel controlled phase gate method mediated by the Bose-coded bus provided by this invention; Figure 2 A schematic diagram of the structure of a superconducting parallel controlled phase gate system mediated by a Bose-coded bus provided by the present invention; Figure 3 A schematic diagram of the auxiliary exchange dual state and parallel closed-loop control sequence in the three-level scheme provided by this invention; Figure 4 A schematic diagram of a Bose-coded bus performing parallel controlled phase operations on a selected target set, provided by this invention; Figure 5A schematic diagram of a star-shaped controlled phase gate sequence between superconducting qubits mediated by a Bose-coded bus provided by the present invention; Figure 6 The present invention provides a schematic diagram of the first-order process error budget and cat-state amplitude operating point calibration under a specified instant readout timing for the three-level and four-level temporary storage implementation methods. Detailed Implementation

[0029] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, provides a further detailed account of the Bose-coded bus-mediated superconducting parallel controlled phase gate method and system proposed in this invention. The advantages and features of this invention will become more apparent from the following description and claims.

[0030] The term "comprising" and its variations as used herein are open-ended inclusions, meaning "including but not limited to". The term "based on" means "at least partially based on". The term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments". Definitions of other terms will be given in the description below.

[0031] It should be noted that all directional indicators (such as up, down, left, right, front, back, etc.) in the embodiments of this application are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicator will also change accordingly.

[0032] First, let's explain the terms that appear in this embodiment: Bosonic cat states and cat-state qubits: These refer to two coherent states within a microwave resonant mode. and Zhang Cheng's two-dimensional logic manifold. This mode can be maintained within the manifold through engineered two-photon dissipation, Kerr nonlinearity combined with two-photon drive, or an equivalent stabilization mechanism. Cat-state stabilizing units provide a constrained logic manifold during gates and, in conjunction with assisted transitions and co-exchange control of multi-level superconducting qubits, generate native parallel gates.

[0033] Stable cat-state mode: refers to a microwave storage mode that remains within the cat-state logic manifold during gate execution. Its annihilation operator is denoted as... The cat-state projection operator is The logical Pauli operator is Choosing the phase gauge makes Let be a real number, and define finite overlap.

[0034] To ensure the closed definition of the axis under finite u, we take the normalized even and odd cat states.

[0035] It is an orthogonal basis, and is defined as follows:

[0036]

[0037]

[0038] Swapping the even, odd order, or Pauli axis naming only changes the local representation, not the physical content of the gate.

[0039] Transmon-type multilevel superconducting qubits and assisted transitions: Transmon-type multilevel superconducting qubits are superconducting quantum devices with multiple non-equidistant energy levels. Hereinafter, they will be simply referred to as "multilevel superconducting qubits". In this embodiment, each multilevel superconducting qubit is reserved with respect to... , , Three energy levels, with , Store computational information, and in As an auxiliary transition that involves conditional exchange with the cat-state mode.

[0040] native A gate is a multi-target controlled phase operation performed by a stable cat-state qubit and n multi-level superconducting qubits from the same target set within the same interaction window. Its ideal logical action is...

[0041] Where c represents the cat-state qubit, and A represents the set of multi-level superconducting qubits selected in this study. "Native" here means that the product is not composed of n sequentially executed ordinary two-bit gates, but is directly generated within a common action window by the same projected exchange Hamiltonian.

[0042] Common effective coupling and common phase exchange: Defining binary selection variables for the j-th multilevel superconducting qubit. The selected target satisfies Unselected target satisfies In this embodiment, all selected targets use the same effective coupling envelope. and the same interchange axis phase The term "same" here includes the equivalent realization of each target having the same effective rotation angle and rotation axis through pre-calibration.

[0043] Return pulse: refers to the auxiliary transition applied in parallel to all selected multi-level superconducting qubits after the cat-state conditional exchange is completed. A pulse is used to return temporarily occupied auxiliary energy level components to the computational energy level and close the required logic phase.

[0044] Operant block shared events and target local events: Operant block shared events are a native event. Error events shared across the entire operation block, such as single-photon loss in cat-mode occurring within the logic manifold. An event; a target local event is an event related to the energy level decay or decoherence of a specific multi-level superconducting qubit. The distinction between the two accurately reflects the first-order error structure of a native parallel gate consisting of a shared event plus a target local event.

[0045] First Embodiment See Figures 1-6 This embodiment provides a superconducting parallel controlled phase gate method mediated by a Bose-coded bus, comprising: preparing and stabilizing a two-dimensional logical encoding subspace for a microwave storage mode used as a stabilized Bose-coded quantum bus; wherein the projection of the annihilation operator of the microwave storage mode onto the encoding subspace has a non-zero diagonal dominant term, the dominant term having the same modulus and phase difference on two orthogonal logical ground states. The process involves suppressing deviations from the dominant term and leakage from the encoded subspace through encoding parameters and stability control; selecting one or more multi-level superconducting qubits to form a target set, each target having a two-dimensional computational subspace and at least one auxiliary exchange dual state containing an energy level outside the computational subspace; directly using the computational state participating in the controlled phase as the first state of the auxiliary exchange dual state, or mapping it to the first state through temporary storage operations; selectively activating the effective exchange between the auxiliary exchange dual state and the microwave storage mode involving annihilation operators and their Hermitian conjugate operators, and suppressing non-target transitions and exchanges of unselected multi-level superconducting qubits; enabling each target to simultaneously complete conditional half-exchanges within the common action window; commuting the conditional exchange terms of different targets under the projection approximation corresponding to the dominant term; ending the effective exchange, and performing parallel execution of local return, temporary storage release, and phase closure for each target, returning each target to its original computational subspace; computational states not participating in the controlled phase remaining unchanged or having only compensable phases; and outputting a controlled phase with the quantum bus as the common control terminal and the selected target as the target terminal. The product of phase gates.

[0046] Specifically, the stable Bose-coded quantum bus described in this embodiment is formed by a microwave storage mode. During the execution of gate operations, the microwave storage mode is prepared and stabilized to keep it within a preset two-dimensional logic encoding subspace.

[0047] Let P be the two-dimensional coded projection of the microwave storage mode. , Let the two orthogonal logic ground states in the two-dimensional logic encoding subspace be defined as follows:

[0048] For microwave storage modes that actually participate in the exchange, the annihilation operator Within the two-dimensional logical encoding subspace, the following conditions are met:

[0049] in, The non-zero diagonal dominant terms constituting the projection of the annihilation operator have dominant coefficients with the same magnitude and phase difference in action on the two orthogonal logic ground states. , The phase can be included in the corresponding control calibration; This represents the projection correction that deviates from the dominant term. It is suppressed through the stabilizing effect of the microwave storage mode, encoding parameters, and corresponding control processes. And leakage caused by actions outside the coding subspace. It should be noted that simply forming a two-dimensional coding subspace or making the annihilation operator have different diagonal elements in the two logical ground states does not automatically guarantee that controlled behavior will be achieved after the same conditional half-commutation process. Phase gates also need to satisfy the above non-zero diagonal dominant terms and subsequent conditional exchanges and closure control relationships.

[0050] During a parallel controlled phase gate operation, one or more multi-level superconducting qubits are selected from multiple multi-level superconducting qubits to form the target set A corresponding to this gate operation. For the j-th target in target set A, it has a two-dimensional computational subspace. , and auxiliary exchange dual state , The assisted exchange dual state contains at least one energy level located outside the two-dimensional computational subspace. The computational state involved in the controlled phase operation... It can be directly used as the first state of an auxiliary commutative doublet. Alternatively, you can first perform a temporary storage operation. Mapped to .

[0051] Subsequently, the auxiliary exchange dual state of each selected target is selectively activated for effective exchange between the selected target and the microwave storage mode. Effective exchange is achieved by the annihilation operator of the microwave storage mode. and its Hermitian conjugate operator Participation. In actual control, the exchange channels corresponding to the current target set are selected, and non-target transitions are suppressed; for unselected multi-level superconducting qubits, their corresponding exchanges are kept closed or fully detuned, so that they do not participate in the conditional exchanges within the current interaction window. The controller can save the current target set, the effective area and phase of each channel, the return sequence, and the release sequence when using the temporary storage scheme, and coordinately call the corresponding selectable coupling channels and local control ports.

[0052] Under the projection approximation corresponding to the non-zero diagonal dominant term, for the j-th target, the effective conditions can be interchanged as follows:

[0053] in,

[0054] in, This represents the effective coupling envelope corresponding to the j-th target. This indicates the corresponding exchange axis phase. Each It remains fixed within the corresponding action window. For different objectives j and k, the corresponding conditional exchange terms... and Interchangeable, even if different targets use interchangeable axis phases and They are not the same, nor do they affect the aforementioned commutation relationship.

[0055] Control all selected targets to simultaneously exchange conditions within the same interaction window, and ensure that each target satisfies the following at the end of the interaction window:

[0056] Therefore, for the quantum bus logic state eigenvalues The target branch participating in the exchange satisfies the following after the conditional half-exchange is completed:

[0057] Since the conditional exchange terms corresponding to different targets commutate with each other, each target can complete the above-mentioned conditional half-exchange simultaneously within the same common action window, without having to execute multiple ordinary two-bit controlled phase gates in chronological order.

