A method for preparing a three-dimensional quantum entangled state based on photon-assisted Raman transition

Abstract

The present application belongs to the technical field of three-dimensional quantum entangled state preparation, and relates to a three-dimensional quantum entangled state preparation method based on photon-assisted Raman transition, which utilizes photon-assisted Raman transition to construct a three-level system, and then utilizes the dynamic symmetry of the three-level system to directly prepare a three-dimensional Bell state through a single-step operation, and through optimizing quantum circuit design, the three-dimensional Bell state can be prepared into a three-dimensional GHZ state or a non-local entangled state; the photon-assisted Raman transition technology adopted by the present application has the advantages of short operation time, high fidelity and easy calibration; through reducing operation steps and optimizing quantum circuit design, error accumulation can be significantly reduced, and evolution time can be shortened, so that fast and high-fidelity three-dimensional quantum bit entangled state preparation is realized, and a new efficient and reliable technical solution is provided for the field of quantum information processing.

Description

Technical Field

[0001] This invention belongs to the field of three-dimensional quantum entangled state preparation technology, specifically relating to a method for preparing three-dimensional quantum entangled states based on photon-assisted Raman transitions. Background Technology

[0002] Existing methods for preparing three-dimensional entangled states primarily rely on the construction of complex quantum circuits using multiple two-qubit gates and three-dimensional qubit gate operations. While these methods are theoretically feasible, they face several significant limitations in practical applications. First, in multi-step quantum circuits, the combination of multiple quantum gates leads to the gradual accumulation of errors. The relatively low fidelity of current two-qubit gate operations further exacerbates this error accumulation effect, significantly reducing the fidelity of three-dimensional entangled qubit states. Second, multi-step quantum circuits themselves require long evolution times, especially the time-consuming two-qubit gate operations. This makes the quantum state more susceptible to decoherence effects during evolution, further reducing the fidelity of three-dimensional entangled qubit states. In summary, existing preparation methods place extremely stringent demands on the decoherence time and quantum manipulation precision of quantum systems, making the rapid preparation of high-fidelity three-dimensional quantum entangled states highly challenging. Summary of the Invention

[0003] To address the problems of long operation time and low fidelity in the preparation of entangled states of three-dimensional qubits in existing technologies, this invention proposes a method for preparing entangled states of three-dimensional qubits based on photon-assisted Raman transitions.

[0004] To achieve the objectives of this invention, the following technical solutions are adopted.

[0005] A method for preparing three-dimensional quantum entangled states based on photon-assisted Raman transitions is disclosed. This method utilizes photon-assisted Raman transitions between neighboring three-dimensional qubit pairs to construct a nearly degenerate three-level system. Then, by utilizing the dynamic symmetry of the nearly degenerate three-level system, a three-dimensional Bell state can be directly prepared in a quantum chip through a single-step operation within 110 nanoseconds. Furthermore, by designing quantum circuits for preparing three-dimensional GHZ states or nonlocally entangled states, the three-dimensional Bell state can be prepared into a three-dimensional GHZ state or a nonlocally entangled state.

[0006] As a preferred embodiment of the present invention, the specific method for preparing the three-dimensional quantum entangled state includes the following steps:

[0007] Step 1: Calibrate the three-dimensional quantum operation by adjusting the frequency and amplitude of the microwave driving field;

[0008] Step 2: By adjusting the frequency and amplitude of the microwave driving field, observe the photon-assisted Raman transition phenomenon and determine the dependence of the transition intensity and resonant frequency on the amplitude of the driving field.

[0009] Step 3: Simultaneously excite two photons to assist Raman transitions, calibrate the frequency shift, and directly prepare three-dimensional Bell states in a single-step operation;

[0010] Step 4: Based on the designed quantum circuit, extend the three-dimensional Bell state into a three-dimensional GHZ state or a non-locally entangled state.

