Preparation method of pseudopure state, nuclear magnetic resonance quantum computer and calculation method thereof

Abstract

The present invention discloses a method for preparing a pseudopure state, a nuclear magnetic resonance quantum computer and a calculation method thereof. The method for preparing a pseudopure state comprises: transmitting a first radio frequency pulse to a sample, the first radio frequency pulse is used to perform a first unitary operation on the thermal equilibrium state of the sample, and obtain a first transition state having a first density matrix, the sub-diagonal elements in the first density matrix are the same, and non-zero items appear in the non-diagonal elements of the first density matrix; stopping transmitting the first radio frequency pulse to the sample, and maintaining the time of stopping transmitting the radio frequency pulse to the sample for a first preset time, so as to obtain a pseudopure state of the sample. The method prepares a pseudopure state by utilizing the relaxation process of the sample itself without using a gradient field, and effectively reduces the difficulty of preparing a pseudopure state.

Description

Technical Field

[0001] The present invention belongs to the technical field of quantum information and / or nuclear magnetic resonance, and in particular, relates to a preparation method of a pseudopure state, a nuclear magnetic resonance quantum computer and a calculation method thereof. Background Art

[0002] In NMR quantum computing, preparing the initial state of quantum computing - pseudopure state is an essential step, and its importance is the same as the initialization in other computing systems. The dynamic performance and measurement performance of pseudopure state are the same as those of pure state.

[0003] The existing pseudopure state preparation methods include time averaging method (PRA57, 3348), space averaging method (PNAS 94, 1634), control transmission method (PRA 82, 032315), etc. Taking the experiment of n quantum bits as an example, each preparation method is briefly explained. 1. Time averaging method: It is necessary to repeat the experiment 2 n -1 times, and finally add the experimental results together as the final experimental result. The time complexity is high and the nuclear magnetic quantum computer needs to have good time stability. Second, the spatial averaging method: It requires multiple pulse gradient fields (n quantum bit experiments require n gradient fields), and the efficiency of preparing pseudo-pure states is low (the signal strength is based on 3. Controlled transmission method: It requires multiple use of pulse gradient fields.

[0004] Therefore, existing pseudo-pure state preparation methods usually require the use of gradient fields, which are difficult to prepare and have high technical barriers. Summary of the invention

[0005] In view of the above problems, the present invention is proposed to provide a method for preparing a pseudopure state, a nuclear magnetic resonance quantum computer and a calculation method thereof that overcome the above problems or at least partially solve the above problems. In particular, one of the technical problems to be solved by the present invention is: how to prepare a pseudopure state of a nuclear magnetic resonance quantum computing system without using a gradient field and under technical conditions of relatively low difficulty.

[0006] The present application discloses a method for preparing a pseudo-pure state, comprising:

[0007] Step S1: transmitting a first radio frequency pulse to a sample, wherein the first radio frequency pulse is used to perform a first unitary operation on a thermal equilibrium state of the sample to obtain a first transition state having a first density matrix, wherein subdiagonal elements in the first density matrix are identical to each other, and non-zero terms appear in non-diagonal elements of the first density matrix;

[0008] Step S2: Stop transmitting the first radio frequency pulse to the sample, and maintain the stop time of transmitting the radio frequency pulse to the sample for a first preset time to obtain a pseudo-pure state of the sample.

[0009] Optionally, in step S2, the sample in the first transition state uses a spontaneous relaxation process to convert non-zero terms appearing in non-diagonal elements of the first density matrix to zero.

[0010] Optionally, in step S2, the sample in the first transition state uses a spontaneous dephasing relaxation process to convert non-zero terms appearing in non-diagonal elements of the first density matrix to zero.

[0011] Optionally, in step S2, the sample changes from the first transition state to the pseudopure state by a spontaneous relaxation process.

[0012] Optionally, the first preset time is selected from (0, 1] seconds.

[0013] Optionally, the first preset time is selected from (0, 200] milliseconds, or (0, 300] milliseconds, or (0, 400] milliseconds, or (0, 500] milliseconds, or [50, 400] milliseconds.

[0014] Optionally, the first preset time is 50 milliseconds, or 100 milliseconds, or 150 milliseconds, or 200 milliseconds, or 250 milliseconds, or 300 milliseconds, or 350 milliseconds, or 400 milliseconds, or 450 milliseconds, or 500 milliseconds, or 550 milliseconds, or 600 milliseconds.

[0015] Optionally, the first preset time is the time required for all non-zero items appearing in the non-diagonal elements of the first density matrix in step S2 to become zero.

[0016] Optionally, after waiting for a first preset time, the sample in the first transition state obtains a second transition state having a second density matrix, and the non-diagonal elements of the second density matrix are all zero.

[0017] Optionally, after performing step S1 and step S2, the pseudopure state preparation method further comprises:

[0018] Step S3: transmitting a second radio frequency pulse to the sample, and performing a second unitary operation on the sample to exchange the relative positions of the sub-diagonal elements in the second density moment;

[0019] Step S4: Stop transmitting the second radio frequency pulse to the sample, and maintain the stop time of transmitting the radio frequency pulse to the sample for a second preset time.

[0020] Optionally, in step S4, the sample utilizes a spontaneous depolarization relaxation process to adjust the size of the sub-diagonal elements of the second density matrix.

[0021] Optionally, step S3 and step S4 are repeated multiple times.

[0022] Optionally, after executing step S3 and step S4 once or multiple times, the sample changes from the second transition state to a pseudo-pure state.

[0023] Optionally, the second transition state is a pseudopure state, and step S3 and step S4 are performed to improve the fidelity of the pseudopure state.

[0024] Optionally, the second preset time is the same as or different from the first preset time.

[0025] Optionally, the second preset time in each step S4 is the same, or different, or not completely the same.

[0026] Optionally, the non-diagonal elements in the density matrix of the pseudopure state are zero, and the sub-diagonal elements in the density matrix of the pseudopure state are identical to each other.

[0027] Optionally, the size of the sub-diagonal element in the density matrix of the pseudopure state satisfies the formula:

[0028]

[0029] Among them, x i It is used to represent the secondary diagonal elements, m is used to represent the number of secondary diagonal elements, and m is a natural number greater than or equal to 3, 1≤i≤m and i is a natural number, and X is used to represent the main diagonal elements.

[0030] Optionally, the module values ​​of the non-diagonal elements in the density matrix of the pseudopure state satisfy the formula:

[0031]

[0032] Where D is used to represent any off-diagonal element, |D| represents the modulus, and x i It is used to represent the secondary diagonal elements, m is used to represent the number of secondary diagonal elements, and m is a natural number greater than or equal to 3, 1≤i≤m and i is a natural number, and X is used to represent the main diagonal elements.

[0033] Optionally, the pseudopure state is a pseudopure state of a quantum information processing system or a pseudopure state of a nuclear magnetic resonance system.

[0034] Optionally, the pseudopure state is a pseudopure state of a nuclear magnetic resonance quantum computing system, and the sample is a sample having at least two quantum bits.

[0035] Optionally, when the sample is a nuclear magnetic resonance sample having two quantum bits, the first unitary operation is:

[0036]

[0037] in, β1 and β2 are both rotation coefficients.

[0038] Optionally, when the sample is a nuclear magnetic resonance sample having two quantum bits, the second unitary operation is:

[0039]

[0040] Optionally, when the sample is a nuclear magnetic resonance sample having three quantum bits, the first unitary operation is:

[0041]

[0042] in, β1, β2, β3, β4, β5, and β6 are all rotation coefficients.

[0043] Optionally, when the sample is a nuclear magnetic resonance sample having three quantum bits, the second unitary operation is:

[0044]

[0045] Optionally, the method for preparing the pseudopure state is a method for preparing the pseudopure state of a nuclear magnetic resonance quantum computer, the nuclear magnetic resonance quantum computer comprises a magnet, a radio frequency control unit and the sample, the magnet is used to generate a constant magnetic field, the constant magnetic field is used to control and operate the magnetic moment of the spin nuclei in the sample, the radio frequency control unit is used to transmit radio frequency pulses to the sample and collect detection signals from the sample;

[0046] In step S1, the radio frequency control unit is used to transmit the first radio frequency pulse to the sample;

[0047] In step S2, the RF control unit stops transmitting the first RF pulse to the sample, and the RF control unit keeps stopping transmitting the RF pulse to the sample for a first preset time.