[0058] It should be noted that in the above-described higher-level control method, it is not required that different targets use the exact same effective coupling envelope or exchange axis phase. Different targets can be controlled and calibrated separately, as long as each target meets the corresponding conditional half-exchange requirement at the end of the common action window. In one embodiment, each target can also use the same effective coupling envelope and the same exchange axis phase, or the control channels of different targets can be pre-calibrated to ensure that each target obtains the same effective rotation angle and rotation axis.

[0059] After the conditional half-swap is completed, the effective swap is terminated first. Then, a local return operation matching the swap phase is executed in parallel for each selected target to return the quantum state components temporarily entering the auxiliary energy level to the corresponding computational subspace and compensate for the local phase unrelated to the quantum bus logic state. When the computational state participating in the controlled phase is mapped to the auxiliary swap dual state through a temporary storage operation before the conditional swap, a release storage operation is further executed after the local return is completed to restore the corresponding quantum state components to the original computational state. Through the return operation, the necessary release storage, and phase closure, the computational state participating in the controlled phase obtains a state related to the quantum bus logic state. The computational state that does not participate in the controlled phase remains unchanged, or only has a local phase that can be further compensated.

[0060] After the above control is completed, each selected target returns to its original two-dimensional computational subspace, controlled by a stable Bose-coded quantum bus as the common control terminal, and each multi-level superconducting qubit in the target set as the target terminal, thus obtaining the following on the target set:

[0061] Therefore, the above-mentioned multiple controlled The product of phase gates is directly generated within the same co-operation window through conditional exchanges of mutual commutation, rather than by multiple controlled... The phase-double bit gate is obtained by executing it sequentially in time.

[0062] The following will provide a more detailed explanation of the specific implementation and functionality of the Bose-coded bus-mediated superconducting parallel controlled phase gate method provided in this embodiment: In one or more embodiments, the coding subspace is a two-component cat-state coding subspace, or a compressed cat-state coding subspace obtained by applying the same compression transformation to the two-component cat-state coding subspace; based on the cat-state amplitude and the compression parameters when using the compression transformation, the effective amplitude and phase of the non-zero diagonal dominant term are determined, and the conditional half-exchange and return control are calibrated accordingly.

[0063] Specifically, the encoding subspace is a two-component cat-state encoding subspace. The orthogonal logical basis of ordinary cat states can be taken as:

[0064]

[0065] in, and These represent the normalized even-cat state and odd-cat state, respectively. The cat-state amplitude is represented by the two-component cat-state encoded subspace, which is spanned by the two orthogonal logic ground states mentioned above.

[0066] In one implementation, the same compression transform can be applied to both cat-state coding subspaces to form a compressed cat-state coding subspace. For the real-valued compression parameter r, the compression transform is defined as:

[0067] The compressed logical ground state is defined as follows:

[0068] That is, apply the same compression transformation to the two orthogonal logic ground states in the two-component cat-state encoding subspace. The corresponding compressed logic ground state is obtained, and the compressed cat state encoding subspace is formed by the compressed logic ground state.

[0069] Within the compressed logic basis, let the overlap parameter of the finite cat states be:

[0070] The physical annihilation operator in microwave storage mode The projection within the compressed cat-state coding subspace can be represented as:

[0071] in, This represents the projection operator corresponding to the compressed cat-state coded subspace. , This represents the logical Pauli operator under this compressed logic basis. Therefore, the effective magnitude of the non-zero diagonal dominant term in the projection is:

[0072] The relative off-diagonal correction is related to the finite overlap parameter u and the compression parameter r, and its relative correction amount is: Therefore, when using the compressed cat-state coding subspace, the compression parameter r will change the effective magnitude of the non-zero diagonal dominant terms that actually participate in the conditional exchange, and will correspondingly affect the finite overlap correction. Therefore, it is not possible to simply replace the ordinary cat-state coding name with the compressed cat-state coding and still use the original gate control parameters.

[0073] Directly utilizing physical annihilation operators When an effective exchange occurs between the auxiliary exchange dual state of the target multilevel superconducting qubit and the target multilevel superconducting qubit, the amplitude of the cat state is determined according to... The compression parameter *r* determines the effective amplitude and phase of the non-zero diagonal dominant term, and accordingly recalibrates the conditional half-commutation control parameters of each target so that each target satisfies the required conditional half-commutation relationship at the end of the co-operation window. Simultaneously, the corresponding local return phase is recalibrated based on the effective amplitude and phase, and leakage outside the coding subspace that may occur under compressed coding conditions is controlled. In other words, in the compressed cat-state implementation, it is necessary to redetermine the half-commutation area, return phase, and related leakage control parameters for the compressed physical operator projection.

[0074] In one implementation, the ideal dissipative stability target matching the compressed cat-state coding can be expressed as:

[0075] This expression can be used to describe an effective stabilizing operator that matches the compression coding, but it does not mean that a normal two-photon loss port automatically has the above-mentioned stabilizing effect without proper configuration.

[0076] In another implementation, when the stable Bose-coded quantum bus has not yet become entangled with other quantum systems, an inverse compression transformation can be performed on the compressed cat-state coded subspace. This is then converted to a normal cat-state working subspace; subsequently, controlled phase gate operations or full star gate operations are performed within the normal cat-state working subspace, followed by a compression transformation. This causes the quantum bus to return to the compressed cat-state encoding subspace. For this control path, the round-trip time and corresponding error between the compressed encoding and the ordinary cat-state encoding need to be factored into the overall error budget of the entry operation. Accordingly, the preparation, logical Hadamard transformation, readout, and reset operations in the compressed branch should also be transformed accordingly; for example, the logical Hadamard transformation can be expressed as:

[0077] Among them, the error coefficients obtained under ordinary cat-state coding cannot be directly used to compress cat-state branches without recalculation or calibration.

[0078] In one or more embodiments, the same effective coupling envelope and the same exchange axis phase are applied to each target in the target set; or, the control channels of each target are pre-calibrated so that each target obtains the same effective rotation angle and rotation axis to complete the conditional half-exchange within the common action window.

[0079] Specifically, the target selection and waveform control unit are used to set the selection variables corresponding to each multi-level superconducting qubit. and apply a common envelope to all selected targets. and common phase Choose a variable Used to determine whether the corresponding multi-level superconducting qubit is included in this interaction window; for Selected targets selectively activate effective switching between their auxiliary exchange dual-state and microwave storage modes, for If the target is not selected, its corresponding exchange remains closed or fully detuned.

[0080] In the typical cat-mode common axis embodiment, the controller applies a common force to each selected connection. and This allows all selected targets to exchange conditions within the same common action window. For the ordinary cat-state master implementation, the common pulse area satisfies:

[0081] in, Let T represent the cat-state amplitude, and T represent the conditional exchange duration corresponding to the co-action window. This ensures that all selected targets simultaneously reach the predetermined conditional half-exchange state within the co-action window; subsequently, return and phase compensation are performed in parallel on all selected targets.

[0082] It should be noted that the actual device parameters of different targets may differ. Therefore, even if the same raw control waveform is applied to each target without calibration, completely consistent effective conditional exchange may not be achieved. To address this, the control channels corresponding to each target can be pre-calibrated, and the corresponding control parameters can be adjusted according to the actual effective coupling relationship of each target, so that different targets ultimately obtain the same effective rotation angle and rotation axis. Thus, although the specific control parameters corresponding to each target can be calibrated individually, logically they can be equivalent to using a common effective coupling envelope and a common exchange axis phase, and completing the conditional half-exchange within the same common action window.

[0083] Furthermore, different targets do not necessarily need to use the same exchange axis phase. For the j-th target, its effective conditional exchange can be determined according to the corresponding... and Each target is calibrated separately, as long as the corresponding conditional half-commutation requirements are met at the end of the same co-operation window; the conditional commutation terms corresponding to different targets can still commutate with each other under the dominant projection approximation.

[0084] In one or more embodiments, each target is , Energy levels are used as computational states, with , The energy levels constitute the auxiliary exchange dual state; State components enter through conditional half-exchange The state, after the effective exchange ends, returns via local area. Pulse return The phase closure is achieved through pulse phase setting or virtual Z-correction. The state does not participate in condition exchange.

[0085] Specifically, each target multi-level superconducting qubit adopts a three-level scheme. For the j-th multi-level superconducting qubit, the following is retained: , and Three energy levels, of which, and As a computational state, with and This constitutes an auxiliary exchange dual state that undergoes conditional exchange with the microwave storage mode. Correspondingly, the auxiliary exchange subspace of the j-th multilevel superconducting qubit can be defined with a corresponding Pauli operator:

[0086]

[0087]

[0088] For a target set consisting of n target multilevel superconducting qubits, its logical computation space can be represented as:

[0089] in, This represents the logic space corresponding to a stable Bose-encoded quantum bus.