[0011] As a preferred embodiment of the present invention, the specific method for preparing the three-dimensional Bell state includes the following steps:

[0012] S21, from calibrating a single three-dimensional quantum bit Q i In the operation (i = 1, 2, ... N), the calibrated three-dimensional qubit operation π is selected. 01 and π 12 ;

[0013] S22, From calibrating the nearest neighbor three-dimensional qubit pair Q i -Q j Photon-assisted Raman transitions between (|ij|=1) and symmetrical In the middle, the photon-assisted Raman transition is selected for calibration. and

[0014] S23, using the calibrated π 01 and π 12 The near-degenerate three-level system is initialized to the |20> state by sequentially applying microwave drive to Q1. Simultaneously, microwave drive is applied to the three-dimensional qubits Q1 and Q2 respectively, and the drive frequency is adjusted to compensate for the frequency shift. When the intensity of the microwave-induced photon-assisted Raman transition is the same and the absolute value of the detuning is the same, according to the dynamic symmetry of the near-degenerate three-level system, the |01> state and the |12> state will evolve synchronously. When the population evolution curve of the |01> state or the |12> state intersects with the population evolution curve of the |20> state, the populations of the three are equal. After simple phase calibration, the three-dimensional Bell state is prepared.

[0015] As a preferred embodiment of the present invention, the and Both are achieved by driving three-dimensional qubits Q. j Achieve a leap forward.

[0016] As a preferred embodiment of the present invention, the The transition process is achieved through two coherent Raman processes. and It was achieved.

[0017] As a preferred embodiment of the present invention, the The transition process is achieved through two coherent Raman processes. and accomplish.

[0018] As a preferred embodiment of the present invention, the preparation of the three-dimensional GHZ state quantum circuit is as follows: assuming that at the initial moment, the three-dimensional qubits Q1 and Q2 are in the three-dimensional Bell state, and Q3 is in the |0> state, that is, the initial state of the system Q1-Q2-Q3 is:

[0019]

[0020] Step 1: Apply to Q3 The system evolved to:

[0021]

[0022] Step 2: Apply to Q2 The system evolved to:

[0023]

[0024] Step 3: Apply the following to Q3 sequentially. The system evolved to:

[0025]

[0026] Step 4: Apply to Q2 The system evolved to:

[0027]

[0028] Step 5: Apply to Q2 The system eventually evolved into:

[0029]

[0030] Thus, a GHZ state of three three-dimensional qubits was successfully prepared.

[0031] As a preferred embodiment of the present invention, the quantum circuit acts on the last two three-dimensional qubits, and can be extended to the N-qubit case through iteration.

[0032] As a preferred embodiment of the present invention, the preparation of the quantum circuit in the nonlocal Bell state is as follows: assuming that at the initial moment, the three-dimensional qubits Q1 and Q2 are in the three-dimensional Bell state, and Q3 is in the |0> state, that is, the initial state of the system Q1-Q2-Q3 is:

[0033]

[0034] Step 1: Apply to Q2 The system evolved to:

[0035]

[0036] Step 2: Apply to Q2 The system evolved to:

[0037]

[0038] Step 3: Apply to Q3 The system eventually evolved into:

[0039]

[0040] Thus, a nonlocal Bell state of 3 three-dimensional qubits was successfully prepared.

[0041] As a preferred embodiment of the present invention, the quantum circuit acts on the last two three-dimensional qubits, and can be extended to the N-qubit case through iteration.

[0042] Beneficial effects

[0043] (1) Improve the preparation speed and fidelity of three-dimensional entangled states. This invention utilizes photon-assisted Raman transitions and the symmetry of three-level systems to significantly shorten the operation time for preparing three-dimensional entangled states, thereby significantly improving preparation efficiency and fidelity, and providing high-quality quantum resources for quantum information processing.

[0044] (2) Simplified quantum circuit design: The quantum circuit designed in this invention is based on photon-assisted Raman transition. This simplified quantum circuit design not only avoids the low fidelity problem of traditional two-qubit gate operation, but is also easy to calibrate and implement, further improving the stability and reliability of quantum operation.