[0048] Optionally, the method for preparing the pseudopure state is a method for preparing the pseudopure state of a nuclear magnetic resonance quantum computer, the nuclear magnetic resonance quantum computer comprises a magnet, a radio frequency control unit and the sample, the magnet is used to generate a constant magnetic field, the constant magnetic field is used to control and operate the magnetic moment of the spin nuclei in the sample, the radio frequency control unit is used to transmit radio frequency pulses to the sample and collect detection signals from the sample;

[0049] In step S1, the radio frequency control unit is used to transmit the first radio frequency pulse to the sample;

[0050] In step S2, the RF control unit stops transmitting the first RF pulse to the sample, and the RF control unit keeps stopping transmitting the RF pulse to the sample for a first preset time.

[0051] Optionally, in step S3, the radio frequency control unit is used to transmit the second radio frequency pulse to the sample;

[0052] In step S4, the RF control unit stops transmitting the second RF pulse to the sample, and the RF control unit keeps stopping transmitting the RF pulse to the sample for a second preset time.

[0053] Optionally, in step S2, the sample changes from the first transition state to the pseudopure state by a spontaneous dephasing relaxation process.

[0054] The present application also discloses a calculation method of a nuclear magnetic resonance quantum computer, the calculation method comprising:

[0055] Preparing a pseudo-pure state, wherein the method for preparing the pseudo-pure state is any one of the methods described above; and

[0056] After preparing the pseudopure state, transmitting a third radio frequency pulse to the sample and collecting a detection signal from the sample to perform quantum computing;

[0057] The third radio frequency pulse is used to change the energy level structure of the quantum bit of the sample.

[0058] The present application also discloses a nuclear magnetic resonance quantum computer, comprising:

[0059] A sample having at least two qubits;

[0060] A radio frequency control unit, used for transmitting radio frequency pulses to the sample and collecting detection signals from the sample;

[0061] When preparing a pseudopure state, the radio frequency control unit is used to transmit a first radio frequency pulse to the sample, and the first radio frequency pulse is used to perform a first unitary operation on the thermal equilibrium state of the sample to obtain a first transition state having a first density matrix, wherein the sub-diagonal elements in the first density matrix are identical to each other, and non-zero terms appear in the non-diagonal elements of the first density matrix;

[0062] After performing the first unitary operation on the sample, the RF control unit stops transmitting the first RF pulse to the sample and maintains the stop time of transmitting the RF pulse to the sample for a first preset time to obtain a pseudopure state of the sample.

[0063] Optionally, after the pseudopure state is prepared, the radio frequency control unit is used to transmit a third radio frequency pulse to the sample and collect a detection signal from the sample to perform quantum computing;

[0064] The third radio frequency pulse is used to change the energy level structure of the quantum bit of the sample.

[0065] Optionally, within the first preset time, the sample in the first transition state uses a spontaneous relaxation process to convert non-zero terms appearing in non-diagonal elements of the first density matrix to zero.

[0066] Optionally, within the first preset time, the sample in the first transition state uses a spontaneous dephasing relaxation process to convert non-zero terms appearing in non-diagonal elements of the first density matrix to zero.

[0067] Optionally, within the first preset time, the sample changes from the first transition state to the pseudopure state by a spontaneous relaxation process.

[0068] Optionally, the first preset time is selected from (0, 1] seconds.

[0069] Optionally, the first preset time is selected from (0, 200] milliseconds, or (0, 300] milliseconds, or (0, 400] milliseconds, or (0, 500] milliseconds, or [50, 400] milliseconds.

[0070] Optionally, the first preset time is 50 milliseconds, or 100 milliseconds, or 150 milliseconds, or 200 milliseconds, or 250 milliseconds, or 300 milliseconds, or 350 milliseconds, or 400 milliseconds, or 450 milliseconds, or 500 milliseconds, or 550 milliseconds, or 600 milliseconds.

[0071] Optionally, the first preset time is the time required for all non-zero items appearing in the non-diagonal elements of the first density matrix to become zero.

[0072] Optionally, after waiting for the first preset time, the sample in the first transition state obtains a second transition state having a second density matrix, and the non-diagonal elements of the second density matrix are all zero.

[0073] Optionally, when preparing the pseudopure state, after stopping transmitting the radio frequency pulse to the sample for the first preset time, the radio frequency pulse control unit is further used to transmit a second radio frequency pulse to the sample, and perform a second unitary operation on the sample to exchange the relative positions of the sub-diagonal elements in the second density moment;

[0074] After performing the second unitary operation on the sample, the radio frequency control unit stops transmitting the second radio frequency pulse to the sample, and keeps stopping transmitting the radio frequency pulse to the sample for a second preset time.

[0075] Optionally, within the second preset time, the sample uses a spontaneous depolarization relaxation process to adjust the size of the sub-diagonal elements in the second density matrix.

[0076] Optionally, the radio frequency control unit transmits the second radio frequency pulse to the sample multiple times at intervals, and after each second unitary operation, stops transmitting the radio frequency pulse for the second preset time.

[0077] Optionally, when the radio frequency control unit performs the second unitary operation on the sample once and maintains stopping transmitting radio frequency pulses to the sample for the second preset time, the sample changes from the second transition state to a pseudopure state; or

[0078] When the RF control unit performs the second unitary operation on the sample multiple times at intervals and after each second unitary operation, stops transmitting RF pulses to the sample for the second preset time, the sample changes from the second transition state to a pseudopure state.

[0079] Optionally, the second transition state is a pseudopure state, and the RF control unit transmits the second RF pulse to the sample, and maintains stopping transmitting the RF pulse to the sample for the second preset time, so as to improve the fidelity of the pseudopure state.

[0080] Optionally, the second preset time is the same as or different from the first preset time.

[0081] Optionally, each second preset time is the same, or different, or not completely the same.

[0082] Optionally, the non-diagonal elements in the density matrix of the pseudopure state are zero, and the sub-diagonal elements in the density matrix of the pseudopure state are identical to each other.

[0083] Optionally, the size of the sub-diagonal element in the density matrix of the pseudopure state satisfies the formula:

[0084]

[0085] Among them, xi It is used to represent the secondary diagonal elements, m is used to represent the number of secondary diagonal elements, and m is a natural number greater than or equal to 3, 1≤i≤m and i is a natural number, and X is used to represent the main diagonal elements.

[0086] Optionally, the module values ​​of the non-diagonal elements in the density matrix of the pseudopure state satisfy the formula:

[0087]

[0088] Where D is used to represent any off-diagonal element, |D| represents the modulus, and x i It is used to represent the secondary diagonal elements, m is used to represent the number of secondary diagonal elements, and m is a natural number greater than or equal to 3, 1≤i≤m and i is a natural number, and X is used to represent the main diagonal elements.

[0089] Optionally, the sample is a sample having at least two quantum bits.

[0090] Optionally, the pseudopure state is a pseudopure state of a nuclear magnetic resonance quantum computing system.

[0091] Optionally, the sample is a liquid sample.

[0092] Optionally, when the sample is a nuclear magnetic resonance sample having two quantum bits, the first unitary operation is:

[0093]

[0094] in, β1 and β2 are both rotation coefficients.

[0095] Optionally, when the sample is a nuclear magnetic resonance sample having two quantum bits, the second unitary operation is:

[0096]

[0097] Optionally, the NMR sample comprises dimethyl phosphite.

[0098] Optionally, when the sample is a nuclear magnetic resonance sample having three quantum bits, the first unitary operation is:

[0099]

[0100] in, β1, β2, β3, β4, β5, and β6 are all rotation coefficients.