[0090] In the three-level scheme, The state does not participate in the selection Conditional exchanges, therefore, can be used as computational branches unaffected by the auxiliary exchanges; The quantum state component corresponding to the state is conditionally exchanged during the gate operation through an effective exchange between the auxiliary exchange dual state and the microwave storage mode. state. It is only temporarily occupied during the gate execution, and the corresponding quantum state component is returned by a return operation after the gate operation is completed. This state allows the target multi-level superconducting qubit to eventually return to its original state. and The original computational subspace constituted.

[0091] In the three-level scheme, within a suitable rotational framework, the selected multi-level superconducting qubits... The efficient exchange between assisted transition and microwave storage mode can be expressed as:

[0092] in, Indicates an effective coupling envelope. Indicates the phase of the interchange axis. The annihilation operator represents the microwave storage mode. The Hermitian conjugate operator represents the annihilation operator; Let j be the binary selection variable corresponding to the j-th multilevel superconducting qubit, and let the selected target satisfy... Unselected target satisfies Let the set of selected targets be:

[0093] For the implementation using uncompressed two-component cat-state coding, the projection of the annihilation operator of the microwave storage mode onto the cat-state logic manifold can be expressed as:

[0094] in, Let u represent the cat-state amplitude, and let u represent the finite cat-state overlap parameter. , Let represent the logical Pauli operator corresponding to the cat-state logic space. Substituting the above cat-state projection relation into the effective commutation, and absorbing the common commutation phase into the auxiliary level rotation frame and the return phase, we can obtain the projected effective Hamiltonian:

[0095] in, , , These represent the j-th target in , The corresponding Pauli operator in the auxiliary commutative subspace.

[0096] exist Under the ideal limit, the above-mentioned effective Hamiltonian for projection is further reduced to:

[0097] in, And for any different target ,satisfy:

[0098] Therefore, the ideal evolution operator can be factorized as follows:

[0099] Therefore, under the dominant projection of the cat-state logic manifold, the conditional commutation terms corresponding to different objectives commutate with each other, and their co-evolution can be decomposed into multiple conditional rotation products controlled by the same cat-state. Thus, a stable cat-state mode can simultaneously control multiple multi-level superconducting qubits within the same co-operation window without having to execute the controlled phase operations corresponding to multiple objectives sequentially in time. This commutation factorization constitutes the core physical mechanism for realizing natively parallel controlled phase gates in this embodiment.

[0100] Furthermore, after selecting the target set, selective activation is performed on the selected targets. The effective exchange between the auxiliary exchange dual-state and microwave storage mode enables all selected targets to simultaneously perform conditional half-exchanges within the same common action window. For the ordinary cat-state common-axis implementation, a common effective coupling envelope can be simultaneously applied to all selected targets. and common axis phase And make the common pulse area satisfy:

[0101] in, Let represent the cat-state amplitude, and T represent the co-action time corresponding to the conditional half-commutation. For a square wave... The corresponding action time is:

[0102] Therefore, State components enter through conditional half-exchange state.

[0103] After completing the conditional half-swap, the valid swap is terminated first, and then the local return operation is performed in parallel on all selected targets. In one implementation, a phase is applied to the selected targets. of Local Return pulse to temporarily occupy The quantum state component of the state is returned. Alternatively, an equivalent return pulse can be used to first complete the energy level return, and then the phase closure can be completed through virtual Z correction.

[0104] For a single objective, if the conditional semi-commutation is denoted as The return pulse is denoted as The corresponding closure operation can be expressed as:

[0105] And has:

[0106] and:

[0107] Right now, The state remains uninvolved in the exchange during conditional exchange and return. The state components are then passed through The state completes the condition exchange and return, and finally obtains the phase action determined by the logic state of the quantum bus.

[0108] Therefore, for the j-th target, the logical interaction between the multi-level superconducting qubit and the quantum bus can be expressed as:

[0109] in, Represents the identity operator in the logic space of the quantum bus. This represents the logical Z operator corresponding to the quantum bus. The product of the logical actions corresponding to multiple selected targets constitutes the natively parallel controlled operation. Phase gate.

[0110] Furthermore, it is important to note that in this embodiment, the multi-level superconducting quantum bit can be a transmon quantum bit. The transmon quantum bit is a weakly nonharmonic oscillator, and its... , , , These energy levels belong to the same energy ladder; the transition frequencies between adjacent energy levels are different but relatively close. Non-zero anharmonicity makes... , and Adjacent transitions can be distinguished by frequency, but in selective activation... During assisted transitions, other adjacent transitions do not automatically disappear. Therefore, during gate operation, adjustable couplers, parametric sideband frequency selection, or equivalent control can be used, combined with the setting or pre-calibration of pulse bandwidth, drive strength, coupler operating point, and phase parameters, to ensure that the microwave storage mode primarily interacts with the target transition within the common operation window. Assisted transitions establish effective swapping while suppressing , Non-target transitions and the resulting high-level leakage; for cases where there are differences in device parameters between different targets, the corresponding control channels can be pre-calibrated to enable each selected target to obtain a predetermined conditional half-exchange angle and phase within the common action window.

[0111] In one or more embodiments, each target is , Energy levels are used as computational states, with , Energy levels constitute an auxiliary exchange dual state; parallel operation is performed before conditional exchange. Temporarily store state components to state, then through and Conditional half-swap, local return and to The temporary storage is released and the system returns to the original computational subspace. The phase of each pulse is set to close the control path consisting of the temporary storage, conditional half-exchange, local return, and temporary storage release.

[0112] Specifically, the multi-level superconducting qubits for each target employ a four-level scheme. Each target still uses... , As a long-term computational state, maintain Calculate the encoding and further utilize it. , The two auxiliary energy levels constitute an auxiliary exchange dual state. Unlike the three-level scheme, this embodiment first performs a conditional exchange before... Local The pulse will participate in controlled phase operation Temporarily store state components to State, reuse , The auxiliary exchange dual state and microwave storage mode complete the conditional half-exchange.

[0113] Specifically, for each selected target in the target set, conditions are applied in parallel before the exchange begins. Local Temporary pulse, will State components are Complete transfer of state to state, and The state remains unchanged from the original computational state. After the temporary storage is complete, The state is the first state involved in conditional commutation in the auxiliary commutative double state. The state is used as the other state in the auxiliary commutative dual state and is selectively activated. The effective exchange between the auxiliary exchange dual state and the microwave storage mode enables each selected target to complete the conditional half-exchange simultaneously within the common action window.

[0114] Complete the above After the conditional half-swap, the valid swaps are terminated first, and then the selected targets are executed in parallel. Local return operation, allowing entry via conditional half-swap. The quantum state component of the state is returned. State; then, execute in parallel. Release the temporary storage operation, so that the temporary storage is... The quantum state component of the state is returned. Therefore, during the conditional exchange process, a temporary state is entered. , The quantum state components of the auxiliary energy level all return to their original state after the gate operation. , Compute the subspace. All similar pulse layers can be executed in parallel, and the return operation should be performed only after all valid swaps have been completed.

[0115] Furthermore, to ensure phase closure of the control path comprised of the aforementioned temporary storage, conditional half-commutation, local return, and release of temporary storage, the phases of the pulses at each stage need to be configured accordingly. Following the convention of operators acting sequentially from right to left, the operation sequence of the four-level scheme can be expressed as:

[0116] in, Indicates phase as of Local Temporary pulse, Indicates the exchange phase is of Conditional half-commutation Indicates phase as of Local return pulse, Indicates phase as of Cancel temporary storage pulse.

[0117] Each pulse phase satisfies:

[0118] This enables the entire control path, consisting of temporary storage, conditional half-exchange, local return, and release of temporary storage, to achieve phase closure. Setting all phases to zero can be considered a specific setting that satisfies the above phase closure relationship; furthermore, different targets can also calibrate their corresponding return phases according to their actual exchange phases, without requiring all targets to use the exact same specific phase parameters.

[0119] In a typical cat-state and corresponding square-wave coupling implementation, the gate operation time of the four-level scheme can be expressed as:

[0120] in, Indicates the amplitude of the cat state. express Effective coupling strength between assisted exchange dual-state and microwave storage mode Indicates local area The duration of the pulse.

[0121] Of course, the four-level scheme described in this embodiment is only used to illustrate the energy level closure path for realizing controlled phase gates by extending the multi-level superconducting qubits, but it does not mean that its gate fidelity is higher than that of the three-level scheme under the same hardware conditions.

[0122] In some embodiments, to quantitatively evaluate the actual performance of the aforementioned parallel controlled phase gates, process unfidelity is used as the primary evaluation index, and leakage is treated as a separate diagnostic metric. Specifically, process unfidelity is defined as:

[0123] Let the dimension of the input logic space be:

[0124] Where n represents the number of target multi-level superconducting qubits; V represents the equidistant embedding from the logical input space to the physical space. This indicates ideal gate output embedding. For a complete physical channel:

[0125] Process fidelity can be defined as:

[0126] Leakage L is defined as:

[0127] Leakage L characterizes the degree to which the system deviates from the ideal output coding space after a gate operation. The above performance evaluation is not renormalized according to the success survival probability, nor is the process fidelity recalculated after deleting the leaking branch; the process fidelity itself already includes the loss of ideal output overlap due to leakage, and leakage L is listed as a separate diagnostic quantity, which cannot be directly added to the process fidelity.

