A method of implementing a hybrid dimensional quantum phase gate in a superconducting quantum system

Abstract

This invention belongs to the field of superconducting quantum computing technology and relates to a method for realizing a mixed-dimensional quantum phase gate in a superconducting quantum system. The system includes: a microwave cavity as a quantum resonator for carrying photons and encoding target qubits; a superconducting flux three-level qubit as a three-level quantum system used as control bits, coupled to the microwave cavity via a capacitor; and a classical microwave pulse source for applying a controllable microwave driving field to the superconducting flux three-level qubit. The method utilizes the dispersive coupling between the superconducting flux three-level qubit and the microwave cavity in the superconducting quantum system, combined with the controllable microwave driving field applied to the superconducting flux three-level qubit, to deterministically control the phase of the cavity field by the quantum state of the superconducting flux three-level qubit through a one-step evolution process. This invention has a 100% success rate and its operational reliability is far superior to probabilistic optical solutions.

Description

Technical Field

[0001] This invention belongs to the field of quantum computing technology, specifically relating to a method for realizing a mixed-dimensional quantum phase gate in a superconducting quantum system. Background Technology

[0002] In the literature (Linxiang Zhou, Qiao Xu, Tianfeng Feng, Xiaoqi Zhou, Experimental realization of a three-photon asymmetric maximally entangled state and its application to quantum state transfer, Sci. Adv. 10, eadj9251(2024)), the success rate of preparing a three-photon asymmetric maximally entangled state ((2,2,4) state) in an optical system is low, with an overall success rate of only 1 / 54. Even with optimization (such as performing specific basis measurements on the auxiliary photon and applying a Z operation), the success rate can only be increased to 1 / 27. Such a low success rate severely limits the practical application value of this experimental scheme. In quantum information processing, a high success rate is a fundamental requirement for realizing scalable and practical quantum networks and quantum computing. The low success rate mainly stems from the linear optical elements used in the experiment and the post-selection-based manipulation method, which are inherently probabilistic and extremely sensitive to experimental losses and noise.

[0003] Current quantum computing technology is mainly based on two- or three-dimensional qubit systems, which have inherent limitations in terms of information encoding density and computational efficiency. Existing technologies face the following key problems:

[0004] 1. Dimensionality limitations and interface deficiencies: Most existing quantum gate schemes are limited to single-dimensional systems, such as all-qubit or all-qutrit systems, lacking a hybrid-dimensional quantum interface that can directly and efficiently interconnect qubits of different dimensions, such as qutrit-control and qubit-target. This leads to complex encoding conversions when integrating quantum resources of different dimensions, increasing circuit complexity and error rate.

[0005] 2. Operational complexity and nondeterminism: Many existing solutions, especially those involving high-dimensional or mixed-dimensional systems, often require multi-step operations or auxiliary systems, making it difficult to achieve one-step, deterministic operations, thereby reducing the overall efficiency and reliability of the system.

[0006] Practical feasibility challenges: In superconducting quantum systems, there are various non-ideal coupling and decoherence effects, which pose a huge challenge to realizing high-fidelity mixed-dimensional quantum gates. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for realizing a mixed-dimensional quantum phase gate in a superconducting quantum system.

[0008] To achieve the objectives of this invention, the following technical solutions are adopted.

[0009] A superconducting quantum system, comprising:

[0010] A microwave cavity, as a quantum resonator used to carry photons and encode target qubits;

[0011] The superconducting flux three-level quantum bit, as a three-level quantum system used as a control bit, is coupled to a microwave cavity via a capacitor;

[0012] A classic microwave pulse source is used to apply a controllable microwave driving field to a superconducting flux three-level qubit.

[0013] Furthermore, quantum information is encoded in the vacuum state and single-photon state of the microwave cavity.

[0014] Furthermore, the energy levels of the three-level quantum system, from lowest to highest, are as follows: .

[0015] A method for realizing a mixed-dimensional quantum phase gate using a superconducting quantum system: Utilizing the dispersive coupling between a superconducting flux three-level qubit and a microwave cavity in the superconducting quantum system, and combining this with a controllable microwave driving field applied to the superconducting flux three-level qubit, a deterministic conditional control of the cavity field phase by the quantum state of the superconducting flux three-level qubit is achieved through a one-step evolution process; wherein:

[0016] The energy levels of the superconducting flux three-level quantum bit and the dispersion coupling are configured as follows:

[0017] Microwave cavity and superconducting flux three-level quantum bit The transitions involve dispersive coupling and satisfy the large detuning condition: detuning ≫ coupling strength; simultaneously, the microwave cavity and the superconducting flux three-level qubit... and High degree of mistuning in the transition;

[0018] Controllable microwave driving field applied to superconducting flux three-level qubits The transition is on the high level and satisfies the large detuning condition: detuning amount ≫ Rabi frequency.