[0101] Optionally, when the sample is a nuclear magnetic resonance sample having three quantum bits, the second unitary operation is:

[0102]

[0103] Optionally, the NMR sample comprises trifluoroiodoethylene.

[0104] Optionally, the nuclear magnetic resonance quantum computer further comprises a magnet, which is used to generate a constant magnetic field, and the constant magnetic field is used to control and operate the magnetic moment of the spin nuclei in the sample.

[0105] Optionally, within the first preset time, the sample changes from the first transition state to the pseudopure state by a spontaneous dephasing relaxation process.

[0106] Compared with the prior art, the pseudopure state preparation method, nuclear magnetic resonance quantum computer and calculation method disclosed in the present invention have the following technical effects:

[0107] This method uses the sample's own relaxation process to prepare a pseudo-pure state without using a gradient field, effectively reducing the difficulty of preparing a pseudo-pure state. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] Figure 1 This is a flow chart of the preparation method of the pseudo-pure state according to Example 1 of the present invention;

[0109] Figure 2 Schematic diagram of quantum state population change after the first unitary operation of Example 1 of the present invention;

[0110] Figure 3 Schematic diagram of the dephasing relaxation process of the first embodiment of the present invention;

[0111] Figure 4 Schematic diagram of the depolarization relaxation process of Example 1 of the present invention;

[0112] Figure 5 is another flow chart of the preparation method of the pseudo-pure state in Example 1 of the present invention;

[0113] Figure 6 A circuit diagram for preparing a pseudopure state in Example 1 of the present invention;

[0114] Figure 7 Schematic diagram of the depolarization relaxation process and quantum state changes before and after the second unitary operation in Example 1 of the present invention;

[0115] Figure 8 This is a schematic diagram of a nuclear magnetic resonance quantum computer according to the third embodiment of the present invention. DETAILED DESCRIPTION

[0116] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0117] Before describing the various embodiments of the present application in detail, the technical concept of the present application is first briefly described: Several types of pseudopure state preparation methods in the prior art usually require the use of gradient fields for preparation, and the preparation difficulty and complexity are relatively large. To this end, the present application provides a method for preparing a pseudopure state, firstly, the population of other energy eigenstates except the ground state is balanced by a first unitary operation, and then the coherent terms introduced by the first unitary operation are eliminated by dephasing relaxation to prepare a pseudopure state. The preparation method does not need to use a gradient field, and uses the relaxation process of the nuclear spin system itself to achieve pseudopure state preparation, and the technical complexity of the preparation process is low.

[0118] Both pseudopure states and mixed states belong to state representations in quantum mechanics. The relationship between them can be described as follows: pseudopure states are a special type of mixed states that have properties similar to pure states in certain application scenarios (such as nuclear magnetic resonance quantum computing).

[0119] In quantum mechanics, the density matrix is ​​used to describe mixed states, that is, the state of a system that may be in multiple energy eigenstates.

[0120] The density matrix of the mixed state is a Hermitian matrix whose diagonal elements represent the population probabilities (also called population degrees) of eigenstates of different energies, while the off-diagonal elements represent the internal coherence of the system.

[0121] The density matrix of a pseudopure state is a special type of density matrix of a mixed state, used to describe quantum systems that resemble pure states but are actually mixed states.

[0122] For the purpose of clear and concise expression, the diagonal elements used to represent the layout probability of the ground state in the density matrix are defined as the main diagonal elements, and the diagonal elements used to represent each excited state in the density matrix are defined as the sub-diagonal elements. Accordingly, the diagonal elements in the density matrices such as the first density matrix, the second density matrix, and the density matrix of the pseudo-pure state involved in this application document all include the main diagonal elements and multiple sub-diagonal elements.

[0123] The off-diagonal elements of the density matrix of the pseudopure state are zero, and the sub-diagonal elements in the density matrix of the pseudopure state are identical to each other. It should be noted that the off-diagonal elements of the density matrix of the pseudopure state are zero, including two cases: the off-diagonal elements are completely zero (that is, the off-diagonal elements are real numbers 0) and the modulus of the off-diagonal elements is approximately zero; the "identical" in the sub-diagonal elements in the density matrix of the pseudopure state are identical to each other includes two cases: "completely identical" and "approximately identical".

[0124] Ideally, the off-diagonal elements of the density matrix of the pseudopure state are completely zero, that is, the real number 0, and the sub-diagonal elements in the density matrix of the pseudopure state are completely identical to each other. However, in reality, the modulus of each off-diagonal element of the density matrix of the pseudopure state is generally approximately zero, but it does not rule out the possibility that the off-diagonal elements are completely zero. The sub-diagonal elements in the density matrix of the pseudopure state are not completely identical to each other, but there are situations where they are approximately identical. For example, some sub-diagonal elements are completely identical, some sub-diagonal elements are approximately identical; or, the sub-diagonal elements are approximately identical to each other.

[0125] For those skilled in the art, it is understandable that when preparing pseudopure states, due to differences in the material, process, number of quantum bits, magnetic field strength, etc. of each quantum computer itself, or / and due to the influence of external environment such as temperature, it is foreseeable that there are errors within a certain range in the preparation of pseudopure states; in addition, the relevant steps for preparing pseudopure states are also relatively difficult to achieve precise control, etc. Therefore, pseudopure states within a certain error range are acceptable and can be used as the initial state for subsequent quantum calculations. Accordingly, in the density matrix of the pseudopure state actually prepared, the sub-diagonal elements generally include the situation where two sub-diagonal elements are approximately the same, and the non-diagonal elements generally include the situation where the modulus value of the non-diagonal elements is approximately zero.

[0126] For example, the density matrix ρ of the pseudopure state PPS It can be expressed as:

[0127]

[0128] Among them, x i It is used to represent the sub-diagonal elements, 1≤i≤m and i is a natural number, m is used to represent the number of sub-diagonal elements, and m is a natural number greater than or equal to 3, X is used to represent the main diagonal elements, D is used to represent any non-diagonal element, and D is a complex number.

[0129] When m=3, X is replaced by a to represent x i In other words, the density matrix ρ of the pseudopure state is PPS It can be expressed as:

[0130]

[0131] For the NMR sample using two quantum bits, the density matrix of the pseudopure state can be represented by the above 4-row 4-column matrix, which will be discussed below.

[0132] In this application, the size of the sub-diagonal element in the density matrix of the pseudopure state is defined to satisfy Formula 1:

[0133]

[0134] Among them, x i It is used to represent the secondary diagonal elements, m is used to represent the number of secondary diagonal elements, and m is a natural number greater than or equal to 3, 1≤i≤m and i is a natural number, and X is used to represent the main diagonal elements.

[0135] It is clear from the above content that the sub-diagonal elements that satisfy Formula 1 include two cases: completely identical and approximately identical.

[0136] Furthermore, the module values ​​of the off-diagonal elements of the density matrix of the pseudopure state are defined to satisfy Formula 2:

[0137]

[0138] Where D is used to represent any off-diagonal element, |D| represents the modulus, and x i It is used to represent the secondary diagonal elements, m is used to represent the number of secondary diagonal elements, and m is a natural number greater than or equal to 3, 1≤i≤m and i is a natural number, and X is used to represent the main diagonal elements.

[0139] It is clear from the above that the off-diagonal elements that satisfy Formula 2 include two situations: the off-diagonal elements are completely zero and the modulus of the off-diagonal elements is approximately zero. Among them, when D is a non-real number zero and satisfies Formula 2, the modulus of the off-diagonal elements |D| is approximately zero.

[0140] Specifically, if Figure 1 As shown, the preparation method of the pseudo-pure state of the first embodiment includes the following steps:

[0141] Step S1: transmitting a first radio frequency pulse to the sample, the first radio frequency pulse is used to perform a first unitary operation on the thermal equilibrium state of the sample to obtain a first transition state having a first density matrix, wherein the sub-diagonal elements in the first density matrix are the same and non-zero terms appear in the non-diagonal elements of the first density matrix;

[0142] Step S2: Stop transmitting the first radio frequency pulse to the sample, and maintain the stop time of transmitting the radio frequency pulse to the sample for a first preset time to obtain a pseudo-pure state of the sample.