[0128] Under the conditions of the same input space, the same output projection, and the same physical channel, the unconditional average pure-state fidelity satisfies the following relationship with process fidelity and leakage:

[0129] Accordingly:

[0130] Of course, the above conversion relationships only apply to the same input space, the same output projection, and the same physical channel. The output fidelity corresponding to a single input state, the conditional fidelity corresponding to a specific measurement result, and the probability of a specific transition event are not the same evaluation objects as the process fidelity and unconditional average fidelity mentioned above.

[0131] When the numerical model itself has a coherent baseline error under zero noise conditions, the process disfidelity increment relative to the same zero-noise control sequence can also be defined:

[0132] The It is used to distinguish the process error added by additional noise, but is not equivalent to the total gate error.

[0133] Furthermore, for the general cat-state master implementation using uncompressed two-component cat-state coding, finite cat-state overlap will cause the annihilation operator projection to be dominant. In addition to the term, there is a finite overlap correction. According to the aforementioned Pauli operator convention for auxiliary transitions, this finite overlap term is expressed as:

[0134] Where u represents the finite cat-state overlap parameter. For a single target, under the conditions of nominal conditional half-exchange duration, ideal local return, and phase correction, let:

[0135] The process fidelity under finite overlap can then be expressed as:

[0136] The corresponding fidelity of the finite overlap process is:

[0137] Its leading-edge leakage is also:

[0138] Therefore, when the finite cat-state overlap parameter u is small, the process disfiguration caused by finite overlap decreases from... The order begins to appear. This relationship can be used to analyze the coherence error caused by the finite overlap of cat-state encoding, and to provide a basis for the selection of cat-state amplitude and corresponding gate control parameters.

[0139] In some embodiments, to further analyze the error sources of the above-mentioned parallel controlled phase gate under the action of actual physical noise, the first-order physical error channel during gate operation can be characterized based on the aforementioned process fidelity and leakage evaluation.

[0140] make For the ideal evolution including the control pulses in discussion, for the first... Physics-like errors, whose jump operators are denoted as Defined in the interaction representation corresponding to ideal evolution For the corresponding error rate The first-order error representation channel can be represented as:

[0141] Among them, the dissipative superoperator satisfies:

[0142] Here, T represents the duration of the analyzed gate operation or the interval of the gate operation. The above expression is used to describe the first-order dissipative correction introduced by different physical error processes based on the ideal gate evolution.

[0143] When the noiseless control sequence can accurately achieve the target gate, in the above error representation, let Represents the projection of the logical input space onto the physical space, and lets The process fidelity generated by the corresponding first-order physical error channel can be expressed as:

[0144] The corresponding first-order leakage can be expressed as:

[0145] Therefore, the contributions of physical error channels to the unfidelity of the target gate process and the leakage outside the coding subspace can be evaluated separately. It should be noted that when budgeting physical errors, the trace correction term in the process unfidelity expression cannot be omitted from the budget of simple energy level residence or transition events. Therefore, calculating the event probability based solely on the residence time of the quantum state at a certain energy level is not necessarily equivalent to the complete process unfidelity.

[0146] Furthermore, in the implementation using ordinary uncompressed cat-state coding, the shared cat-state loss due to the stable Bose-coded quantum bus and the local physical error channels of each target multi-level superconducting quantum bit can be considered separately.

[0147] In the normal cat-state dominant projection and a single native action region Internally, the single-photon loss in microwave storage mode corresponds to the shared logic in the cat-state logic space. An error channel can be represented as:

[0148] in,

[0149] in, This represents the single-photon loss rate in microwave storage mode. This represents the cat-state amplitude. Since the cat-state mode serves as the common control degree of freedom for the entire native parallel controlled phase gate operation block, a single cat-state single-photon loss corresponds to a shared error event within the native parallel gate operation block. Within a shared action interval, this shared process is counted once, and is not repeatedly counted as the number of targets n increases.

[0150] For adoption , As a computational state, and using As a three-level scheme for auxiliary exchange dual states, considering only the relaxation of adjacent levels, the corresponding first-order process disfiguration and leakage can be expressed as:

[0151] as well as:

[0152] in, ,express state The relaxation rate of the state; ,express state The relaxation rate of the state. Therefore, in this implementation, the cat-state single-photon loss is counted once as an operation block shared event, while the energy level relaxation contribution of each target multi-level superconducting qubit is counted separately according to the target.

[0153] It should be noted that when a target multi-level superconducting qubit undergoes a local physical transition, its error in the ideal gate representation can simultaneously involve both the cat-state mode and the corresponding target undergoing the transition. Therefore, it is not appropriate to simply replace this physical error with several independent ordinary two-qubit gate errors. When the environments corresponding to each target are independent, the simultaneous occurrence of independent relaxation events of two different targets in the same gate operation constitutes a higher-order contribution; however, the above conclusion does not exclude the possibility of a first-order collective error term when multiple targets are coupled with a common environment.

[0154] In some embodiments, a collective error channel arising when the cat-state mode employs finite two-photon stabilization is further considered. Regarding the two-photon stabilization effect... Under the big-cat state and the approximation satisfying the adiabatic elimination condition, we can obtain the first-order collective dissipation term corresponding to the finite stabilization:

[0155] in:

[0156]

[0157] The fidelity contribution of the first-order process generated by this finitely stabilized collective channel can be expressed as:

[0158] Furthermore, the aforementioned finite-stabilized collective channel and its first-order process disfiguration expression are based on the assumptions of the big-cat state and the adiabatic elimination approximation. To characterize the scale separation relationship between finite stabilization and common exchange as the number of targets increases, a dimensionless scale parameter can be defined:

[0159] Within the parameter range applicable to approximate analysis, it should be made .in, This indicates the number of targets participating in this parallel controlled phase gate operation. This indicates the effective coupling strength between the auxiliary exchanged dual state and the cat state mode. Indicates the two-photon stabilization intensity. This represents the cat-state amplitude. Therefore, within the effective coupling strength... Two-photon stabilization intensity and cat-state amplitude With the target number remaining unchanged, Increase, This corresponding increase further narrows the applicability of adiabatic elimination and finite stabilization approximations. Therefore, for larger target sets, the scale separation condition, occupancy outside the encoded subspace, and truncation convergence of the numerical model should be checked simultaneously to confirm that the adopted approximation model is still within the effective parameter range.

[0160] in, denoted by , where represents the two-photon stabilization intensity, and G represents the effective coupling strength between the assisted transition and the cat mode.

[0161] because Since the summation of different targets lies within the same dissipative component, this finitely stabilized error channel can contain interference terms between different targets. Although the scalar process disfiguration contribution obtained by the above analytical approximation varies linearly with the number of targets n, this does not mean that the physical error channel can be equivalently decomposed into n independent target error channels.

[0162] In one or more embodiments, the coding subspace employs uncompressed two-component cat-state coding; based on the single-photon loss rate of the acquired or calibrated microwave storage mode, the effective coupling strength of the auxiliary transition corresponding to the auxiliary exchange dual state, the relaxation rate of the relevant energy level, and the local pulse duration, the error budget during conditional exchange and local control is evaluated, the cat-state amplitude operating point is determined, and the bus preparation, stabilization control, and exchange pulse parameters are set accordingly to execute the controlled phase gate.

[0163] Specifically, the coding subspace employs uncompressed two-component cat-state coding, and an error budget is established for the actual execution sequence of the controlled phase gate to determine the cat-state amplitude. The operating point. The error budget should at least consider the single-photon loss of the microwave storage mode, the effective coupling of the auxiliary transitions corresponding to the auxiliary exchanged dual state, the error contribution from the correlated level relaxation and the local control pulse.

[0164] To adopt , As a computational state, adopt Taking the three-level scheme as an example for auxiliary switching, let's illustrate... G represents the single-photon loss rate in microwave storage mode, and G is the selected... Effective coupling strength between assisted transition and microwave storage mode , They represent state and The relaxation rate of the adjacent energy level corresponding to the state Indicates local area Pulse duration. The above parameters can be obtained from device parameters or calibrated through actual gate operation.

[0165] definition:

[0166]

[0167] The relaxation error contribution in the complete gate sequence can then be written as the sum of the contribution of the commutation interval and the contribution of the local impulse interval, i.e.:

[0168] For the three-level scheme:

[0169]

[0170] For the four-level scheme:

[0171]

[0172] Where n represents the target number in this gate operation.

[0173] Further considering decoherence, we also define:

[0174] in, And satisfy:

[0175] Its dissipation term is:

[0176] This single-operator model not only provides the decoherence intensity of adjacent energy levels, but also specifies the correlation between frequency fluctuations of different energy levels. Therefore, only the decoherence intensity of adjacent energy levels is given. This is not sufficient to uniquely determine the complete decoherent noise model.

[0177] Further definition:

[0178] For the three-level scheme:

[0179] For the four-level scheme:

[0180]

[0181] For cases where other relevant decoherence models are used, the calculation can be recalculated based on the aforementioned first-order leakage and process disfiguration expressions.

