Quantum adiabatic control method capable of realizing any high-order precision in three-energy-level system

Abstract

The invention relates to a quantum adiabatic control method capable of realizing any high-order precision in a three-level system, and the method comprises the steps: constructing a typical three-level system, and obtaining a quantum bit subspace; applying a pumping pulse driving field and a Stokes pulse driving field to the three-level system to obtain a two-photon resonance system; adding laser into the two-photon resonance system to obtain an initial state; selecting N discrete points on the change path of the control parameters according to the change process relationship between the evolution path from the initial state to the target state and the control parameters of the pump pulse driving field and the Stokes pulse driving field, and sequentially applying pulses on the N discrete points of the change path, so that the initial state is evolved for a certain time to obtain the target state, wherein N is a natural number. According to the quantum adiabatic control method capable of achieving any high-order precision in the three-energy-level system, system errors can be restrained in a large range, and the precision of preparing the target state is improved.

Description

Technical Field

[0001] The present invention relates to the field of quantum control, and particularly to a method for realizing arbitrary high-order precision quantum adiabatic control in a three-level system. Background Art

[0002] The precise manipulation of quantum states is a research hotspot in the fields of quantum optics, quantum control, quantum information, and quantum simulation. Obtaining the target quantum state through controllable, fast, and efficient population transfer is an important topic for realizing the precise manipulation of quantum states. Quantum state preparation is an important concept in quantum information science, and its main purpose is to prepare a quantum system from a known initial state to a target state as precisely as possible. The quantum system is initially in a certain energy level, and through the driving of external fields such as lasers, the quantum system is promoted to evolve towards the target state, realizing the preparation of the quantum state. Quantum state preparation has important application significance in the fields of quantum computing, quantum communication, and quantum simulation.

[0003] Currently, the common method for manipulating three-level quantum states is the stimulated Raman adiabatic passage control method. Please refer to Figure 1 , for a typical three-level system with {|0>, |+1>, |-1>} as the basis vectors, the two states |+1> and |-1> of this system have no coupling and the energy difference is small. The subspace they span can be used as the qubit subspace, and arbitrary state manipulation can be performed in this qubit subspace. Pump pulse driving field Ω p (t) and Stokes pulse driving field Ω s (t) are respectively applied to the three-level system:

[0004]

[0005] where Ω is the output Rabi frequency, T is the total evolution time, τ is the interval time between the two pulses, and σ is the pulse full width at half maximum.

[0006] The preparation and manipulation of the quantum state are realized by controlling the driving field. However, this manipulation method requires a long evolution time, and it is difficult to prepare an ideal target quantum state in a short time. Summary of the Invention

[0007] Based on this, the purpose of the present invention is to provide a method for realizing arbitrary high-order precision quantum adiabatic control in a three-level system, which can achieve a wide range of error suppression, thereby precisely controlling the preparation of the quantum state.

[0008] A method for realizing arbitrary high-order precision quantum adiabatic control in a three-level system includes:

[0009] Constructing a typical three-level system to obtain a qubit subspace;

[0010] A pump pulse driving field and a Stokes pulse driving field are applied to a three-level system to obtain a two-photon resonance system;

[0011] A laser action is applied to the two-photon resonance system to obtain an initial state;

[0012] According to the relationship between the evolution path from the initial state to the target state and the change process of the control parameters of the pump pulse driving field and the Stokes pulse driving field, N discrete points are selected on the change path of the control parameters, and pulses are applied sequentially at the N discrete points on the change path, so that the initial state evolves through a certain time to obtain the target state, where N is a natural number.

[0013] Furthermore, the number of selected discrete points and the corresponding number of applied pulses are increased to suppress the error in the evolution process of the three-level system.

[0014] Furthermore, the control parameters {P 1 , P 2 ,..., P N} corresponding to the N discrete points satisfy the following N equations:

[0015]

[0016] where the definition of S n is:

[0017]

[0018] where θ k is:

[0019]

[0020] where j and k are natural numbers.