[0143] Before starting step S1, it is necessary to wait for the sample to be in thermal equilibrium. The sample in each embodiment of the present application is a sample having at least two quantum bits. Exemplarily, the sample is a nuclear magnetic resonance sample having two quantum bits.

[0144] Furthermore, the initial spin state of the NMR sample always tends to the thermal equilibrium state, so the thermal equilibrium state can be obtained without additional operations. For a two-qubit NMR sample, the density matrix form of its thermal equilibrium state can be expressed as:

[0145]

[0146] is the Hamiltonian of nuclear spin in a static magnetic field, and Z is a normalization constant.

[0147] For a NMR sample with multiple qubits, the density matrix of the thermal equilibrium state of the NMR sample is ρ eq The population satisfies the Boltzmann distribution, and the density matrix ρ eq It can be expressed as:

[0148]

[0149] ω0 is the Larmor frequency of the nuclear spin, K B is the Boltzmann constant, T is the temperature of the system in thermal equilibrium, To reduce Planck's constant, k is a positive integer, k∈[1,n], and n is the number of nuclear spins used as quantum bits.

[0150] For example, the sample is dimethyl phosphite, and the thermal equilibrium state of the sample is using dimethyl phosphite. 1 H nucleus and 31 The P core constructs a quantum state of two qubits, and the density matrix of the thermal equilibrium state is:

[0151]

[0152] in, They are 1 H nucleus and 31 The resonant frequency of P nuclei in the same static magnetic field. For the convenience of description, the letters a, b, c, and d are used to represent the population of the four energy eigenstates |00><00|, |01><01|, |10><10|, and |11><11|, that is, the population probability. The diagonal elements in the density matrix of the thermal equilibrium state are different and the non-diagonal elements are all zero. It should be noted that the NMR sample can also use other samples that can construct quantum states of multiple quantum bits, and all samples used for NMR quantum computing are applicable.

[0153] The spins in thermal equilibrium are in a mixed state superposed with classical probability, and before performing quantum calculations, it is usually necessary to initialize the quantum states of all nuclear spins to pure states. Since the sample of liquid NMR quantum calculations does not allow all nuclear spins to be suppressed to the ground state by cooling, room temperature NMR quantum calculations require the preparation of the so-called pseudo-pure state (PPS). The pseudo-pure state is not a true pure state, but compared with the true pure state, the dynamic behavior of the two is exactly the same. The density matrix form of the pseudo-pure state can be expressed as:

[0154]

[0155] Where n is the number of quantum bits and α is the coefficient. The significance of pseudopure state is that since the maximum mixed state I (i.e., unit matrix) in nuclear magnetic resonance quantum computing will not produce any readout signal when detected, if the thermal equilibrium state is subjected to certain operations, the prepared quantum state can be expressed as the sum of the maximum mixed state I and the pure state, then the observable dynamic behavior of this quantum state is completely consistent with the true pure state, and this quantum state can be considered a pseudopure state.

[0156] Exemplarily, in step S1, for a sample of two quantum bits, a first unitary operation is performed on the thermal equilibrium state of the sample using a first radio frequency pulse to obtain a first transition state having a first density matrix. In essence, the role of the first radio frequency pulse is to adjust the occupancy of other energy eigenstates (also called excited states) |01><01|, |10><10|, |11><11| in the thermal equilibrium state except the ground state |00><00| to be the same. It should be noted that the same here includes two situations: completely the same and approximately the same. The approximately the same here also satisfies the above formula one.

[0157] like Figure 2 As shown, the first unitary operation can be expressed as:

[0158]

[0159] in, β1 and β2 are both rotation coefficients. By adjusting the rotation coefficients β1 and β2 to appropriate values, 1 H and 31 In the density matrix of the thermal equilibrium state composed of P, the populations of other energy eigenstates except the ground state |00><00| are the same, and the first transition state is obtained. The first density matrix ρ1 of the first transition state can be expressed as:

[0160]

[0161] Since the first radio frequency pulse will cause the quantum state to produce a coherent term, that is, the non-zero non-diagonal element Δ of the density matrix of the first transition state. At this time, the difference between the first transition state and the pseudopure state to be prepared is that the first density matrix ρ1 of the first transition state has a non-zero non-diagonal element Δ, while the density matrix ρ of the pseudopure state PPS There is no off-diagonal element Δ, so the pseudopure state can be obtained by changing the non-zero terms appearing in the off-diagonal elements of the first density matrix ρ1 of the first transition state to zero. It should be noted that the module value of the off-diagonal element Δ does not satisfy the above formula 2, so the off-diagonal element Δ is a non-zero term.

[0162] When the sample is a nuclear magnetic resonance sample with three quantum bits, a first radio frequency pulse is used to perform a first unitary operation on the thermal equilibrium state of the nuclear magnetic resonance sample. The first unitary operation can be expressed as:

[0163]

[0164] in, β1, β2, β3, β4, β5, and β6 are all rotation coefficients.

[0165] As described above, there are two situations in which the sub-diagonal elements in the first density matrix ρ1 of the first transition state are identical to each other, namely, identical and approximately identical. The zero terms in the non-diagonal elements of the first density matrix ρ1 include non-diagonal elements whose modulus is approximately zero and non-diagonal elements are completely zero, that is, all non-diagonal elements except those whose modulus is approximately zero and non-diagonal elements are completely zero can be considered as non-zero terms.

[0166] Exemplarily, in step S2, after stopping transmitting the first radio frequency pulse to the sample, the sample in the first transition state uses a spontaneous relaxation process to change the non-zero terms appearing in the non-diagonal elements of the first density matrix ρ1 to zero. Wherein, the spontaneous relaxation process of the sample includes a dephasing relaxation process. Exemplarily, in step S2, the sample in the first transition state uses a spontaneous dephasing relaxation process to change the non-zero terms appearing in the non-diagonal elements of the first density matrix ρ1 to zero.

[0167] Specifically, in an NMR sample, the relaxation process of nuclear spins refers to the process in which the system spontaneously returns to a thermal equilibrium state, wherein the reduction in the polarization of nuclear spins perpendicular to the static magnetic field (transverse relaxation) caused by spin-spin coupling and magnetic field inhomogeneity is called the dephasing relaxation process. For example, Figure 3 As shown in the figure, if a certain quantum state is described by the density matrix ρ3, dephasing relaxation means that the off-diagonal elements of the density matrix ρ3 (such as Figure 3 The b and c items in the equation (a) gradually decrease to 0, and the new quantum state can be represented by the density matrix ρ'3. The dephasing is based on Attenuation, T2 represents the dephasing decay time constant, and t represents the decay time. Therefore, the sample utilizes the spontaneous dephasing relaxation process, and after the first preset time t1, the non-zero items appearing in the non-diagonal elements of the first density matrix ρ1 decay to 0 to obtain a pseudopure state.

[0168] Optionally, the first preset time t1 is the time required for all non-zero items appearing in the non-diagonal elements of the first density matrix ρ1 in step S2 to become zero. For the first embodiment, the first preset time t1 can be selected as the time required for all non-zero items appearing in the non-diagonal elements of the first density matrix ρ1 to decay to zero during the dephasing relaxation process. Exemplarily, the first preset time t1 is selected in (0, 1] seconds.

[0169] Furthermore, the first preset time t1 can be selected from (0, 200] milliseconds, or (0, 300] milliseconds, or (0, 400] milliseconds, or (0, 500] milliseconds, or [50, 400] milliseconds.

[0170] As an optional embodiment, the first preset time t1 may be 50 milliseconds, or 100 milliseconds, or 150 milliseconds, or 200 milliseconds, or 250 milliseconds, or 300 milliseconds, or 350 milliseconds, or 400 milliseconds, or 450 milliseconds, or 500 milliseconds, or 550 milliseconds, or 600 milliseconds.