[0182] In some embodiments, when the parallel controlled phase gate serves as a coherent native gate that can be invoked by subsequent quantum operations, the stable Bose-coded quantum bus typically needs to maintain a coherent state until the return operation is complete. Therefore, single-photon loss in microwave storage mode occurs not only during the conditional exchange interval but also needs to take into account the duration of the local return pulse.

[0183] Under the same cat-state amplitude and stability conditions, the contribution of the next-order shared single-photon loss of the dominant projection can be expressed as:

[0184] in, This represents the single-photon loss rate in microwave storage mode. This represents the local area in the complete gate sequence that needs to be executed while maintaining bus coherence. Number of pulse layers. For a three-level scheme, we can take... For the four-level scheme, we can take... 3.

[0185] In a specific control timing scheme for error budget comparison, the cat-state mode can be read out immediately after the exchange. Specifically, in the implementation using a temporary storage operation, the temporary storage operation of the target multilevel superconducting qubit is performed first, followed by the preparation and stabilization of the cat-state mode; then, a conditional exchange between the cat-state mode and the target multilevel superconducting qubit is performed, and the cat-state mode is read out immediately after the common exchange window ends. The local return and release of the temporary storage operation of the target multilevel superconducting qubit are performed after the cat-state readout. In the implementation without a temporary storage operation, the above temporary storage step is omitted, and the cat-state mode is read out after the common exchange window ends, followed by the target's local return operation. See also Figure 6 Using the above timing, in the corresponding error budget, the coherent information of the cat-mode only needs to be maintained until the end of the common switching window. Therefore, the contribution of the cat-mode single-photon loss to this budget only accumulates within the common switching interval, and the duration of the subsequent target return pulse is no longer included in this cat-mode single-photon loss budget. It should be noted that this processing stems from changes in gate operation timing and error budget caliber, and does not mean that the intrinsic single-photon loss of the microwave storage mode is turned off after the switching ends; furthermore, this instantaneous readout timing is applicable to scenarios such as... Figure 6 The budget comparison shown cannot be directly used for subsequent control sequences that still need to maintain coherent information of the quantum bus, such as the aforementioned three-layer star-shaped controlled phase gate.

[0186] In some implementations, specifically for a three-level scheme, the following is taken into account: Related decoherence is obtained from the decoherence parameters of adjacent energy levels. and define:

[0187] as well as:

[0188] Where n represents the number of targets selected in this gate operation. The main characterization is the contribution of process errors associated with multi-level superconducting qubits within the conditional exchange interval. The contribution of relevant process errors during the corresponding local pulse period.

[0189] For the ordinary cat state, the selected auxiliary transition, and the leading-order error model, the cat state amplitude can be established based on the actual gate timing. The corresponding first-order process non-fidelity budget:

[0190] in, denoted by , the two-photon stabilization strength, and the last term of the above budget expression represents the leading-order error contribution generated by finite stabilization within the exchange interval; c is used to reflect the single-photon loss contribution corresponding to whether the quantum bus coherence is maintained during the return phase.

[0191] Specifically, when the controlled phase gate serves as a coherent native gate that can be reused, the quantum bus is typically maintained until the return operation is complete; therefore, single-photon loss must also be factored into the return operation duration. For the three-level scheme, if the same cat state and stability conditions are maintained during the return phase, then:

[0192] Correspondingly, the cat-state loss occurs not only during the conditional exchange interval but also during the execution of the return pulse. For a specific timing where the cat-state is read out immediately after the exchange, we can take... This situation indicates that cat-state noise accumulates only within the exchange interval and does not mean that the single-photon loss of the microwave storage mode itself is turned off.

[0193] As can be seen from the above error budget, given other parameters, the cat-state amplitude Changes in this factor will simultaneously alter the error contributions from different sources. Specifically, the main error term corresponding to the cat-state single-photon loss changes with... The error term of a multi-level superconducting qubit increases with increasing energy level, while the error term related to conditional exchange in the multi-level superconducting qubit increases with increasing energy level. Reduced. Therefore, it can be determined based on the actual acquired or calibrated data. G , , Other noise parameters used are used to determine the cat-state amplitude operating point that minimizes the overall error budget within the actual achievable range of the device. .

[0194] In the implementation that ignores the finite stabilization error term, let:

[0195]

[0196] The operating point of the cat-state amplitude then satisfies:

[0197] when Then, we can further obtain:

[0198] Therefore, the cat-state amplitude operating point corresponding to the current device parameters and the target number can be directly obtained by solving the above one-dimensional equation.

[0199] In an implementation that further retains the finite stabilization error term, let:

[0200] The corresponding stationary point equation can be expressed as:

[0201] The above equations can be numerically solved within the range that satisfies the applicable conditions of the adopted error model and the reach of the actual device, so as to obtain the corresponding cat-state amplitude operating point.

[0202] Determining the operating point of the cat-state amplitude Subsequently, the preparation parameters and stabilization control parameters of the stable Bose-encoded quantum bus can be set accordingly. Combined with the effective coupling strength G corresponding to the auxiliary exchange dual state, the amplitude, duration, and related control parameters of the conditional exchange pulse can be set to ensure that the conditional exchange satisfies the corresponding half-exchange condition. At the same time, the local return control can be set according to the local pulse duration and the corresponding energy level relaxation parameters, thereby executing the controlled phase gate.

[0203] In one or more embodiments, a controlled phase gate with a quantum bus as the control terminal is used to construct a star-shaped controlled phase gate between superconducting qubits, including: selecting another multi-level superconducting qubit that does not belong to the target set as the control qubit; preparing the quantum bus into a superposition state of equal amplitude and in-phase of two logical ground states; executing a controlled phase gate once with the control qubit as a single target and applying a logical Hadamard transform to the quantum bus; executing a parallel controlled phase gate within a common interaction window with the multi-level superconducting qubit in the target set as the target, then applying a logical Hadamard transform to the quantum bus again, and executing a controlled phase gate again with the control qubit as a single target; de-entanglement of the quantum bus with the control qubit and the target set and returning to the equal amplitude and in-phase superposition state, outputting a controlled phase gate with the control qubit as the common control terminal and the multi-level superconducting qubit in the target set as the target terminal. The product of phase gates.

[0204] Specifically, the natively parallel controlled phase gate, with a stable Bose-coded quantum bus as the common control terminal, can be further used to construct a star-shaped controlled phase gate between multiple superconducting qubits. Another multi-level superconducting qubit not belonging to the target set is selected as the control qubit, and a one-to-many controlled phase relationship is established between the control qubit and multiple multi-level superconducting qubits in the target set through the stable Bose-coded quantum bus as an intermediary.

[0205] make Let T represent the control qubit, and let T represent the qubit that does not contain a control qubit. The target index set corresponding to the index, the target multi-level superconducting quantum bit set is represented as: Before executing the star-shaped controlled phase gate, the quantum bus is prepared as a superposition of its two logic ground states with equal amplitude and in phase, i.e.:

[0206] In this context, the subscript C indicates a stable Bose-coded quantum bus.

[0207] Then, the first layer of control qubit-quantum bus association operation is performed. Specifically, this involves controlling the qubits. As a single objective, the natively controlled phase gate between the aforementioned stable Bose-coded quantum bus and the multi-level superconducting qubit is invoked. Execute once between the quantum bus C and Operation. This operation belongs to the aforementioned native parallel controlled phase gate in the target number A special case of this. After completing the single-target controlled phase operation, a logical Hadamard transform is applied to the quantum bus. This will control the quantum bits. The conditional phase relationship established with the quantum bus C is converted into a logical relationship suitable for subsequent one-to-many fan-out operations.

[0208] Next, perform the second-layer quantum bus-target set native one-to-many fan-out operation. Maintain control of the qubits. Do not participate in this collaborative window, and set the target set As the selected target set, the aforementioned native parallel controlled phase gate is invoked within the same common action window, making the quantum bus C the common control terminal, and simultaneously executing on each multi-level superconducting qubit in the target set:

[0209] Here, the product represents a native parallel operation completed within a common action window, rather than executing multiple time-sequential two-bit gates sequentially according to the number of target qubits.

[0210] After completing the native parallel controlled phase gate between the quantum bus and the target set, a logical Hadamard transform is applied to the quantum bus again. Subsequently, control of the qubits was used again. As a single objective, in controlling qubits A second execution between the quantum bus C and the quantum bus C The operation reverses the conditional association between the control qubits and the quantum bus established in the first-level operation. Thus, the entire star gate consists of two single-target controlled phase operations between the control qubits and the quantum bus, one natively parallel controlled phase operation between the quantum bus and the target set, and two logical Hadamard transformations of the quantum bus.

[0211] According to the convention that operators act from right to left, the overall operator of the above star gate can be represented as:

[0212] Among them, the one on the right and This corresponds sequentially to the first layer of association operations and the first Hadamard transformation of the quantum bus logic; the middle one... The corresponding quantum bus performs a native one-to-many parallel controlled phase operation on the target set; on the left and This is then used to reverse the aforementioned condition association.