[0045] (3) Preparation of nonlocal three-dimensional entangled states: This invention further designs a method for realizing nonlocal three-dimensional Bell states and three-dimensional GHZ states through local operations. Attached Figure Description

[0046] Figure 1 This is a flowchart of the specific preparation method described in this invention;

[0047] Figure 2 This is a schematic diagram of the energy spectrum and photon-assisted Raman transition process of a pair of coupled three-dimensional qubits according to the present invention.

[0048] Figure 3This is a waveform timing diagram showing the change in intensity of the photon-assisted Raman transition process as a function of driving intensity, as described in this invention.

[0049] Figure 4 This is an evolution diagram of the population and fidelity described in this invention;

[0050] Figure 5 This is a quantum circuit diagram for preparing the GHZ state as described in this invention;

[0051] Figure 6 This is a quantum circuit diagram for preparing nonlocal Bell states as described in this invention. Detailed Implementation

[0052] The present invention will be further described in conjunction with the embodiments and accompanying drawings.

[0053] Three-dimensional quantum entangled states can be viewed as a natural extension of the commonly used two-dimensional quantum entangled states, possessing richer entanglement structures. All three-dimensional Bell states can be represented as:

[0054]

[0055] Where j, k∈(0,1,2), ω=exp(i2π / 3). These 9 mutually orthogonal three-dimensional Bell states constitute the complete basis of two coupled three-dimensional qubit systems. Our target state here is the three-dimensional Bell state with k=2. Different types of three-dimensional Bell states can be accessed through the X gate or X gate of the three-dimensional qubit. -1 Gates can be converted into each other. The three-dimensional GHZ state can be simply generalized as:

[0056]

[0057] This invention utilizes photon-assisted Raman transitions to construct a nearly degenerate three-level system, and leverages the system's symmetry to prepare three-dimensional Bell states through single-step operations. Building upon this, through optimized quantum circuit design, the three-dimensional Bell states are extended to three-dimensional GHZ states or nonlocally entangled states.

[0058] As an embodiment of the present invention, such as Figures 1 to 6 As shown, a method for preparing three-dimensional quantum entangled states based on photon-assisted Raman transitions is first to calibrate a single three-dimensional qubit Q. i Operations on (i = 1, 2, ..., N) mainly include π 01 and π 12 Two quantum operations. These operations can be used for system initialization, transformations between three-dimensional Bell states, and the extension of three-dimensional Bell states to three-dimensional GHZ states or nonlocally entangled states. Secondly, calibration of nearest-neighbor three-dimensional qubit pairs Q... i -Q jPhoton-assisted Raman transitions between (|ij|=1) and symmetrical The energy spectrum and related transition processes of nearest-neighbor three-dimensional qubit pairs, such as Figure 2 As shown, where, By driving the three-dimensional quantum bit Q i This is achieved when the driving frequency is approximately equal to the corresponding energy level difference. This transition process actually involves two coherent Raman processes. and To achieve. Similarly, By driving the three-dimensional quantum bit Q j This is achieved when the driving frequency is approximately equal to the corresponding energy level difference. This transition process actually involves two coherent Raman processes. and Implementation. For the purpose of preparing three-dimensional Bell states, we will focus here on... or By scanning Rabi-type oscillations and fitting polynomials, we can calibrate the relationship between the corresponding transition intensity and the driving intensity. Then we use the calibrated π... 01 and π 12 By sequentially applying microwaves to Q1, the system is initialized to the |20> state. Then, suitable microwave drives are simultaneously applied to the three-dimensional qubits Q1 and Q2, ensuring that the intensity of the microwave-induced photon-assisted Raman transitions is the same. The driving frequency is appropriately adjusted to compensate for the frequency shift, making the absolute value of the detuning the same. At this point, due to the symmetry of the three-level system, |01> and |12> will evolve synchronously, and non-resonant driving can significantly accelerate the evolution rate. From a geometric perspective, as... Figure 4 As shown, when the population evolution curves of the |01> state or |12> state intersect with the population evolution curve of the |20> state, the populations of the three states are equal. After simple phase calibration, the three-dimensional Bell state is prepared. Figure 1 As shown. In actual experiments, the phase can be easily calibrated using Ramsey interference. Considering that the intensity of photon-assisted Raman transitions varies with the driving intensity, we use square wave pulses, where both the rising and falling edges are Gaussian waveforms, to adiabatically suppress leakage, which is also the main source of error in this scheme, as shown. Figure 3 As shown. To verify the effectiveness of a method for preparing three-dimensional quantum entangled states based on photon-assisted Raman transitions, we performed numerical calculations. The results show that the frequencies of the two three-dimensional qubits are 6.0 GHz and 5.0 GHz, respectively, with detuning set to 250 MHz. The total evolution time is 110 ns, with the rise (fall) edge set to 45 ns, and the final three-dimensional Bell state is obtained. The fidelity is greater than 99.99%, such as Figure 4 As shown.