[0171] Furthermore, in the NMR sample, the relaxation process of the nuclear spin also includes the depolarization relaxation process, in which the nuclear spin polarization caused by the spin-lattice interaction relaxes toward the static magnetic field direction (longitudinal relaxation), such as Figure 4 As shown, if a certain quantum state is described by the density matrix ρ4, depolarization relaxation means that the diagonal elements of the density matrix ρ4 (the population of the energy eigenstate, i.e. Figure 4 The new quantum state can be represented by the density matrix ρ'4. It should be pointed out that due to the existence of the dephasing process, the off-diagonal elements of the density matrix ρ4 (such as Figure 4 b, c) will also gradually decrease to 0. Depolarization is based on Attenuation, T1 represents the depolarization decay time constant. Since the depolarization relaxation process changes the population of the energy eigenstate, it has an adverse effect on the preparation of pseudopure states by the dephasing relaxation process, so it is necessary to further eliminate the adverse effects of the depolarization relaxation process.

[0172] Specifically, we first need to consider the time difference between the dephasing relaxation process and the depolarization relaxation process. For the first case, when the dephasing decay time constant T2 is much smaller than the depolarization decay time constant T1, the time required for dephasing relaxation is much smaller than the time required for the depolarization relaxation process, and the occupancy of the quantum state will not change significantly, and the impact of the depolarization relaxation process can be ignored. At this time, the sample in the first transition state obtains a second transition state with a second density matrix ρ2 after waiting for the first preset time t1. The non-diagonal elements of the second density matrix ρ2 are all zero, and the occupancy of other energy eigenstates except the ground state |00><00| in the second density matrix ρ2 can be regarded as the same as each other, so the second transition state can be regarded as the final pseudopure state, that is, ρ PPS =ρ2.

[0173] For the second case, when the dephasing decay time constant T2 is close to the depolarization decay time constant T1, the time required for dephasing relaxation is close to the time required for the depolarization relaxation process, and the occupancy of the quantum state will change significantly. At this time, the influence caused by the depolarization relaxation process cannot be ignored. At this time, the sample in the first transition state obtains a second transition state with a second density matrix ρ2 after waiting for the first preset time t1. The non-diagonal elements of the second density matrix ρ2 are all zero. At this time, the occupancy of other energy eigenstates except the ground state |00><00| in the second density matrix ρ2 cannot be regarded as the same, so the second transition state cannot be used as the final pseudopure state. Further operations need to be taken on the second transition state obtained in step S2.

[0174] Specifically, Figure 5 As shown, after executing step S1 and step S2, the preparation method of the pseudo-pure state further includes:

[0175] Step S3: transmitting a second radio frequency pulse to the sample, and performing a second unitary operation U2 on the sample to exchange the relative positions of the sub-diagonal elements in the second density moment;

[0176] Step S4: Stop transmitting the second radio frequency pulse to the sample, and maintain the time of stopping transmitting the radio frequency pulse to the sample for a second preset time.

[0177] In step S4, the sample uses a spontaneous depolarization relaxation process to adjust the size of the sub-diagonal element in the second density matrix ρ2. After executing step S3 and step S4 once or multiple times, the sample changes from the second transition state to a pseudopure state.

[0178] Exemplarily, when the sample is a nuclear magnetic resonance sample with two qubits, the second unitary operation can be expressed as:

[0179]

[0180] When the sample is a nuclear magnetic resonance sample with three qubits, the second unitary operation can be expressed as:

[0181]

[0182] It should be noted that, for the first case, although the impact of the depolarization relaxation process is very small, the second transition state obtained at this time can be directly used as a pseudopure state, but steps S3 and S4 can also be performed once or multiple times to further improve the fidelity of the prepared pseudopure state.

[0183] For example, the second preset time t2 may be the same as or different from the first preset time t1, depending on the actual situation. When performing step S4 multiple times, the second preset time t2 in each step S4 is the same, different, or not completely the same.

[0184] Exemplarily, the second preset time t2 is selected from (0, 1] seconds.

[0185] Furthermore, the second preset time t2 can be selected from (0, 200] milliseconds, or (0, 300] milliseconds, or (0, 400] milliseconds, or (0, 500] milliseconds, or [50, 400] milliseconds.

[0186] As an optional embodiment, the second preset time t2 can be 50 milliseconds, or 100 milliseconds, or 150 milliseconds, or 200 milliseconds, or 250 milliseconds, or 300 milliseconds, or 350 milliseconds, or 400 milliseconds, or 450 milliseconds, or 500 milliseconds, or 550 milliseconds, or 600 milliseconds.

[0187] Combination Figure 6 and Figure 7 , for the second transition state of the two-qubit NMR sample, after one or more second unitary operations U2 and spontaneous depolarization relaxation processes, the size of the sub-diagonal elements in the second density matrix ρ2 can be adjusted to the same, and finally a pseudopure state is obtained. In the second case, the second density matrix ρ2 and the density matrix ρ of the pseudopure state obtained are PPS They can be expressed as follows:

[0188]

[0189] Among them, the sub-diagonal elements of the second density matrix ρ2 are e1, e2, and e3, respectively, and the three are not the same as each other. For example, some of them are the same, some are different, or they are different from each other. Therefore, the second transition state cannot be directly regarded as a pseudopure state.

[0190] Furthermore, the density matrix of the pseudopure state can be expanded into the following form:

[0191]

[0192] Among them, the second term of the above formula is the unit matrix When it is measured in nuclear magnetic resonance quantum computing, no readout signal is generated. The signal intensity obtained when the pseudopure state prepared above is detected is (ae).

[0193] It should be noted that the magnitude relationship between the dephasing decay time constant T2 and the depolarization decay time constant T1, such as "far less than" or "close to", is not judged in the preparation method of the pseudopure state. Usually, the quantum computer will be tested before it leaves the factory, and then the corresponding software, hardware and other conditions will be adjusted accordingly to meet the preparation requirements of the pseudopure state. In the above, the magnitude relationship between the dephasing decay time constant T2 and the depolarization decay time constant T1 is explained to enable readers to better understand the reasons, preparation principles, etc.

[0194] For example but not limited to, the first method: after step S1 and step S2, if the preparation requirements of the pseudo-pure state are met, step S3 and step S4 are omitted;

[0195] The second method: on the basis of the first method, step S3 and step S4 are performed once or multiple times to improve the fidelity of the pseudopure state;

[0196] The third method: after step S1 and step S2, if the pseudopure state has not been reached, then step S3 and step S4 are performed to obtain the pseudopure state;

[0197] The fourth method: regardless of whether a pseudopure state is obtained after step S1 and step S2, step S3 and step S4 will be executed multiple times, and finally a pseudopure state will be obtained.

[0198] Generally, the fourth method is used to obtain a pseudopure state, which does not require judging the magnitude relationship between the dephasing decay time constant T2 and the depolarization decay time constant T1.

[0199] Of course, it is understandable that the tester will judge the size relationship between the dephasing decay time constant T2 and the depolarization decay time constant T1 based on the test results, and then adjust the software and hardware accordingly.

[0200] Although the pseudopure state prepared in the first embodiment is described by taking the pseudopure state of the nuclear magnetic resonance quantum computing system as an example, it is scalable for a person skilled in the art to extend the preparation method of the pseudopure state to other suitable systems, such as but not limited to nuclear magnetic resonance systems, quantum information processing systems, etc. Therefore, as long as the above-mentioned pseudopure state preparation method is adopted, no matter which suitable system is applied to, it should fall within the protection scope of the present application.