[0021] Furthermore, the laser is used to read |m s =0> for the first time and initialize the electron spin, and a π pulse is applied to make |m s =0> transition to |m s =-1>, and then N pulses containing the P j parameter are applied; the laser is used to read the population of |m s =0> for the second time and initialize the electron spin, and a π pulse is applied to make |m s =0> transition to |m s =-1>, and then N pulses containing the P j parameter are applied; where, a π pulse is added before the second reading to measure the population of |m s =-1>, and the fidelity of preparing the target state is calculated according to the population, and arbitrary high-order precision quantum adiabatic control is realized by combining the fidelity and the number of applied pulses.

[0022] Furthermore, in the case of two-photon resonance, the Hamiltonian of the three-level system can be written as

[0023] H(p) = Ω p (p) |-1><0| + Ω s (p) |+1><0| + h.c.

[0024] where p is the control parameter of the driving field, and the relationship between the pump pulse Ω p and the control parameter p is Ω p (p) = Ωsin(p), and the relationship between the Stokes pulse Ω s and the control parameter p is Ω s (p) = Ωcos(p), and Ω is the output Rabi frequency, and is a constant value.

[0025] Furthermore, within the total evolution time T, the initial state |-1> is prepared into any target state in the qubit subspace where |-1> is the initial state, |+1> is the other excited state, and p(T) ≡ p T = P N+1 is an arbitrary value; N discrete points {P T}, {P 1},..., {P 2},..., {P N} are selected in p ∈ [0, p j , and the pulses H(P π ) are applied in sequence, and the action time of each pulse is t

[0026] ≡ π / Ω. s Furthermore, the triplet ground states of a single NV color center, namely the states of spin |m s = 0> and spin |m s = ±1>, are selected to form the three-level system, and an external magnetic field is applied to cause Zeeman splitting of the two states of spin |m

[0027] For better understanding and implementation, the present invention will be described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a schematic diagram of the principle of the three-level system.

[0029] Figure 2 It is a flowchart of the quantum adiabatic control method that can achieve arbitrary high-order precision in the three-level system according to the present invention.

[0030] Figure 3Schematic diagram showing that for the present invention, N = 3, 4, and 5 discrete points are taken on the evolution path, and pulses are sequentially applied at these discrete points.

[0031] Figure 4 For the present invention, N = 4 pulses are used to achieve the state transfer of p T = π / 2, and the waveform diagram of the Stokes pulse Ω s amplitude in the control field with respect to the time variation of the pump pulse Ω p amplitude.

[0032] Figure 5 For the present invention, N = 5 pulses are used to achieve the state transfer of p T = π / 2, and the waveform diagram of the Stokes pulse Ω s amplitude in the control field with respect to the time variation of the pump pulse Ω p amplitude.

[0033] Figure 6 For the present invention, various numbers of pulses for achieving the state transfer of p T = π / 2, and the relationship diagram of the fidelity with respect to the pulse amplitude error.

[0034] Figure 7 For the present invention, various numbers of pulses for achieving the state transfer of p T = π / 4, and the relationship diagram of the fidelity with respect to the pulse amplitude error.

[0035] Figure 8 For the present invention, N = 4 specific equation pulses are applied for achieving the state transfer of p T = π / 2, and the relationship diagram of the fidelity with respect to the pulse amplitude error and detuning error.

[0036] Figure 9 For the present invention, N = 7 pulses satisfying specific equations are applied for achieving the state transfer of p T = π / 2, and the relationship diagram of the fidelity with respect to the manipulation error and detuning error.

[0037] Figure 10 For the present invention, the relationship diagram of the fidelity and operation time for applying N = 1, 2, and 3 pulses to achieve the rapid preparation of the target state. Detailed implementation manner

[0038] The applicant carefully analyzed the prior art quantum adiabatic control method and found that the reason for its low manipulation accuracy is that due to the need for a long evolution time, the control field changes slowly, and during the evolution process, the quantum system will couple with the environment, which may lead to decoherence of the quantum system before the control field manipulation is completed, thus resulting in a large manipulation error. Therefore, the applicant tried to select discrete points satisfying specific equations during the preparation process of the quantum state and apply pulse actions, thereby suppressing the manipulation error and improving the quantum state preparation accuracy.