[0059] like Figure 5 As shown. Assume that initially, the three-dimensional qubits Q1 and Q2 are in the three-dimensional Bell state prepared according to the above scheme, and Q3 is in the |0> state, that is, the initial state of the system Q1-Q2-Q3 is:

[0060]

[0061] First, apply to Q3 The system evolved to:

[0062]

[0063] Next, apply to Q2 The system evolved to:

[0064]

[0065] Then, apply sequentially to Q3. The system evolved to:

[0066]

[0067] Subsequently, apply to Q2 The system evolved to:

[0068]

[0069] Finally, apply to Q2 The system eventually evolved into:

[0070]

[0071] Thus, we have successfully prepared GHZ states for three three-dimensional qubits. These operations occur on the last two qubits and can be extended to the N-qubit case iteratively.

[0072] like Figure 6 As shown, assuming that at the initial moment, the three-dimensional qubits Q1 and Q2 are in the three-dimensional Bell state prepared according to the above scheme, and Q3 is in the |0> state, that is, the initial state of the system Q1-Q2-Q3 is:

[0073]

[0074] First, apply to Q2 The system evolved to:

[0075]

[0076] Then, apply to Q2 The system evolved to:

[0077]

[0078] Finally, apply to Q3 The system eventually evolved into:

[0079]

[0080] Thus, we have successfully prepared nonlocal Bell states for three three-dimensional qubits. These operations also apply to the last two qubits, and therefore can be iteratively extended to multi-qubit cases. Similar operations can also be used to prepare nonlocal GHZ states. Our discussion above focuses on the one-dimensional case. For two-dimensional superconducting quantum chips, this scheme can be further combined with topology optimization sorting algorithms to improve the efficiency of quantum circuits.

[0081] As an embodiment of the present invention, a method for preparing three-dimensional quantum entangled states based on photon-assisted Raman transitions includes the following specific steps:

[0082] Step 1: Calibrate the three-dimensional quantum operation by adjusting the frequency and amplitude of the microwave driving field;

[0083] Step 2: By adjusting the frequency and amplitude of the microwave driving field, observe the photon-assisted Raman transition phenomenon and determine the dependence of the transition intensity and resonant frequency on the amplitude of the driving field.

[0084] Step 3: Simultaneously excite two photons to assist Raman transitions, calibrate the frequency shift, and directly prepare three-dimensional Bell states in a single-step operation;

[0085] Step 4: Based on the designed quantum circuit, extend the three-dimensional Bell state into a three-dimensional GHZ state or a non-locally entangled state.