[0019] Furthermore, the derivation process of the effective characterization form of the superconducting quantum system dynamics is as follows:

[0020] Based on the configuration of energy levels and dispersion coupling, the Hamiltonian of a superconducting quantum system under the dispersion coupling scenario and the rotating wave approximation is given by the following equation: assuming ;

[0021] ;

[0022] In the formula: , For the annihilation and generation operators of photons; = The descent operator for qutrit; The ascending operator of qutrit; for Detuning between the transition frequency and the cavity frequency; for The transition frequency is detuned to the driving field frequency;

[0023] Under conditions of large detuning, neglecting energy exchange in superconducting quantum systems, the above Hamiltonian can be simplified to: using the theory of effective Hamiltonians.

[0024] ;

[0025] In the formula: ; ;

[0026] By adjusting the parameters of the superconducting quantum system, And ensure energy levels Initially unoccupied, the Hamiltonian energy is further simplified into an effective form characterizing the dynamics of superconducting quantum systems:

[0027] .

[0028] Furthermore, the implementation method of the quantum phase gate is as follows:

[0029] Based on the effective dynamic characterization form of superconducting quantum systems The evolution operator for a superconducting quantum system is:

[0030] ;

[0031] The evolution operator is specifically expressed as follows:

[0032] ;

[0033] When qutrit is in When in a certain state, the cavity field state remains unchanged;

[0034] When qutrit is in In this state, the cavity field acquires a phase shift of +λt per photon;

[0035] When qutrit is in In this state, the cavity field acquires a phase shift of -λt per photon;

[0036] By controlling the dispersive coupling interaction time t to satisfy the condition λt=2π / 3, the evolution operator is ultimately implemented as follows:

[0037] ;

[0038] In the formula: For the particle number operator of the cavity field;

[0039] Thus, a mixed-dimensional quantum phase gate has been realized: the control state of the qutrit determines the relative phase acquired by the target qubit.

[0040] Furthermore, the process for preparing asymmetric mixed-dimensional maximally entangled states based on the aforementioned quantum phase gate is as follows:

[0041] Initialization: Prepare the initial state of the entire system as follows:

[0042]

[0043] In the formula: It is the maximum superposition state of the cavity field, and qutrit is in the maximum superposition state of its three basis vectors; apply the gate operation: apply the quantum phase gate U implemented above to the initial state. ;

[0044] Obtaining an entangled state: After the operation is completed, the system evolves to the final state:

[0045] ;

[0046] In the formula: This state is a maximally entangled state between the cavity qubit and the flux qutrit.

[0047] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0048] Compared with gates of the same dimension (such as two qutrit gates), this invention enables cross-dimensional operations, provides a direct interface, avoids the complex conversion steps required to encode high-dimensional information into multiple low-dimensional systems, and is more efficient.

[0049] Compared to other hybrid-dimensional solutions (such as optical solutions), this invention is deterministic (100% success rate) and based on a scalable superconducting quantum system, with operational reliability far superior to probabilistic optical solutions. Attached Figure Description

[0050] Figure 1 Figure 1 shows the structure, configuration, and schematic diagram of the quantum processing system of the method described in this invention; wherein: (a) Figure 2 is a structural diagram of the quantum processing system; (b) Figure 3 is a schematic diagram of the energy level configuration and interaction principle.

[0051] Figure 2 To consider the complete energy level relationship diagram including interfering interactions;

[0052] Figure 3 The result graph shows the fidelity as a function of cavity life. Detailed Implementation

[0053] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0054] This invention provides a method for realizing a mixed-dimensional quantum phase gate in a superconducting quantum system. The core concept of this method is to utilize the dispersive interaction between a superconducting magnetic flux qutrit (control bit) and a microwave cavity (target qubit), combined with a carefully tuned classical microwave driving field, to deterministically achieve conditional control of the cavity field phase by the qutrit quantum state through a one-step evolution process.