[0213] For any control qubit and target set of input states When the quantum bus is initially in At that time, the above overall operation satisfies:

[0214] Thus, the intermediate layer is a native parallel process executed by the quantum bus as the common control terminal. The gate is converted into a control for the qubits. As a common control terminal, each multi-level superconducting quantum bit in the target set serves as the target terminal. As the target end of the star-shaped controlled Phase gate product:

[0215] This enables a single controllable multilevel superconducting qubit to simultaneously form a controlled phase relationship with multiple target multilevel superconducting qubits.

[0216] Ideally, after completing the third entanglement layer, the quantum bus C and the control qubits... And all target qubits are unentangled and deterministically return to the initial superposition state of equal amplitude and in-phase. Therefore, after the star-shaped controlled phase gate is completed, the quantum bus can remain in this logic state for subsequent gate operations to call again, without having to make the measurement of the quantum bus a necessary step for the star gate to complete normally.

[0217] In one diagnostic implementation, after completing the star gate, X-basis measurements and necessary resets can be performed on the quantum bus. Ideally, the quantum bus returns... The corresponding X-basis measurements yield the expected results; deviations from the expected measurement results can serve as physical indicators of this star gate operation. However, this physical indicator is only optional diagnostic information; the absence of an indicator does not guarantee that the entire gate operation is error-free, and this indicator is not equivalent to the verification syndrome or leakage criterion in quantum error correction.

[0218] In some embodiments, the aforementioned parallel controlled phase gate and related control sequence can be verified through numerical calculations. It should be noted that the results in this embodiment are analytical calculation, projection model simulation, or full oscillator numerical verification results, and should not be confused with device experimental results. Different models may have different input spaces, noise conditions, and physical degrees of freedom; therefore, each numerical result should be used within the range of its corresponding model assumptions and parameters.

[0219] In one implementation, the aforementioned method can be used. , As a computational state, with As a three-level scheme for assisting exchanged dual states, its process disfiguration under given device parameters is numerically calculated. For example, taking the cat-state amplitude... Effective coupling strength Local area Pulse duration By setting the corresponding cat-state lifetime, relaxation time of multi-level superconducting qubit energy level, and decoherence time of adjacent energy levels, different energy level control schemes can be compared in a numerical model that retains multiple transmon energy levels and non-resonant sidebands.

[0220] Figure 6 In the diagram, A represents the three-level scheme, and A-2 represents the four-level temporary storage scheme. The comparison focuses on a single target, employing a strongly stable projection model, retaining seven multi-level superconducting qubit energy levels and non-resonant sidebands, with anharmonicity set to -220 MHz. Under the aforementioned amplitude, effective coupling strength, and local pulse duration conditions, the cat-state single-photon lifetime is 416.782 μs, the first excited state relaxation time is 80 μs, and the relaxation rates of each excited level are proportional to their energy level indices. Starting from the lowest energy level, the decoherence times of adjacent energy levels are successively set to 150, 75, 30, 15, 8, and 5 μs, and the aforementioned single-operator correlation decoherence model is used. This comparison uses a timing sequence where temporary storage precedes cat-state preparation, cat-state readout occurs immediately after exchange, and target return occurs later; therefore, cat-state single-photon loss only accumulates within the common exchange window. This data does not directly represent... Figure 5 The three-segment star gate needs to maintain the performance of bus coherent information.

[0221] Figure 6 The process fidelity increment used is the process fidelity of the noisy channel minus the zero-noise coherent baseline of the same control sequence. Figure 6(a) According to the first-order budget of the increment decomposed by single-photon loss, energy level relaxation and related decoherence, the sum of A and A-2 is about 0.401% and 0.917%, respectively; at the same reference point, the total numerical process fidelity including the coherent baseline is about 0.430% and 0.932%, respectively, and should not be confused with the above increment. Figure 6 In (b), lines represent first-order predictions, dots represent projected Lindblad values, and asterisks indicate the analytical amplitude squared operating point of the leading-order model, with A and A-2 approximately 9.00 and 26.45, respectively. This operating point is used for calibration reference and is not the exact numerical optimum of the total error of the complete channel. Figure 6 It also does not include the verification results of the four objectives of finitely stabilized full oscillators.

[0222] Furthermore, in the numerical verification of a full oscillator with a four-target native parallel controlled phase gate, the aforementioned three-level scheme can be selected, taking... , , It disables single-photon loss in microwave storage mode and slow noise in multi-level superconducting qubits, while retaining finite stabilization and local return pulses, and performs numerical verification on the complete logic input space, rather than calculating only a pre-prepared input state.

[0223] Under the above parameter conditions, when the oscillator cutoff is 40 and 50 respectively, the process disfiguration is approximately:

[0224]

[0225] Corresponding target leakage The average is approximately:

[0226] Therefore, at this specific verification point, the difference in fidelity between the two oscillator cutoff processes is approximately [missing information]. This indicates that the verification point has good numerical convergence within the oscillator cutoff range used.

[0227] It should be noted that the above numerical results represent a specific verification point obtained under given finite stabilization conditions, with a process error of approximately 2.4405%. This value cannot be interpreted as the actual gate performance under conditions including all hardware noise, nor can it be used as the upper or lower limit of the performance of the technical solution of this application under arbitrary device parameters.

[0228] In the above numerical verification, target leakage This parameter is used to statistically determine the probability that the target multi-level superconducting qubit will leave its computational subspace. This parameter is not the same evaluation metric as the aforementioned joint encoding leakage L; joint encoding leakage also involves the joint output projection of the quantum bus encoding space and the target computational space. Therefore, target leakage should not be considered solely as a metric. Directly substitute the aforementioned conversion relationship between fidelity and average fidelity. Under this verification condition, the probability that the quantum bus deviates from the cat-state logic manifold is approximately... This value should be evaluated separately from the target leakage.

[0229] For the same verification point, the error of the first-order analytical process under the aforementioned finite two-photon stabilization condition can be determined by:

[0230] Make an estimate. When , , At that time, its analytical estimate was approximately 0.02545. This analytical result is on the same order of magnitude as the numerical verification result of the full oscillator mentioned above, but the two are not strictly equal. This is because the analytical expression was obtained under approximate conditions such as the big cat state and adiabatic elimination, while the full oscillator model retains more complete physical degrees of freedom. Therefore, the above analytical expression is mainly used for error trend analysis and parameter calibration, and should not be regarded as an accurate full oscillator result under arbitrary parameter conditions.

[0231] In other embodiments, numerical verification can also be performed on the aforementioned three-layer star-shaped controlled phase gate mediated by a stable Bose-encoded quantum bus. For example, specific control qubits and target qubit input states can be selected, and under ideal instantaneous bus logic Hadamard transform conditions, a full oscillator test can be performed on the complete star-shaped gate sequence consisting of a control qubit-quantum bus single-target controlled phase gate, a quantum bus-target set parallel controlled phase gate, and a quantum bus-control qubit decoupling. This numerical test can be used to verify the executability of the aforementioned star-gate control sequence under selected input and model conditions.

[0232] Second Embodiment Based on the same concept, see Figure 2This embodiment also provides a Bose-coded bus-mediated superconducting parallel controlled phase gate system, which can be used to execute the Bose-coded bus-mediated superconducting parallel controlled phase gate method as described in any one of the first embodiments. The system includes: a resonant structure providing a microwave storage mode, multiple multi-level superconducting qubits, a selectable coupling channel connecting the microwave storage mode and each qubit to assist in exchanging dual states, and a controller connected to the resonant structure, the coupling channel, and the local control ports of each qubit. The controller is used to prepare and stabilize a two-dimensional logical encoding subspace of the microwave storage mode, such that the projection of the annihilation operator of the microwave storage mode into the encoding subspace has the same mode and a phase difference on two orthogonal logical ground states. The controller selects multi-level superconducting qubits to form a target set, suppresses non-target transitions and exchanges of unselected multi-level superconducting qubits, and activates effective exchanges involving annihilation operators and their Hermitian conjugate operators through coupling channels, enabling each target to simultaneously complete conditional half-exchanges within a common window. Under the projection approximation corresponding to the dominant term, the conditional exchange terms of each target commutate with each other. The controller then ends the effective exchange, and performs return, necessary release of temporary storage, and phase closure in parallel through the local control port, so that each target returns to its original computational subspace. The computational states that do not participate in the controlled phase remain unchanged or only have compensable phases. The output is a controlled phase with the quantum bus as the common control terminal and the selected target as the target terminal. The product of phase gates.

[0233] Specifically, the control system includes a resonant structure, multiple multi-level superconducting qubits, selectable coupling channels connecting the microwave storage mode provided by the resonant structure to the auxiliary exchange dual state of each multi-level superconducting qubit, and a controller connected to the resonant structure, the selectable coupling channels, and the local control port of each multi-level superconducting qubit. The resonant structure provides a microwave storage mode as a stable Bose-coded quantum bus; each selectable coupling channel, under the control of the controller, selectively establishes effective exchanges between the auxiliary exchange dual state of the corresponding multi-level superconducting qubit and the microwave storage mode; the local control port executes corresponding return pulses, temporary storage and de-temporalization operations, and necessary phase corrections. The controller coordinates the resonant structure, stabilization control, the selectable coupling channels corresponding to each target, and the local control port to complete target selection, common condition exchange, and post-gate closure return.

