Three-dimensional quantum entangled state preparation method based on photon-assisted Raman transition

Abstract

The invention 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, a three-energy-level system is constructed by using photon-assisted Raman transition, a three-dimensional Bell state is directly prepared through single-step operation by using the dynamic symmetry of the three-energy-level system, and by optimizing the quantum circuit design, the three-dimensional quantum entangled state is prepared. A three-dimensional Bell state can be prepared into a three-dimensional GHZ state or a non-local entangled state; the adopted photon-assisted Raman transition technology has the advantages of being short in operation time, high in fidelity and easy to calibrate; by reducing operation steps and optimizing quantum circuit design, error accumulation can be remarkably reduced, evolution time can be shortened, rapid and high-fidelity three-dimensional quantum bit entangled state preparation is achieved, and an efficient and reliable new technical scheme is provided for the field of quantum information processing.

Description

Technical Field

[0001] The present invention belongs to the technical field of three-dimensional quantum entangled state preparation, and specifically relates to a three-dimensional quantum entangled state preparation method based on photon-assisted Raman transition. Background Art

[0002] Existing methods for preparing three-dimensional entangled states primarily rely on constructing complex quantum circuits using multiple two-qubit gates and three-qubit gate operations. While theoretically feasible, these methods face significant limitations in practical applications. First, in multi-step quantum circuits, the combination of multiple quantum gates leads to a 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 quantum states. Second, multi-step quantum circuits inherently require long evolution times, particularly the long two-qubit gate operations. This makes the quantum state more susceptible to decoherence effects during evolution, further reducing the fidelity of three-dimensional qubit entangled states. In summary, existing preparation methods place extremely stringent requirements on the decoherence time of quantum systems and the precision of quantum manipulation, making the rapid preparation of high-fidelity three-dimensional quantum entangled states extremely challenging. Summary of the Invention

[0003] In response to the problems of long operation time and low fidelity in the existing technology for preparing three-dimensional quantum bit entangled states, the present invention proposes a method for preparing three-dimensional quantum bit entangled states based on photon-assisted Raman transitions.

[0004] In order to achieve the purpose of the present invention, the present invention is implemented by adopting the following technical solutions.

[0005] A method for preparing three-dimensional quantum entangled states based on photon-assisted Raman transitions. The method uses photon-assisted Raman transitions between neighboring three-dimensional quantum bit pairs to construct a nearly degenerate three-level system. Then, utilizing the dynamical symmetry of the nearly degenerate three-level system, a three-dimensional Bell state is directly prepared in a quantum chip through a single-step operation within 110 nanoseconds. By designing a quantum circuit for preparing a three-dimensional GHZ state or a quantum circuit for preparing a non-local entangled state, the three-dimensional Bell state can be prepared into a three-dimensional GHZ state or a non-local entangled state.

[0006] As a preferred embodiment of the present invention, the specific method for preparing the three-dimensional quantum entangled state comprises 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 resonance frequency on the driving field amplitude;

[0009] Step 3: Simultaneously stimulate two photon-assisted Raman transitions, calibrate the frequency shift, and directly generate three-dimensional Bell states in a single-step operation;

[0010] Step 4: According to the designed quantum circuit, the three-dimensional Bell state is expanded into a three-dimensional GHZ state or a non-local entangled state.

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

[0012] S21. From calibrating a single 3D quantum bit Q i Among the operations (i=1,2,...N), select the calibration three-dimensional quantum bit operation π 01 and π 12 ;

[0013] S22, from calibrating the neighboring three-dimensional quantum bit pair Q i -Q j Photon-assisted Raman transition between (|ij|=1) and symmetrical , select Calibration Photon Assisted Raman Transition and

[0014] S23, using the calibrated π 01 and π 12 The near-degenerate three-level system is initialized to the |20> state by acting on Q1 in sequence. Microwave drive is simultaneously applied to the three-dimensional quantum bits Q1 and Q2, and the drive frequency is adjusted to compensate for the frequency shift. When the intensities of the microwave-induced photon-assisted Raman transitions are the same and the absolute values of the detuning are the same, the |01> state and the |12> state will evolve synchronously according to the dynamical symmetry of the near-degenerate three-level system. When the population evolution curve of the |01> state or the |12> state intersects with the population evolution curve of the |20> state, the three populations are equal. After a simple phase calibration, the three-dimensional Bell state is prepared.

[0015] As a preferred embodiment of the present invention, and All of them are driven by three-dimensional quantum bits Q j Achieve transition.

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

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

[0018] As a preferred embodiment of the present invention, the quantum circuit for preparing a three-dimensional GHZ state is as follows: assuming that at the initial moment, the three-dimensional quantum bits 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 on Q3 The system evolved to:

[0021]

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

[0023]

[0024] Step 3: Apply to Q3 in sequence The system evolved to:

[0025]

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

[0027]

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

[0029]

[0030] At this point, the GHZ state of three three-dimensional quantum bits has been successfully prepared.