[0055] I. System Structure

[0056] The quantum processing system architecture that implements this method is as follows: Figure 1 As shown in Figure (a), it mainly includes:

[0057] 1. Microwave cavity: As a quantum resonator, it is used to carry photons and encode the target qubit. Its quantum information is encoded in the vacuum state of the cavity. and single-photon state superior.

[0058] 2. Superconducting flux qutrit (Q): As a three-level quantum system (energy levels from low to high are |g>, |e>, |f>), it is used as a control potential. The qutrit is coupled to the microwave cavity via a capacitor.

[0059] Classic microwave pulse source: used to generate and apply a controllable microwave driving field to the qutrit.

[0060] II. Energy Level Configuration and Interaction Principle

[0061] The key to this method lies in the specific configuration of qutrit energy levels and interactions, such as Figure 1 As shown in Figure (b):

[0062] The microwave cavity is dispersively coupled to the qutrit transition |e>↔|f> with a coupling strength of g and a detuning amount of Δ, satisfying the large detuning condition Δ≫g. Simultaneously, the cavity is highly detuned (approximately decoupled) from the transitions |g>↔|e> and |f>↔|h>.

[0063] A classical microwave driven field is applied to qutrit's In the transition, its Rabi frequency is Ω and the detuning is δ, which also satisfies the large detuning condition δ≫Ω.

[0064] III. System Dynamics and Effective Hamiltonian

[0065] Under the above configuration, the Hamiltonian of the system under the interaction picture and rotating wave approximation is given by the following equation (assuming...). ):

[0066]

[0067] In the formula: , For the annihilation and generation operators of photons; = The descent operator for qutrit; The ascending operator of qutrit; for Detuning between the transition frequency and the cavity frequency; for The transition frequency is detuned to the driving field frequency.

[0068] Under conditions of large detuning, the energy exchange of the system is negligible. Using the theory of effective Hamiltonians, the above Hamiltonian can be simplified to:

[0069]

[0070] In the formula: = g² / Δ; = Ω² / (4δ);

[0071] By precisely adjusting the system parameters, = -λ=λ, and ensuring that the energy level |h> is initially unoccupied, the Hamiltonian can be further simplified to an effective form characterizing the core dynamics of the system:

[0072] ;

[0073] IV. Implementation Process of Quantum Phase Gate

[0074] Based on effective Hamiltonian The system's evolution operator is The evolution operator can be specifically expressed as:

[0075] ;

[0076] When qutrit is in the |g> state, the cavity field state remains unchanged;

[0077] When qutrit is in the |e> state, the cavity field gains a phase shift of +λt per photon;

[0078] When qutrit is in the |f> state, the cavity field gains a phase shift of -λt per photon.

[0079] By precisely controlling the interaction time t to satisfy the condition λt = 2π / 3, the evolution operator is ultimately implemented as follows:

[0080] ;

[0081] In the formula: = The particle number operator for the cavity field.

[0082] Thus, a mixed-dimensional quantum phase gate is realized: the control state of the qutrit (|g>,|e>,|f>) determines the relative phase (0,+2π / 3,-2π / 3) obtained by the target qubit (cavity field).

[0083] V. Preparation of Mixed-Dimensional Entangled States

[0084] Based on the aforementioned quantum phase gate, asymmetric mixed-dimensional maximally entangled states can be further prepared. The preparation process is as follows:

[0085] Initialization: Prepare the initial state of the entire system as follows:

[0086] ;

[0087] In the formula, It is the maximum superposition state of the cavity field, and qutrit is in the maximum superposition state of its three basis vectors.

[0088] Apply the gate operation: Apply the quantum phase gate U implemented above to the initial state |ψ0>.

[0089] Obtaining an entangled state: After the operation is completed, the system evolves to the final state:

[0090] ;

[0091] In the formula: This state is a maximally entangled state between the cavity qubit and the flux qutrit.

[0092] VI. Robustness and Feasibility Verification

[0093] To verify the feasibility of this technical solution in a practical system, this invention examines the influence of non-ideal factors through numerical simulation, such as... Figure 2 Various non-ideal scenarios are considered. The simulation uses the parameters currently achievable in experiments listed in Table I (e.g., coupling strength g / 2π = 12 MHz, qutrit decoherence time T1 on the order of hundreds of microseconds), and the quantum gate operation fidelity is calculated by solving the master equation. The results show that within the operation time T_f = 0.38 μs (much smaller than the system's decoherence time), even considering all non-ideal factors, the hybrid-dimensional quantum phase gate proposed in this invention can still achieve a fidelity higher than 99%, such as... Figure 3 As shown, this demonstrates the high feasibility and robustness of the scheme under current quantum technology.