[0234] The control system can also be configured with pump or nonlinear units for preparing, stabilizing, and maintaining the microwave storage mode, ensuring that the microwave storage mode remains stably constrained during gate operation execution. For a common-axis implementation of the cat-state, the control system may include a microwave storage mode stabilized within the cat-state logic manifold, N multi-level superconducting qubits capable of establishing effective exchanges with the microwave storage mode, a target selection and waveform control unit for determining the current set of selected targets, local control ports for each multi-level superconducting qubit, and pump or nonlinear units for preparing, stabilizing, and maintaining the cat-state.

[0235] The controller first controls the formation and stabilization of the microwave storage mode within the two-dimensional logical encoding subspace. Let P be the projection operator corresponding to the two-dimensional logical encoding subspace. , Define two orthogonal logical ground states and define logical operators:

[0236] Annihilation operators actually involved in the exchange in microwave storage mode Within the two-dimensional logical encoding subspace, the following conditions are met:

[0237] in, This constitutes a non-zero diagonal dominant term, which has the same modulus and phase difference in action on the two orthogonal logic ground states. ; The phase can be included in the control calibration parameters stored by the controller. The controller suppresses [the phase] through coded parameter settings, stable control, and corresponding gate control processes. The projection correction and leakage caused by external effects on the encoded subspace enable the microwave storage mode to serve as the common control degree of freedom for subsequent parallel controlled phase gates.

[0238] Each multilevel superconducting qubit possesses a two-dimensional computational subspace and an auxiliary exchange dual state. For the j-th multilevel superconducting qubit, its two-dimensional computational subspace can be denoted as... , Let its auxiliary exchange dual state be denoted as , The auxiliary exchanged doublet contains at least one energy level located outside the computational subspace. The computational state involved in this controlled phase operation can be directly used as the first state of the auxiliary exchanged doublet. Alternatively, a temporary storage operation can be performed first through the local control port to map the corresponding computing state to... .

[0239] During a parallel controlled phase gate operation, the controller determines the target set A based on the gate operation to be performed and sends a gating signal to the corresponding selectable coupling channel. For multi-level superconducting qubits belonging to target set A, the controller activates the annihilation operator between its auxiliary exchanged dual state and microwave storage mode. and its Hermitian conjugate operator Effective exchanges are participated in; for unselected multi-level superconducting qubits, the corresponding exchange channels are kept closed or fully detuned, while non-target transitions are suppressed so that they do not participate in the gate operations within the current interaction window.

[0240] Effective switching can be achieved through tunable couplers, multi-level superconducting qubit frequency modulation, resonant mode frequency modulation, parametric sidebands, or Raman-type two-tone driving. In a typical cat-state implementation, a fixed-frequency multi-level superconducting qubit can be used, and the parametric sideband between the auxiliary transition and the cat-state mode can be selectively activated through tunable couplers or coupling port parameter modulation.

[0241] Under the projection approximation corresponding to the non-zero diagonal dominant term, the controller sets a corresponding effective coupling envelope for the j-th target in the target set. and interchange axis phase The corresponding conditional exchange can be expressed as:

[0242] in,

[0243] For different objectives, the corresponding They commutate with each other. Therefore, the controller enables multiple selected targets to simultaneously perform conditional exchanges within the same co-operation window, and ensures that each target satisfies its corresponding conditional half-exchange requirements at the end of the co-operation window. Each target can use separately calibrated effective coupling and exchange axis phases, or it can use the same effective coupling envelope and the same exchange axis phase, or it can obtain the same effective rotation angle and rotation axis through pre-calibration of each channel.

[0244] In a common-axis cat-mode implementation, a binary selection variable can be set by the controller for each connection. Among them, the selected target satisfies Unselected multi-level superconducting qubits satisfy For all selected targets, the controller applies a common effective coupling envelope. and common axis phase .

[0245] The controller can store the target set, the effective operating area and phase parameters corresponding to each selectable coupling channel, the local return sequence, and the release sequence corresponding to the temporary storage implementation. After completing the conditional half-exchange of each target, the controller first ends the effective exchange between each selected target and the microwave storage mode, and then applies phase-matched return pulses in parallel through the local control ports corresponding to each multi-level superconducting qubit, returning the quantum state components temporarily occupying the auxiliary energy level to the corresponding computational state; for targets that used temporary storage operations before the conditional exchange, the release operation is then performed, and phase closure is completed through pulse phase setting or virtual Z correction.

[0246] After the above control is completed, each selected target returns to its original two-dimensional computational subspace. The computational branches involved in the controlled phase receive the phase action determined by the logic state of the quantum bus, while the computational states not involved in the controlled phase remain unchanged or only generate a compensable local phase. Thus, using a stable Bose-coded quantum bus formed in microwave storage mode as the common control terminal and multi-level superconducting qubits in the selected target set as the target terminals, the following is output in the logic space:

[0247] That is, multiple controlled entities are formed within a single interaction window. The product of phase gates, rather than executing multiple two-bit controlled phase gates sequentially according to the target number.

[0248] In one or more embodiments, the controller is configured to apply the same effective coupling envelope and the same exchange axis phase to each target in the target set; or to precalibrate the control channels of each target to give each target the same effective rotation angle and rotation axis to complete the conditional half-exchange within the common action window.

[0249] Specifically, the target selection and waveform control unit in the control system are used to set the selection variables corresponding to each target. Common and effective coupling envelope and common exchange axis phase .for The goal is for the controller to activate effective switching between the corresponding auxiliary switching dual state and microwave storage mode; for For unselected multi-level superconducting qubits, the corresponding exchange is turned off or fully detuned, so that the unselected multi-level superconducting qubits do not participate in the conditional exchange within the current interaction window.

[0250] For the common axis implementation using standard cat-state coding, the controller applies a common signal to all selected connections. and And control the duration of the common action window so that the common pulse area meets the conditional half-exchange requirement:

[0251] For the effective coupling envelope of a square wave In this case, the corresponding exchange time is:

[0252] This ensures that all selected targets in the target set complete a conditional half-exchange at the end of the same interaction window.

[0253] In practical devices, the effective parameters of each multi-level superconducting qubit and its corresponding coupling channel can differ. Therefore, in another equivalent implementation, the controller pre-calibrates the control channel corresponding to each target and sets the control parameters of each channel based on the pre-calibration results, so that different targets ultimately obtain the same effective rotation angle and rotation axis within the common interaction window. That is, it is not required that different targets use exactly the same physical driving parameters before calibration, as long as each target obtains the equivalent conditional exchange action after pre-calibration.

[0254] The controller can save the target set, the effective area and phase parameters corresponding to each coupling channel, and call the selectable coupling channel corresponding to each target according to the pre-calibration parameters. After completing the pre-calibration, the controller simultaneously activates each selected target within the same common action window, so that each target reaches the predetermined conditional half-exchange state; after the conditional exchange is completed, the effective exchange is ended and parallel return and phase closure are performed according to the aforementioned implementation method.

[0255] In one or more embodiments, the controller is further configured to select a multi-level superconducting qubit that does not belong to the target set as the control qubit, and control the bus logic basis transformation port to sequentially execute the controlled phase gate between the control qubit and the quantum bus, the bus logic Hadamard transformation, the parallel controlled phase gate between the quantum bus and the target set, the bus logic Hadamard transformation, and the controlled phase gate between the control qubit and the quantum bus, so that the quantum bus, which is initially in a superposition state of equal amplitude and in phase of two logic ground states, returns to the initial state and is unentangled, forming a star-shaped controlled phase gate between superconducting qubits with the control qubit as the common control terminal.

[0256] Specifically, the control system is also equipped with a bus logic base transformation port. The controller can call the bus logic base transformation port to perform logic base transformation on the stable Bose-coded quantum bus, and further combine the aforementioned controlled phase gates with the quantum bus as the common control terminal into star-shaped controlled phase gates between superconducting qubits. The controller stores the corresponding target set, the single-target controlled phase gate calling order, and the bus logic base transformation order, and coordinates the calling of each coupling channel and the bus logic base transformation port according to a predetermined control sequence.

[0257] The controller selects a multi-level superconducting qubit from among multiple multi-level superconducting qubits that does not belong to the target set as the control qubit. For example, let... Let T represent the control qubit, and let T represent the absence of... The target index set corresponding to the index, the target set is represented as Before executing the star-shaped controlled phase gate, the controller first prepares the stabilized Bose-coded quantum bus C into a superposition of two logic ground states with equal amplitude and in phase. .

[0258] Subsequently, the controller first invokes the single-target controlled phase gate once to control the qubit. Execution between quantum bus C This single-target controlled phase gate can be implemented using the aforementioned native controlled phase gate between the stable Bose-coded quantum bus and the multi-level superconducting qubits, when the target quantity is 1. After completing the single-target controlled phase gate, the controller applies the first logical Hadamard transformation to the quantum bus through the bus logic basis transformation port. .