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

[0032] As a preferred embodiment of the present invention, the quantum circuit for preparing a non-local Bell state is as follows: assuming that at the initial moment, the three-dimensional quantum bits 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 on Q2 The system evolved to:

[0035]

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

[0037]

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

[0039]

[0040] At this point, the non-local Bell state of three three-dimensional quantum bits has been successfully prepared.

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

[0042] Beneficial effects

[0043] (1) Improve the preparation speed and fidelity of three-dimensional entangled states. The present 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, significantly improve the preparation efficiency and fidelity, and provide high-quality quantum resources for quantum information processing.

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

[0045] (3) Prepare non-local three-dimensional entangled states. The present invention further designs a method for realizing non-local three-dimensional Bell states and three-dimensional GHZ states through local operations. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Flow chart of the specific preparation method of the present invention;

[0047] Figure 2 Schematic diagram of the energy spectrum and photon-assisted Raman transition process of a pair of coupled three-dimensional quantum bits of the present invention;

[0048] Figure 3This is a waveform timing diagram showing how the intensity of the photon-assisted Raman transition process described in the present invention changes with the driving intensity;

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

[0050] Figure 5 This is a quantum circuit diagram for preparing GHZ states according to the present invention;

[0051] Figure 6 This is the quantum circuit diagram for preparing non-local Bell states as described in the present invention. DETAILED DESCRIPTION

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

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

[0054]

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

[0056]

[0057] This paper uses photon-assisted Raman transitions to construct a nearly degenerate three-level system and exploits the symmetry of this system to create a three-dimensional Bell state in a single step. Furthermore, through optimized quantum circuit design, the three-dimensional Bell state is expanded to a three-dimensional GHZ state or a nonlocally entangled state.

[0058] As an embodiment of the present invention, Figures 1 to 6 As shown in the figure, a method for preparing three-dimensional quantum entangled states based on photon-assisted Raman transition is first calibrated to obtain a single three-dimensional quantum bit Q i (i=1,2,...N) operations, mainly including π 01 and π 12 Two quantum operations. These operations can be used to initialize the system, transform between three-dimensional Bell states, and expand three-dimensional Bell states to three-dimensional GHZ states or non-local entangled states. Secondly, calibrate the neighboring three-dimensional quantum bit pair Q i -Q jPhoton-assisted Raman transition between (|ij|=1) and symmetrical The energy spectrum of neighboring three-dimensional quantum bit pairs and the related transition processes, such as Figure 2 As shown, By driving the three-dimensional quantum bit Q i The driving frequency is approximately equal to the corresponding energy level difference. This transition process actually passes through two coherent Raman processes. and Similarly, By driving the three-dimensional quantum bit Q j The driving frequency is approximately equal to the corresponding energy level difference. This transition process actually passes through two coherent Raman processes. and For the purpose of preparing three-dimensional Bell states, we focus on or By scanning and polynomial fitting of Rabi-type oscillations, we can calibrate the relationship between the corresponding transition strength and the driving strength. 01 and π 12 Acting on Q1 in turn, the system is initialized to the |20> state. Then, appropriate microwave drive is applied to the three-dimensional quantum bits Q1 and Q2 respectively to ensure that the intensity of the microwave-induced photon-assisted Raman transition is the same, and the drive frequency is appropriately adjusted to compensate for the frequency shift so that the absolute value of the detuning is the same. At this time, according to the symmetry of the three-level system, |01> and |12> will evolve synchronously, and non-resonant drive can greatly accelerate the evolution rate. From a geometric perspective, such as Figure 4 As shown in , 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 a simple phase calibration, the three-dimensional Bell state is prepared, as shown in Figure 1 As shown. In actual experiments, the phase is easily calibrated using Ramsey interferometry. Considering that the intensity of the photon-assisted Raman transition varies with the driving intensity, we use a square wave pulse, in which both the rising and falling edges are Gaussian waveforms, to adiabatically suppress leakage, which is also the main error source of this scheme, as shown in Figure 3 As shown. In order 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 of the numerical calculations show that the frequencies of the two three-dimensional quantum bits are 6.0 GHz and 5.0 GHz, respectively, and the detuning is set to 250 MHz. The total evolution time is 110 ns, of which the rising edge (falling edge) is set to 45 ns, and the final three-dimensional Bell state is The fidelity is greater than 99.99%, such as Figure 4 shown.

[0059] like Figure 5 As shown. Assume that at the initial moment, the three-dimensional quantum bits 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 to Q3 The system evolved to:

[0066]

[0067] Then, 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 a GHZ state involving three 3D qubits. These operations occur on the last two qubits and can be extended to the N-bit case through iteration.