[0039] Please refer to Figure 2 , the method for realizing arbitrary high-order precision quantum adiabatic control in a three-level system of this application is achieved through the following steps:

[0040] Construct a typical three-level system to obtain a qubit subspace. Preferably, select the triplet ground state of a single NV color center, namely the state of spin |m s =0> and the states of spin |m s =±1> to form a three-level system, and apply an external magnetic field to cause Zeeman splitting of the two states of spin |m s =±1>. Among them, the NV color center is a luminescent point defect where a nitrogen atom replaces a carbon atom in diamond.

[0041] Apply a pump pulse driving field and a Stokes pulse driving field to the three-level system to obtain a two-photon resonance system. Through the pump pulse Ω p couple |-1> and |0>, and through the Stokes pulse Ω s couple |+1> and |0>. In the case of two-photon resonance, the Hamiltonian of the three-level system can be written as

[0042] H(p)=Ω p (p)|-1><0|+Ω s (p)|+1>(0|+h.c.

[0043] where p is the control parameter of the driving field, and the relationship between the pump pulse Ω p and the control parameter p is Ω p (p)=Ωsin(p), and the relationship between the Stokes pulse Ω s and the control parameter p is Ω s (p)=Ωcos(p). Ω is the output Rabi frequency, and is a fixed value, which is set to 2π×4.0 MHz. When there is a manipulation error ∈, there will be an error in Ω, and the output Rabi frequency becomes (1+∈)Ω. At this time, the prepared quantum state will deviate from the target quantum state, and the degree of deviation increases with the increase of the manipulation error. Therefore, to improve the precision of quantum state preparation, it is necessary to suppress the manipulation error.

[0044] Preferably, apply two microwave driving fields with Rabi frequencies of Ω p and Ω s respectively through an arbitrary waveform generator to provide the pump pulse driving field and the Stokes pulse driving field, and adjust the frequencies of the two microwaves so that they are respectively in resonance with the transition from |m s =0> to |m sresonates at a frequency of |m = ±1> to form a two - photon resonance system. It can be understood that if the frequency of any microwave and the frequency of the transition from |m s = 0> to |m s = ±1> are not equal, a detuning error will occur, and the magnitude of this error is the difference between the two frequencies. The detuning error will directly reduce the fidelity of the prepared target state. Therefore, to improve the precision of quantum state preparation, it is necessary to suppress the detuning error.

[0045] Apply laser action to the two - photon resonance system to obtain the initial state. Preferably, use a laser to initialize the system to the ground state |m s = 0>, and then apply a π - pulse to cause the transition of |m s = 0> to |m s = - 1> as the initial state.

[0046] According to the relationship between the evolution path from the initial state to the target state and the change process of the control parameters of the pump - pulse driving field and the Stokes - pulse driving field, select N discrete points on the change path of the control parameters, and apply pulses sequentially at these N discrete points on the change path so that the initial state evolves through a certain time to obtain the target state, where N is a natural number. Specifically, within the total evolution time T, prepare the initial state | - 1> into any target state in the qubit subspace where p(T)≡p T = P N+1 can be any value.

[0047] Please refer to Figure 3 , select N discrete points {P T}, {P 1},..., {P 2},..., {P N} in p ∈ [0, p j , and apply pulses H(P j ) sequentially at these discrete points, and the action time of each pulse is π / Ω.

[0048] Among them, the N discrete points {P 1}, {P 2},..., {P N} satisfy the following N equations:

[0049]

[0050] where the definition of S n is:

[0051]

[0052] where θ k is:

[0053]

[0054] Please combine Figure 4 with Figure 5 , and through N equations, the numerical solutions of N discrete points {P 1 , P 2 ,..., P N} can be obtained. Based on this, the corresponding Stokes pulse Ω s and the amplitude-time relationship of the pump pulse Ω p can be obtained. Through N pulses {H(P 1 ), H(P 2 ),..., H(P N )) that meet the requirements for control, the system will evolve towards the target quantum state over time. Among them, the dashed line is the pump pulse Ω p , and the solid line is the Stokes pulse Ω s .