[0201] Furthermore, the preparation method of the pseudopure state provided in the first embodiment can be used as a preparation method of the pseudopure state of a nuclear magnetic resonance quantum computer, the nuclear magnetic resonance quantum computer includes a magnet, a radio frequency control unit and a sample, the magnet is used to generate a constant magnetic field, the constant magnetic field is used to control and operate the magnetic moment of the spin nuclei in the sample, and the radio frequency control unit is used to transmit radio frequency pulses to the sample and collect detection signals from the sample;

[0202] In step S1, the radio frequency control unit is used to transmit a first radio frequency pulse to the sample;

[0203] In step S2, the RF control unit stops transmitting the first RF pulse to the sample, and the RF control unit keeps stopping transmitting the RF pulse to the sample for a first preset time.

[0204] In step S3, the radio frequency control unit is used to transmit a second radio frequency pulse to the sample;

[0205] In step S4, the RF control unit stops transmitting the second RF pulse to the sample, and the RF control unit keeps stopping transmitting the RF pulse to the sample for a second preset time.

[0206] This second embodiment also discloses a calculation method of a nuclear magnetic resonance quantum computer, the calculation method comprising the following steps:

[0207] Step 1: preparing a pseudo-pure state, wherein the method for preparing the pseudo-pure state is the method of the above-mentioned embodiment 1;

[0208] Step 2: After preparing the pseudopure state, a third radio frequency pulse is emitted to the sample, and a detection signal from the sample is collected to perform quantum computing; wherein the third radio frequency pulse is used to change the energy level structure of the quantum bit of the sample.

[0209] like Figure 8 As shown, this embodiment three also discloses a nuclear magnetic resonance quantum computer, which includes a sample 10 and a radio frequency control unit 20, wherein the sample 10 has at least two quantum bits, and the radio frequency control unit 20 is used to transmit a radio frequency pulse to the sample 10, and to collect a detection signal from the sample 10; when preparing a pseudopure state, the radio frequency control unit 20 is used to transmit a first radio frequency pulse to the sample, and the first radio frequency pulse is used to perform a first unitary operation on the thermal equilibrium state of the sample 10 to obtain a first transition state having a first density matrix, wherein the sub-diagonal elements in the first density matrix are the same, and non-zero terms appear in the non-diagonal elements of the first density matrix; after performing the first unitary operation on the sample 10, the radio frequency control unit 20 stops transmitting the first radio frequency pulse to the sample 10, and maintains the time of stopping transmitting the radio frequency pulse to the sample 10 for a first preset time to obtain the pseudopure state of the sample 10.

[0210] Furthermore, after the pseudopure state is prepared, the RF control unit 20 is used to transmit a third RF pulse to the sample 10 and collect a detection signal from the sample 10 for quantum computing; wherein the third RF pulse is used to change the energy level structure of the quantum bit of the sample 10.

[0211] Exemplarily, the sample of the third embodiment can be a nuclear magnetic resonance sample with at least two quantum bits, and the nuclear magnetic resonance sample can be dimethyl phosphite or trifluoroethylene iodide. For the two-qubit nuclear magnetic resonance sample, a first unitary operation is performed on the thermal equilibrium state of the sample using a first radio frequency pulse to obtain a first transition state with a first density matrix. In essence, the role of the first radio frequency pulse is to adjust the occupancy of other energy eigenstates |01><01|, |10><10|, |11><11| in the thermal equilibrium state except the ground state |00><00| to the same. Figure 2 As shown, the first unitary operation can be expressed as:

[0212]

[0213] in, β1 and β2 are both rotation coefficients. By adjusting the rotation coefficients β1 and β2 to appropriate values, 1 H and 31 In the density matrix of the thermal equilibrium state composed of P, the populations of other states except the ground state |00><00| are equal, and the first transition state is obtained. The first density matrix ρ1 of the first transition state can be expressed as:

[0214]

[0215] Since the first radio frequency pulse will cause the quantum state to produce a coherent term, that is, the non-zero non-diagonal element Δ of the density matrix ρ1 of the first transition state. At this time, the difference between the first transition state and the pseudopure state to be prepared is that the first density matrix ρ1 of the first transition state has a non-zero non-diagonal element Δ, while the density matrix ρ PPS There is no off-diagonal element Δ, so the pseudopure state can be obtained by changing the non-zero terms appearing in the off-diagonal elements of the first density matrix ρ1 of the first transition state to zero. It should be noted that the module value of the off-diagonal element Δ does not satisfy the above formula 2, so the off-diagonal element Δ is a non-zero term.

[0216] When the sample is a nuclear magnetic resonance sample with three quantum bits, a first radio frequency pulse is used to perform a first unitary operation on the thermal equilibrium state of the nuclear magnetic resonance sample. The first unitary operation can be expressed as:

[0217]

[0218] in, β1, β2, β3, β4, β5, and β6 are all rotation coefficients.

[0219] When the sample is a nuclear magnetic resonance sample with three quantum bits, a first radio frequency pulse is used to perform a first unitary operation on the thermal equilibrium state of the nuclear magnetic resonance sample. The first unitary operation can be expressed as:

[0220]

[0221] in, β1, β2, β3, β4, β5, and β6 are all rotation coefficients.

[0222] As described above, there are two situations in which the sub-diagonal elements in the first density matrix ρ1 of the first transition state are identical to each other, namely, identical and approximately identical. The zero terms in the module values ​​of the non-diagonal elements of the first density matrix ρ1 include approximately zero terms and completely zero terms, that is, all terms other than approximately zero terms and completely zero terms can be considered as non-zero terms.

[0223] Furthermore, within the first preset time, the sample 10 in the first transition state uses a spontaneous relaxation process to convert non-zero terms appearing in the non-diagonal elements of the first density matrix into zero.

[0224] Exemplarily, after the RF control unit 20 stops transmitting the first RF pulse to the sample, the sample in the first transition state uses a spontaneous relaxation process to change the non-zero terms appearing in the non-diagonal elements of the first density matrix ρ1 to zero. Wherein, the spontaneous relaxation process of the sample includes a dephasing relaxation process. Exemplarily, the sample in the first transition state uses a spontaneous dephasing relaxation process to change the non-zero terms appearing in the non-diagonal elements of the first density matrix ρ1 to zero.

[0225] Specifically, in an NMR sample, the relaxation process of nuclear spins refers to the process in which the system spontaneously returns to a thermal equilibrium state, wherein the reduction in the polarization of nuclear spins perpendicular to the static magnetic field (transverse relaxation) caused by spin-spin coupling and magnetic field inhomogeneity is called the dephasing relaxation process. For example, Figure 3 As shown in the figure, if a certain quantum state is described by the density matrix ρ3, dephasing relaxation means that the off-diagonal elements of the density matrix ρ3 (such as Figure 3 The b and c items in the equation (a) gradually decrease to 0, and the new quantum state can be represented by the density matrix ρ'3. The dephasing is based on Attenuation, T2 represents the dephasing decay time constant, and t represents the decay time. Therefore, the sample utilizes the spontaneous dephasing relaxation process, and after the first preset time t1, the non-zero items appearing in the non-diagonal elements of the first density matrix ρ1 decay to 0, thereby obtaining a pseudopure state.

[0226] The first preset time t1 is the time required for all non-zero items appearing in the non-diagonal elements of the first density matrix ρ1 to become zero. For the third embodiment, the first preset time t1 can be selected as the time required for all non-zero items appearing in the non-diagonal elements of the first density matrix ρ1 to decay to zero by dephasing. Exemplarily, the first preset time t1 is selected in (0, 1] seconds.

[0227] Furthermore, the first preset time t1 can be selected from (0, 200] milliseconds, or (0, 300] milliseconds, or (0, 400] milliseconds, or (0, 500] milliseconds, or [50, 400] milliseconds.

[0228] As an optional embodiment, the first preset time t1 may be 50 milliseconds, or 100 milliseconds, or 150 milliseconds, or 200 milliseconds, or 250 milliseconds, or 300 milliseconds, or 350 milliseconds, or 400 milliseconds, or 450 milliseconds, or 500 milliseconds, or 550 milliseconds, or 600 milliseconds.