[0086] 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 method for preparing three-dimensional quantum entangled states based on photon-assisted Raman transitions, characterized in that: A near-degenerate three-level system is constructed using photon-assisted Raman transitions between nearest-neighbor three-dimensional qubit pairs. Then, utilizing the dynamical symmetry of this near-degenerate three-level system, a three-dimensional Bell state can be directly prepared in a quantum chip through a single-step operation within 110 nanoseconds. Furthermore, by designing quantum circuits for preparing three-dimensional GHZ states or nonlocally entangled states, the three-dimensional Bell state can be prepared into a three-dimensional GHZ state or a nonlocally entangled state. Wherein: The method for preparing the three-dimensional Bell state includes the following steps: S1, from calibrating a single three-dimensional quantum bit In the operation, the calibration of three-dimensional qubits is selected. and ; S2, from calibrating nearest neighbor three-dimensional qubit pairs - Photon-assisted Raman jump and symmetrical In the middle, the photon-assisted Raman transition is selected for calibration. and ; S3, using the calibrated and Acting sequentially The nearly degenerate three-level system is initialized to... The states, simultaneously in three-dimensional qubits and Microwave drive is applied, and the drive frequency is adjusted to compensate for the frequency shift. When the intensity of microwave-induced photon-assisted Raman transitions is the same, and the absolute value of detuning is the same, according to the dynamic symmetry of the near-degenerate three-level system, state and The state will evolve synchronously, when state or Population evolution curve of the state and When the population evolution curves of the three states intersect, the populations of the three states are equal. After simple phase calibration, the three-dimensional Bell state is prepared.

2. The method for preparing three-dimensional quantum entangled states based on photon-assisted Raman transitions according to claim 1, characterized in that: The specific preparation method of the three-dimensional quantum entangled state includes the following steps: Step 1: Calibrate the three-dimensional quantum operation by adjusting the frequency and amplitude of the microwave driving field; Step 2: By adjusting the frequency and amplitude of the microwave driving field, observe the photon-assisted Raman transition phenomenon and determine the dependence of the transition intensity and resonant frequency on the amplitude of the driving field. Step 3: Simultaneously excite two photons to assist Raman transitions, calibrate the frequency shift, and directly prepare three-dimensional Bell states in a single-step operation; Step 4: Based on the designed quantum circuit, extend the three-dimensional Bell state into a three-dimensional GHZ state or a non-locally entangled state.

3. The method for preparing three-dimensional quantum entangled states based on photon-assisted Raman transitions according to claim 2, characterized in that: The Both are achieved by driving three-dimensional qubits. Achieve a leap forward.

4. The method for preparing three-dimensional quantum entangled states based on photon-assisted Raman transitions according to claim 3, characterized in that: The The transition process is achieved through two coherent Raman processes. and It was achieved.

5. The method for preparing three-dimensional quantum entangled states based on photon-assisted Raman transitions according to claim 4, characterized in that: The The transition process is achieved through two coherent Raman processes. and accomplish.

6. The method for preparing three-dimensional quantum entangled states based on photon-assisted Raman transitions according to claim 1, characterized in that: The quantum circuit for preparing the three-dimensional GHZ state is described below: assuming that at the initial moment, the three-dimensional qubit... and In a three-dimensional Bell state, In State, i.e., system The initial state is: ， Step 1: In Apply on The system evolved to: ， Step 2: In Apply on The system evolved to: ， Step 3: In sequence Apply on , The system evolved to: The fourth step is... Apply on The system evolved to: ， Step 5: In Apply on The system eventually evolved into: ， Thus, a GHZ state with three three-dimensional qubits was successfully prepared.

7. The method for preparing three-dimensional quantum entangled states based on photon-assisted Raman transitions according to claim 6, characterized in that: The quantum circuit operates on the last two three-dimensional qubits and can be extended to the N-qubit case through iteration.

8. The method for preparing three-dimensional quantum entangled states based on photon-assisted Raman transitions according to claim 1, characterized in that: The quantum circuit for preparing nonlocal Bell states is described below: assuming an initial time, the three-dimensional qubit... and In a three-dimensional Bell state, In State, i.e., system The initial state is: ， Step 1: In Apply on The system evolved to: , Step 2: In Apply on The system evolved to: ， Step 3: In Apply on The system eventually evolved into: ， Thus, a nonlocal Bell state of 3 three-dimensional qubits was successfully prepared.

9. The method for preparing three-dimensional quantum entangled states based on photon-assisted Raman transitions according to claim 8, characterized in that: The quantum circuit operates on the last two three-dimensional qubits and can be extended to the N-qubit case through iteration.

Images