[0055] Preferably, apply N pulses {H(P j ) with P 1 parameters, H(P 2 ),..., H(P N ). The acting time of each pulse is where satisfies the above N equations. For example, the control parameters for applying 5 pulses are {P 1 = 0.0152π, P 2 = 0927π, P 3 = 0.2500π, P 4 = 0.4073π, P 5 = 0.4848π}.

[0056] Please refer to Table 1-3. Among them, Table 1 shows some numerical solutions of the discrete points P / p T = π / 2 for realizing the target state j ; Table 2 shows some numerical solutions of the discrete points P T / p = π / 4 for realizing the target state T ; Table 3 shows some numerical solutions of the discrete points P j / p T = 3π / 11 for realizing the target state . T j / p T .

[0057] Table 1

[0058] ​

[0059]

[0060] Table 2

[0061]

[0062] Table 3

[0063]

[0064] When applying pulses to evolve to the target state, the evolution process can also be controlled by changing the number of applied pulses.

[0065] In one embodiment, the error is suppressed by increasing the number of applied pulses.

[0066] Specifically, a laser is used to read |m s = 0> while re - initializing the electron spin, and the same operation of applying a π - pulse is repeated to make |m s = 0> transition to |m s = - 1>. Then, N pulses containing the Pj parameter are applied, and a π - pulse is added before the second reading, so as to measure the population of |m s = - 1>. From this, the state of the system after the operation can be known, whether the system is in the target state can be analyzed, and thus the fidelity of preparing the target state can be calculated. Preferably, applying five pulses can eliminate the driving - field amplitude error to the l0 - th order, and the calculated fidelity is F = 1+O(∈ 10 ).

[0067] Due to the existence of the manipulation error ∈, the final state obtained by manipulating the initial state | - 1> is not the ideal target state That is, the fidelity is not exactly equal to 1. Among them, U(p) represents the operation operator of the whole process. The fidelity F reflects the degree of closeness between the target state and the actual state. The higher the fidelity, the higher the degree of closeness, and the closer the quantum system after the operation is to the target state. Applying control pulses {H(P 1 ), H(P 2 ),..., H(P N ))} that satisfy N above - mentioned equations can make the fidelity reach 1 - O(∈ 2N ), that is, the conversion error E≡1 - F = O(∈ 2N ) is suppressed to the 2N - th order, and thus arbitrary high - order precision quantum adiabatic control can be achieved. Please combine Figure 6 with Figure 7 , Figure 6 which shows the relationship diagrams of the number of various pulses for realizing the state transfer of p T = π / 2 with respect to the fidelity and the pulse - amplitude error, Figure 7Shows the relationship diagrams of the number of various pulses for realizing the state transfer of p T = π / 4 with respect to the fidelity and the pulse amplitude error. It can be seen that for different target states, increasing the number of applied pulses can improve the fidelity F. Please refer to Figures 8 to 9 , Figure 8 Shows the relationship diagrams of applying N = 4 pulses that satisfy a specific equation for realizing the state transfer of p T = π / 2 with respect to the fidelity and the pulse amplitude error and the detuning error. Figure 9 Shows the relationship diagrams of applying N = 7 pulses that satisfy a specific equation for realizing the state transfer of p T = π / 2 with respect to the fidelity and the pulse amplitude error and the detuning error; it can be seen that the method for realizing arbitrary high-order precision quantum adiabatic control in a three-level system according to the present invention can suppress the manipulation error and the detuning error, thereby improving the precision of preparing the target state.