[0229] Furthermore, in the NMR sample, the relaxation process of the nuclear spin also includes the depolarization relaxation process, in which the nuclear spin polarization caused by the spin-lattice interaction relaxes toward the static magnetic field direction (longitudinal relaxation), such as Figure 4 As shown, if a certain quantum state is described by the density matrix ρ4, depolarization relaxation means that the diagonal elements of the density matrix (the population of the energy eigenstate, i.e. Figure 4 The population of the two terms a and 1-a in the equation (a) changes towards the thermal equilibrium state, and the new quantum state obtained can be represented by the density matrix ρ'4. It should be pointed out that due to the existence of the dephasing relaxation process, the off-diagonal elements of the density matrix ρ4 (such as Figure 4 b, c) will also gradually decrease to 0. Depolarization is based on Attenuation, T1 represents the depolarization decay time constant. Since the depolarization relaxation process changes the population of the energy eigenstate, it has an adverse effect on the preparation of pseudopure states by the dephasing relaxation process, so it is necessary to further eliminate the adverse effects of the depolarization relaxation process.

[0230] Specifically, we first need to consider the time difference between the dephasing relaxation process and the depolarization relaxation process. For the first case, when the dephasing decay time constant T2 is much smaller than the depolarization decay time constant T1, the time required for dephasing relaxation is much smaller than the time required for the depolarization relaxation process, and the occupancy of the quantum state will not change significantly, and the impact of the depolarization relaxation process can be ignored. At this time, the sample in the first transition state obtains a second transition state with a second density matrix ρ2 after waiting for the first preset time t1. The non-diagonal elements of the second density matrix ρ2 are all zero, and the occupancy of other energy eigenstates except the ground state |00><00| in the second density matrix ρ2 can be regarded as the same as each other, so the second transition state can be regarded as the final pseudopure state, that is, ρ PPS =ρ2.

[0231] For the second case, when the dephasing decay time constant T2 is close to the depolarization decay time constant T1, the time required for dephasing relaxation is close to the time required for the depolarization relaxation process, and the occupancy of the quantum state will change significantly. At this time, the influence caused by the depolarization relaxation process cannot be ignored. At this time, after waiting for the first preset time t1, the sample in the first transition state obtains a second transition state with a second density matrix ρ2, and the non-diagonal elements of the second density matrix ρ2 are all zero. At this time, the occupancy of other energy eigenstates except the ground state |00><00| in the second density matrix ρ2 cannot be regarded as the same, so the second transition state cannot be regarded as the final pseudopure state. Further operations are required on the second transition state.

[0232] Specifically, when preparing the pseudopure state, after stopping the transmission of the radio frequency pulse to the sample 10 for the first preset time, the radio frequency control unit 20 is further used to transmit a second radio frequency pulse to the sample 10, and perform a second unitary operation on the sample 10 to exchange the relative positions of the sub-diagonal elements in the second density moment ρ2;

[0233] After the second unitary operation is performed on the sample 10, the RF control unit 20 stops transmitting the second RF pulse to the sample 10, and maintains the stop of transmitting the RF pulse to the sample 10 for a second preset time t2. During the second preset time t2, the sample uses a spontaneous depolarization relaxation process to adjust the size of the sub-diagonal elements in the second density matrix ρ2.

[0234] Exemplarily, the RF control unit 20 is further configured to transmit the second RF pulse to the sample more than 10 times at intervals, and after each second unitary operation, stop transmitting the RF pulse for a second preset time t2.

[0235] Further, when the RF control unit 20 performs a second unitary operation on the sample 10 and maintains stopping the emission of RF pulses until the sample reaches a second preset time t2, the sample changes from the second transition state to a pseudo-pure state; or, when the RF control unit 20 performs multiple second unitary operations on the sample 10 at intervals and, after each second unitary operation, maintains stopping the emission of RF pulses until the sample 10 reaches a second preset time t2, the sample 10 changes from the second transition state to a pseudo-pure state.

[0236] Exemplarily, when the sample is a nuclear magnetic resonance sample with two qubits, the second unitary operation can be expressed as:

[0237]

[0238] When the sample is a nuclear magnetic resonance sample with three qubits, the second unitary operation can be expressed as:

[0239]

[0240] It should be noted that, for the first case, although the impact caused by the depolarization relaxation process is very small, the second transition state obtained at this time can be directly used as a pseudo-pure state, but the RF control unit 20 can also transmit a second RF pulse to the sample 10, and maintain the stop of transmitting the RF pulse to the sample for a second preset time t2, so as to adjust the size of the sub-diagonal elements in the second density matrix ρ2 to the same, thereby further improving the fidelity of the prepared pseudo-pure state.

[0241] Exemplarily, the second preset time t2 may be the same as or different from the first preset time t1, and is set specifically according to actual conditions. The RF control unit 20 transmits the second RF pulse to the sample 10 multiple times and stops transmitting the RF pulse to the sample 10 for the second preset time t2, and each second preset time t2 is the same, or different, or not completely the same.

[0242] Exemplarily, the second preset time t2 is selected from (0, 1] seconds.

[0243] Furthermore, the second preset time t2 can be selected from (0, 200] milliseconds, or (0, 300] milliseconds, or (0, 400] milliseconds, or (0, 500] milliseconds, or [50, 400] milliseconds.

[0244] As an optional embodiment, the second preset time t2 can be 50 milliseconds, or 100 milliseconds, or 150 milliseconds, or 200 milliseconds, or 250 milliseconds, or 300 milliseconds, or 350 milliseconds, or 400 milliseconds, or 450 milliseconds, or 500 milliseconds, or 550 milliseconds, or 600 milliseconds.

[0245] Furthermore, the module values ​​of the off-diagonal elements of the prepared density matrix of the pseudopure state are zero, and the sub-diagonal elements in the density matrix of the pseudopure state are identical to each other. It should be noted that the module values ​​of the off-diagonal elements of the density matrix of the pseudopure state are zero, including two situations: completely zero and approximately zero, and the sub-diagonal elements in the density matrix of the pseudopure state are identical to each other, including two situations: completely the same and approximately the same.

[0246] like Figure 6 and Figure 7 As shown, for the second transition state of the two-qubit NMR sample, after one or more second unitary operations U2 and spontaneous depolarization relaxation processes, the size of the sub-diagonal elements in the second density matrix ρ2 can be adjusted to the same, and finally a pseudopure state is obtained. In the second case, the second density matrix ρ2 and the density matrix ρ of the pseudopure state obtained are PPS They can be expressed as follows:

[0247]

[0248] Among them, the sub-diagonal elements of the second density matrix ρ2 are e1, e2, and e3, respectively, and the three are not the same as each other. For example, some of them are the same, some are different, or they are different from each other. Therefore, the second transition state cannot be directly regarded as a pseudopure state.

[0249] Furthermore, the density matrix of the pseudopure state can be expanded into the following form:

[0250]

[0251] Among them, the second term of the above formula is the unit matrix When it is measured in nuclear magnetic resonance quantum computing, no readout signal is generated. The signal intensity obtained when the pseudopure state prepared above is detected is (ae).

[0252] Furthermore, the pseudopure state prepared in the third embodiment may be a pseudopure state of a quantum information processing system, a pseudopure state of a nuclear magnetic resonance system, or a pseudopure state of a nuclear magnetic resonance quantum computing system.

[0253] In other embodiments, the sample 10 may be a liquid sample.

[0254] Furthermore, the nuclear magnetic resonance quantum computer also includes a magnet 30, which is used to generate a constant magnetic field, and the constant magnetic field is used to control and operate the magnetic moment of the spin nuclei in the sample.

[0255] The specific implementation methods of the present invention are described in detail above. Although some embodiments have been shown and described, those skilled in the art should understand that these embodiments can be modified and improved without departing from the principles and spirit of the present invention, the scope of which is defined by the claims and their equivalents. These modifications and improvements should also be within the scope of protection of the present invention.