[0259] After the first logical Hadamard transformation is completed, the controller selects multiple multi-level superconducting qubits from the target set as the chosen targets, and calls the aforementioned parallel controlled phase gate within a common action window, making the quantum bus C the common control terminal, and simultaneously executing:

[0260] During the execution of the intermediate parallel controlled phase gate, the control qubits It does not belong to the target set and does not participate in parallel condition exchange within the co-action window.

[0261] After completing the parallel controlled phase gate between the quantum bus and the target set, the controller calls the bus logic basis transformation port again to apply a second logical Hadamard transformation to the quantum bus. Subsequently, the single-target controlled phase gate is invoked again to control the qubit. A second execution between the quantum bus C and the quantum bus C This reverses the control of the qubit. Conditional association with the quantum bus C.

[0262] According to the convention that operators act from right to left, the overall star gate sequence executed by the above controller can be represented as:

[0263] For any control qubit and target set of input states When the quantum bus is initially in At that time, the above overall operation satisfies:

[0264] Thus, the parallel controlled phase gate executed by the quantum bus as the common control terminal in the intermediate layer is converted into a control gate for the qubits. As a common control terminal, each multi-level superconducting quantum bit in the target set serves as the target terminal. As a star-shaped controlled phase gate at the target end.

[0265] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments. Even if various changes are made to the present invention, if these changes fall within the scope of the claims of the present invention and their equivalents, they shall still fall within the protection scope of the present invention.

Claims

1. A superconducting parallel controlled phase gate method mediated by a Bose-coded bus, characterized in that, include: A two-dimensional logical encoding subspace is prepared and stabilized for use as a microwave storage mode under a stable Bose-encoded quantum bus; wherein the projection of the annihilation operator of the microwave storage mode into the encoding subspace has a non-zero diagonal dominant term, the dominant term having the same modulus and phase difference on two orthogonal logical ground states. By using encoding parameters and stability control, corrections deviating from the dominant term and leakage outside the encoding subspace are suppressed; Select one or more multi-level superconducting qubits to form a target set, each target having a two-dimensional computational subspace and an auxiliary exchanged dual state containing at least one energy level outside the computational subspace; make the computational state participating in the controlled phase directly as the first state of the auxiliary exchanged dual state, or map it to the first state through a temporary storage operation; The effective exchange between the auxiliary exchange dual state and the microwave storage mode, involving the annihilation operator and its Hermitian conjugate operator, is selectively activated, while the exchange of non-target transitions and unselected multi-level superconducting qubits is suppressed; the conditional half-exchange of each target is completed simultaneously within the common action window; under the projection approximation corresponding to the dominant term, the conditional exchange terms of different targets commutate with each other; The effective exchange ends, and the local return of each target, the release of temporary storage when temporary storage is used, and the phase closure are executed in parallel, so that each target returns to its original computational subspace. The computational states that did not participate in the controlled phase remain unchanged or only have compensable phases. The controlled phase is output with the quantum bus as the common control terminal and the selected target as the target terminal. The product of phase gates.

2. The superconducting parallel controlled phase gate method mediated by a Bose-coded bus as described in claim 1, characterized in that, The coding subspace is a two-component cat-state coding subspace, or a compressed cat-state coding subspace obtained by applying the same compression transformation to the two-component cat-state coding subspace; based on the cat-state amplitude and the compression parameters when using the compression transformation, the effective amplitude and phase of the non-zero diagonal dominant term are determined, and the conditional half-exchange and return control are calibrated accordingly.

3. The superconducting parallel controlled phase gate method mediated by a Bose-coded bus as described in claim 1, characterized in that, For each target in the target set, apply the same effective coupling envelope and the same exchange axis phase; or, pre-calibrate the control channels of each target to make each target obtain the same effective rotation angle and rotation axis, so as to complete the conditional half-exchange within the common action window.

4. The superconducting parallel controlled phase gate method mediated by a Bose-coded bus as described in claim 1, characterized in that, Each objective , Energy levels are used as computational states, with , The energy levels constitute the auxiliary exchange dual state; The state component enters through conditional half-exchange The state, after the effective exchange ends, returns via local access. Pulse return The phase closure is achieved through pulse phase setting or virtual Z-correction. The state does not participate in the condition exchange.

5. The superconducting parallel controlled phase gate method mediated by a Bose-coded bus as described in claim 1, characterized in that, Each objective , Energy levels are used as computational states, with , The energy levels constitute the auxiliary exchange dual state; before the conditional exchange, parallel processing is performed. Temporarily store state components to state, then through and Conditional half-swap, local return and to The temporary storage is released and the system returns to the original computation subspace. The phase of each pulse is set to close the control path consisting of the temporary storage, conditional half-exchange, local return, and temporary storage release.

6. The superconducting parallel controlled phase gate method mediated by a Bose-coded bus as described in claim 2, characterized in that, The encoded subspace uses uncompressed two-component cat-state encoding; based on the single-photon loss rate of the microwave storage mode, the effective coupling strength of the auxiliary transition corresponding to the auxiliary exchange dual state, the relaxation rate of the relevant energy level, and the local pulse duration, the error budget during conditional exchange and local control is evaluated, the cat-state amplitude operating point is determined, and the bus preparation, stabilization control, and exchange pulse parameters are set accordingly to execute the controlled phase gate.

7. The superconducting parallel controlled phase gate method mediated by a Bose-coded bus as described in claim 1, characterized in that, Using the controlled phase gate with the quantum bus as the control terminal to construct a star-shaped controlled phase gate between superconducting qubits includes: Another multi-level superconducting qubit that does not belong to the target set is selected as the control qubit, and the quantum bus is prepared as a superposition of two logic ground states with equal amplitude and in phase. The controlled phase gate is executed once with the control qubit as a single target, and a logical Hadamard transform is applied to the quantum bus; With the multi-level superconducting qubit in the target set as the target, the parallel controlled phase gate is executed within the common action window. Then, a logical Hadamard transform is applied to the quantum bus again, and the controlled phase gate is executed again with the control qubit as the single target. The quantum bus is de-entangled with the control qubits and the target set, returning to the equal-amplitude, in-phase superposition state. The output is a controlled system with the control qubits as the common control endpoint and the multi-level superconducting qubits in the target set as the target endpoints. The product of phase gates.

8. A superconducting parallel controlled phase gate system mediated by a Bose-coded bus, characterized in that, include: The system provides a resonant structure for microwave storage mode, multiple multi-level superconducting qubits, a selectable coupling channel connecting the microwave storage mode with the auxiliary exchange dual state of each qubit, and a controller connected to the resonant structure, the coupling channel and the local control port of each qubit. The controller is used to prepare and stabilize a two-dimensional logic encoding subspace of the microwave storage mode, such that the projection of the annihilation operator of the microwave storage mode into the encoding subspace has the same mode and phase difference on two orthogonal logic ground states. The non-zero diagonal dominant term is used, and projection correction and external leakage of the coding subspace are suppressed by encoding parameters and stability control; Each of the multi-level superconducting qubits has a two-dimensional computational subspace and an auxiliary exchanged dual state containing at least one energy level outside the computational subspace. The computational state participating in the controlled phase is directly located in the first state of the auxiliary exchanged dual state or mapped to the first state through a temporary storage operation. The controller is also used to select multi-level superconducting qubits to form a target set, suppress non-target transitions and the exchange of unselected multi-level superconducting qubits, and activate the effective exchange involving the annihilation operator and its Hermitian conjugate operator through the coupling channel, so that each target can complete the conditional half-exchange simultaneously within the common action window; under the projection approximation corresponding to the dominant term, the conditional exchange terms of each target commutate with each other. The controller then terminates the effective exchange and performs parallel return, necessary release of temporary data, and phase closure through the local control port, causing each target to return to its original computational subspace. The computational states that did not participate in the controlled phase remain unchanged or only have compensable phases. The controller outputs the controlled phase with the quantum bus as the common control terminal and the selected target as the target terminal. The product of phase gates.

9. The superconducting parallel controlled phase gate system mediated by a Bose-coded bus as described in claim 8, characterized in that, The controller is configured to apply the same effective coupling envelope and the same exchange axis phase to each target in the target set; or to pre-calibrate the control channels of each target to give each target the same effective rotation angle and rotation axis, so as to complete the conditional half-exchange within the common action window.

10. The superconducting parallel controlled phase gate system mediated by a Bose-coded bus as described in claim 8, characterized in that, The controller is also used to select a multi-level superconducting quantum bit that does not belong to the target set as the control quantum bit, and control the bus logic basis transformation port to sequentially execute the controlled phase gate between the control quantum bit and the quantum bus, the bus logic Hadamard transformation, the parallel controlled phase gate between the quantum bus and the target set, the bus logic Hadamard transformation, and the controlled phase gate between the control quantum bit and the quantum bus, so that the quantum bus, which is initially in a superposition state of equal amplitude and in phase of two logic ground states, returns to the initial state and is unentangled, forming a star-shaped controlled phase gate between superconducting quantum bits with the control quantum bit as the common control terminal.

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