[0068] In another experimental example, compared with the stimulated Raman adiabatic passage control method of the prior art, we can reach the same fidelity in a shorter time. Figure 10 Shows the relationship diagrams of applying N = 1, 2, 3 pulses for realizing the rapid preparation of the target state with respect to the fidelity and the operation time, where the maximum amplitude of the pulse is 2πr × 4.0 MHz. Compared with the prior art, the stimulated Raman adiabatic passage control method cannot satisfy the adiabatic condition at the time of t π and thus cannot accurately prepare the target state. While the method of the present invention only requires the time t of one pulse π to achieve a fidelity of 1 and prepare the ideal target state, indicating that the method for realizing arbitrary high-order precision quantum adiabatic control in a three-level system according to the present invention can prepare a target state with higher fidelity within the same evolution time compared with the stimulated Raman adiabatic passage control method of the prior art.

[0069] The above-described embodiments only represent the optimal implementation modes of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and the present invention also intends to include these changes and modifications.

Claims

1. A quantum adiabatic control method that can achieve arbitrary high-order precision in a three-level system, characterized in that: include: Construct a typical three-level system and obtain the quantum bit subspace; Applying a pump pulse driving field and a Stokes pulse driving field to the three-level system to obtain a two-photon resonance system; Adding laser action to the two-photon resonance system to obtain the initial state; According to the relationship between the evolution path from the initial state to the target state and the change process of the control parameters of the pump pulse driving field and the Stokes pulse driving field, N discrete points are selected on the change path of the control parameters, and pulses are applied sequentially at the N discrete points of the change path so that the initial state evolves to the target state after a certain period of time, where N is a natural number.

2. The quantum adiabatic control method capable of realizing arbitrary high-order precision in a three-level system according to claim 1, characterized in that: The number of selected discrete points and their corresponding number of applied pulses are increased to suppress errors in the evolution of the three-level system.

3. The quantum adiabatic control method capable of realizing arbitrary high-order precision in a three-level system according to claim 2, characterized in that: The control parameters corresponding to N discrete points {P1, P2, ..., P N } satisfies the following N equations: Among them, S n is defined as: Among them, θ k for: Among them, j and k are natural numbers.

4. The quantum adiabatic control method capable of realizing arbitrary high-order precision in a three-level system according to claim 3, characterized in that: First time reading with laser s =0> and initialize the electron spin, apply a π pulse to make |m s =0> jump to |m s =-1>, then apply N P j Parameter pulse; laser reading for the second time |m s =0> population and initialize the electron spin, apply a π pulse to make |m s =0> jump to |m s =-1>, then apply N P j Parameter pulse; in which, a π pulse is added before the second reading to measure |m s =-1>, the fidelity of the prepared target state is calculated based on the population number, and quantum adiabatic control with arbitrary high-order accuracy is achieved by combining the fidelity with the number of applied pulses.

5. The quantum adiabatic control method capable of realizing arbitrary high-order precision in a three-level system according to claim 4, characterized in that: In the case of two-photon resonance, the Hamiltonian of this three-level system can be written as H(p)=Ω p (p)|-1><0|+Ω s (p)|+1><0|+h.c. Where p is the control parameter of the driving field, and the pump pulse Ω p The relationship between the change of the control parameter p is Ω p (p) = Ωsin(p), Stokes pulse Ω s The relationship between the change of the control parameter p is Ω s (p) = Ωcos(p), Ω is the output Rabi frequency, and Is a fixed value.

6. The quantum adiabatic control method capable of realizing arbitrary high-order precision in a three-level system according to claim 5, characterized in that: Within the total evolution time T, the initial state |-1> is prepared to any target state |1 in the quantum bit subspace pT >=cosp T |-1>-sinp T |+1>, where |-1> is the initial state, |+1> is another excited state, and p(T)≡p T =P N+1 is any value; in p∈[0,p T ] Select N discrete points {P1,P2,…,P N }, and apply pulses H(P j ), each pulse action time is π / Ω.

7. The quantum adiabatic control method capable of realizing arbitrary high-order precision in a three-level system according to claim 6, characterized in that: Select the triple ground state of a single NV color center, namely spin|m s =0> state and spin |m s = ±1> constitutes the three-level system, and an external magnetic field is applied to make the spin |m s =±1>, the two states undergo Zeeman splitting.

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