[0072] like Figure 6 As shown, assuming that at the initial moment, the three-dimensional quantum bits 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 a 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 3D qubits. These operations also apply to the last two bits, allowing for repeated iterations to be extended to multi-bit cases. Similar operations can also be used to prepare nonlocal GHZ states. While our discussion above focused on the one-dimensional case, for two-dimensional superconducting quantum chips, this approach 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 a three-dimensional quantum entangled state based on photon-assisted Raman transition 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 resonance frequency on the driving field amplitude;

[0084] Step 3: Simultaneously stimulate two photon-assisted Raman transitions, calibrate the frequency shift, and directly generate three-dimensional Bell states in a single-step operation;

[0085] Step 4: According to the designed quantum circuit, the three-dimensional Bell state is expanded into a three-dimensional GHZ state or a non-local entangled state.

[0086] The preferred embodiments of the present invention are described above with reference to the accompanying drawings, but are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and essence of the present invention should be within the scope of the present invention.

Claims

1. A method for preparing a three-dimensional quantum entangled state based on photon-assisted Raman transition, characterized in that: By using photon-assisted Raman transitions between neighboring three-dimensional quantum bit pairs to construct a nearly degenerate three-level system, and then utilizing the dynamical 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. By designing quantum circuits for preparing three-dimensional GHZ states or quantum circuits for preparing non-local entangled states, the three-dimensional Bell state can be prepared into a three-dimensional GHZ state or a non-local entangled state.

2. The method for preparing a three-dimensional quantum entangled state based on photon-assisted Raman transition according to claim 1, characterized in that: The specific preparation method of the three-dimensional quantum entangled state comprises 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 resonance frequency on the driving field amplitude; Step 3: Simultaneously stimulate two photon-assisted Raman transitions, calibrate the frequency shift, and directly generate three-dimensional Bell states in a single-step operation; Step 4: According to the designed quantum circuit, the three-dimensional Bell state is expanded into a three-dimensional GHZ state or a non-local entangled state.

3. The method for preparing a three-dimensional quantum entangled state based on photon-assisted Raman transition according to claim 1, characterized in that: The specific preparation method of the three-dimensional Bell state comprises the following steps: S31. From calibrating a single 3D quantum bit Q i Among the operations (i=1,2,...N), select the calibration three-dimensional quantum bit operation π 01 and π 12 ; S32, from calibrating the neighboring three-dimensional quantum bit pair Q i -Q j Photon-assisted Raman transition between (|ij|=1) and symmetrical , select Calibration Photon Assisted Raman Transition and S33, using the calibrated π 01 and π 12 The near-degenerate three-level system is initialized to the |20> state by acting on Q1 in sequence. Microwave drive is simultaneously applied to the three-dimensional quantum bits Q1 and Q2, and the drive frequency is adjusted to compensate for the frequency shift. When the intensities of the microwave-induced photon-assisted Raman transitions are the same and the absolute values of the detuning are the same, the |01> state and the |12> state will evolve synchronously according to the dynamical symmetry of the near-degenerate three-level system. When the population evolution curve of the |01> state or the |12> state intersects with the population evolution curve of the |20> state, the three populations are equal. After a simple phase calibration, the three-dimensional Bell state is prepared.

4. The method for preparing a three-dimensional quantum entangled state based on photon-assisted Raman transition according to claim 3, characterized in that: described and All of them are driven by three-dimensional quantum bits Q j Achieve transition.

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

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

7. The method for preparing a three-dimensional quantum entangled state based on photon-assisted Raman transition according to claim 1, characterized in that: The quantum circuit for preparing a three-dimensional GHZ state: Assume that at the initial moment, the three-dimensional quantum bits 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: Step 1: Apply on Q3 The system evolved to: Step 2: Apply on Q2 The system evolved to: Step 3: Apply to Q3 in sequence The system evolved to: Step 4: Apply to Q2 The system evolved to: Step 5: Apply on Q2 The system eventually evolved into: At this point, the GHZ state of three three-dimensional quantum bits has been successfully prepared.

8. The method for preparing a three-dimensional quantum entangled state based on photon-assisted Raman transition according to claim 7, characterized in that: The quantum circuit acts on the last two three-dimensional quantum bits and can be extended to the N-bit case through iteration.

9. The method for preparing a three-dimensional quantum entangled state based on photon-assisted Raman transition according to claim 1, characterized in that: The quantum circuit for preparing non-local Bell states: Assume that at the initial moment, the three-dimensional quantum bits 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: Step 1: Apply on Q2 The system evolved to: Step 2: Apply on Q2 The system evolved to: Step 3: Apply on Q3 The system eventually evolved into: At this point, the non-local Bell state of three three-dimensional quantum bits has been successfully prepared.

10. The method for preparing a three-dimensional quantum entangled state based on photon-assisted Raman transition according to claim 9, characterized in that: The quantum circuit acts on the last two three-dimensional quantum bits and can be extended to the N-bit case through iteration.

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