[0094] Table I: Simulation Parameters

[0095]

[0096] In summary, this invention has successfully implemented key operations in mixed-dimensional quantum computing through a simple, efficient, and deterministic method, providing an effective technical solution for building a more powerful quantum information processing platform.

[0097] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A superconducting quantum system, characterized in that: include: Microwave cavity, as a quantum resonator used to carry photons and encode target qubits; A superconducting flux three-level quantum bit, used as a control bit in a three-level quantum system, is coupled to a microwave cavity via a capacitor; A classic microwave pulse source is used to apply a controllable microwave driving field to a superconducting flux three-level quantum bit.

2. The superconducting quantum system according to claim 1, characterized in that: Encoding quantum information in the vacuum state and single-photon state of a microwave cavity.

3. A superconducting quantum system according to claim 2, characterized in that: The energy levels of the three-level quantum system, from lowest to highest, are as follows: .

4. A method for realizing a mixed-dimensional quantum phase gate using a superconducting quantum system according to any one of claims 1 to 3, characterized in that: By utilizing the dispersive coupling between a superconducting flux three-level qubit and a microwave cavity in a superconducting quantum system, and combining this with a controllable microwave driving field applied to the superconducting flux three-level qubit, conditional control of the cavity field phase by the quantum state of the superconducting flux three-level qubit is deterministically achieved through a one-step evolution process; wherein: The energy levels of the superconducting flux three-level quantum bit and the dispersion coupling are configured as follows: Microwave cavity and superconducting flux three-level quantum bit The transitions involve dispersive coupling and satisfy the large detuning condition: detuning ≫ coupling strength; simultaneously, the microwave cavity and the superconducting flux three-level qubit... and High degree of mistuning in the transition; Controllable microwave driving field applied to superconducting flux three-level qubits The transition is on the high level and satisfies the large detuning condition: detuning amount ≫ Rabi frequency.

5. The method according to claim 4, characterized in that: Derivation of an effective characterization of the dynamics of the superconducting quantum system: Based on the configuration of energy levels and dispersion coupling, the Hamiltonian of a superconducting quantum system under the dispersion coupling scenario and the rotating wave approximation is given by the following equation: assuming , ; In the formula: , For the annihilation and generation operators of photons; = The descent operator for qutrit; The ascending operator of qutrit; for Detuning between the transition frequency and the cavity frequency; for The transition frequency is detuned to the driving field frequency; Under conditions of large detuning, neglecting energy exchange in superconducting quantum systems, the above Hamiltonian can be simplified to: using the theory of effective Hamiltonians. ； In the formula: ; ; By adjusting the parameters of the superconducting quantum system, And ensure energy levels Initially unoccupied, the Hamiltonian energy is further simplified into an effective form characterizing the dynamics of superconducting quantum systems: 。 6. The method according to claim 5, characterized in that: The implementation method of the quantum phase gate: Based on the effective dynamic characterization form of superconducting quantum systems The evolution operator for a superconducting quantum system is: ； The evolution operator is specifically expressed as follows: ； When qutrit is in When in a certain state, the cavity field state remains unchanged; When qutrit is in In this state, the cavity field acquires a phase shift of +λt per photon; When qutrit is in In this state, the cavity field acquires a phase shift of -λt per photon; By controlling the dispersive coupling interaction time t to satisfy the condition λt=2π / 3, the evolution operator is ultimately implemented as follows: ； In the formula: For the particle number operator of the cavity field; Thus, a mixed-dimensional quantum phase gate is realized: the control state of the qutrit determines the relative phase obtained by the target qubit.

7. The method according to claim 6, characterized in that: The process for preparing asymmetric mixed-dimensional maximally entangled states based on the aforementioned quantum phase gate is as follows: Initialization: Prepare the initial state of the entire system as follows: In the formula: It is the maximum superposition state of the cavity field, and qutrit is in the maximum superposition state of its three basis vectors; apply the gate operation: apply the quantum phase gate U implemented above to the initial state. ; Obtaining an entangled state: After the operation is completed, the system evolves to the final state: In the formula: This state is a maximally entangled state between the cavity qubit and the flux qutrit.

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