Claims

1. A method for preparing a pseudo-pure state, characterized in that: include: Step S1: transmitting a first radio frequency pulse to a sample, wherein the first radio frequency pulse is used to perform a first unitary operation on a thermal equilibrium state of the sample to obtain a first transition state having a first density matrix, wherein subdiagonal elements in the first density matrix are identical to each other, and non-zero terms appear in non-diagonal elements of the first density matrix; Step S2: Stop transmitting the first radio frequency pulse to the sample, and maintain the stop time of transmitting the radio frequency pulse to the sample for a first preset time to obtain a pseudo-pure state of the sample.

2. The method for preparing a pseudopure state according to claim 1, characterized in that: In step S2, the sample in the first transition state uses a spontaneous relaxation process to convert non-zero items appearing in non-diagonal elements of the first density matrix to zero.

3. The method for preparing a pseudopure state according to claim 2, characterized in that: In step S2, the sample in the first transition state uses a spontaneous dephasing relaxation process to convert non-zero terms appearing in non-diagonal elements of the first density matrix to zero.

4. The method for preparing a pseudopure state according to claim 2, characterized in that: In step S2, the sample changes from the first transition state to the pseudopure state by a spontaneous relaxation process.

5. The method for preparing a pseudopure state according to claim 1, characterized in that: The first preset time is selected from (0, 1] seconds.

6. The method for preparing a pseudopure state according to claim 5, characterized in that: The first preset time is selected from (0, 200] milliseconds, or (0, 300] milliseconds, or (0, 400] milliseconds, or (0, 500] milliseconds, or [50, 400] milliseconds.

7. The method for preparing a pseudopure state according to claim 5, characterized in that: The first preset time is 50 milliseconds, or 100 milliseconds, or 150 milliseconds, or 200 milliseconds, or 250 milliseconds, or 300 milliseconds, or 350 milliseconds, or 400 milliseconds, or 450 milliseconds, or 500 milliseconds, or 550 milliseconds, or 600 milliseconds.

8. The method for preparing a pseudo-pure state according to claim 2 or 3, characterized in that: The first preset time is the time required for all non-zero items appearing in the non-diagonal elements of the first density matrix in step S2 to become zero.

9. The method for preparing a pseudopure state according to claim 1, characterized in that: After waiting for a first preset time, the sample in the first transition state obtains a second transition state having a second density matrix, and the non-diagonal elements of the second density matrix are all zero.

10. The method for preparing a pseudopure state according to claim 9, characterized in that: After performing step S1 and step S2, the preparation method of the pseudo-pure state further includes: Step S3: transmitting a second radio frequency pulse to the sample, and performing a second unitary operation on the sample to exchange the relative positions of the sub-diagonal elements in the second density moment; Step S4: Stop transmitting the second radio frequency pulse to the sample, and maintain the stop time of transmitting the radio frequency pulse to the sample for a second preset time.

11. The method for preparing a pseudopure state according to claim 10, characterized in that: In step S4, the sample uses a spontaneous depolarization relaxation process to adjust the size of the sub-diagonal elements of the second density matrix.

12. The method for preparing a pseudopure state according to claim 10, characterized in that: Repeat steps S3 and S4 multiple times.

13. The method for preparing a pseudopure state according to claim 10 or 12, characterized in that: After executing step S3 and step S4 once or multiple times, the sample changes from the second transition state to a pseudo-pure state.

14. The method for preparing a pseudopure state according to claim 10 or 12, characterized in that: The second transition state is a pseudopure state, and step S3 and step S4 are performed to improve the fidelity of the pseudopure state.

15. The method for preparing a pseudopure state according to claim 10, characterized in that: The second preset time is the same as or different from the first preset time.

16. The method for preparing a pseudopure state according to claim 12, characterized in that: The second preset time in each step S4 is the same, or different, or not completely the same.

17. The method for preparing a pseudopure state according to claim 1, characterized in that: The non-diagonal elements in the density matrix of the pseudopure state are zero, and the sub-diagonal elements in the density matrix of the pseudopure state are identical to each other.

18. The method for preparing a pseudopure state according to claim 17, characterized in that: The size of the sub-diagonal elements in the density matrix of the pseudopure state satisfies the formula: Among them, x i It is used to represent the secondary diagonal elements, m is used to represent the number of secondary diagonal elements, and m is a natural number greater than or equal to 3, 1≤i≤m and i is a natural number, and X is used to represent the main diagonal elements.

19. The method for preparing a pseudopure state according to claim 17 or 18, characterized in that: The module values ​​of the off-diagonal elements in the density matrix of the pseudopure state satisfy the formula: Where D is used to represent any off-diagonal element, |D| represents the modulus, and x i It is used to represent the secondary diagonal elements, m is used to represent the number of secondary diagonal elements, and m is a natural number greater than or equal to 3, 1≤i≤m and i is a natural number, and X is used to represent the main diagonal elements.

20. The method for preparing a pseudopure state according to claim 1, characterized in that: The pseudopure state is a pseudopure state of a quantum information processing system or a pseudopure state of a nuclear magnetic resonance system.

21. The method for preparing a pseudopure state according to claim 1 or 20, characterized in that: The pseudopure state is a pseudopure state of a nuclear magnetic resonance quantum computing system, and the sample is a sample having at least two quantum bits.

22. The method for preparing a pseudopure state according to claim 1, characterized in that: When the sample is a nuclear magnetic resonance sample having two quantum bits, the first unitary operation is: in, β1 and β2 are both rotation coefficients.

23. The method for preparing a pseudopure state according to claim 10, characterized in that: When the sample is a nuclear magnetic resonance sample having two quantum bits, the second unitary operation is:

24. The method for preparing a pseudopure state according to claim 1, characterized in that: When the sample is a nuclear magnetic resonance sample with three quantum bits, the first unitary operation is: in, β1, β2, β3, β4, β5, and β6 are all rotation coefficients.

25. The method for preparing a pseudopure state according to claim 10, characterized in that: When the sample is a nuclear magnetic resonance sample with three quantum bits, the second unitary operation is:

26. The method for preparing a pseudopure state according to claim 1, characterized in that: The pseudopure state preparation method is a pseudopure state preparation method for a nuclear magnetic resonance quantum computer, the nuclear magnetic resonance quantum computer comprises a magnet, a radio frequency control unit and the sample, the magnet is used to generate a constant magnetic field, the constant magnetic field is used to control and operate the magnetic moment of the spin nuclei in the sample, the radio frequency control unit is used to transmit radio frequency pulses to the sample and collect detection signals from the sample; In step S1, the radio frequency control unit is used to transmit the first radio frequency pulse to the sample; In step S2, the RF control unit stops transmitting the first RF pulse to the sample, and the RF control unit keeps stopping transmitting the RF pulse to the sample for a first preset time.

27. The method for preparing a pseudopure state according to claim 10, characterized in that: The pseudopure state preparation method is a pseudopure state preparation method for a nuclear magnetic resonance quantum computer, the nuclear magnetic resonance quantum computer comprises a magnet, a radio frequency control unit and the sample, the magnet is used to generate a constant magnetic field, the constant magnetic field is used to control and operate the magnetic moment of the spin nuclei in the sample, the radio frequency control unit is used to transmit radio frequency pulses to the sample and collect detection signals from the sample; In step S1, the radio frequency control unit is used to transmit the first radio frequency pulse to the sample; In step S2, the RF control unit stops transmitting the first RF pulse to the sample, and the RF control unit keeps stopping transmitting the RF pulse to the sample for a first preset time.

28. The method for preparing a pseudopure state according to claim 27, characterized in that: In step S3, the radio frequency control unit is used to transmit the second radio frequency pulse to the sample; In step S4, the RF control unit stops transmitting the second RF pulse to the sample, and the RF control unit keeps stopping transmitting the RF pulse to the sample for a second preset time.

29. The method for preparing a pseudopure state according to claim 2, characterized in that: In step S2, the sample changes from the first transition state to the pseudopure state by a spontaneous dephasing relaxation process.

30. A calculation method for a nuclear magnetic resonance quantum computer, characterized in that: The calculation method includes: Preparing a pseudopure state, wherein the method for preparing a pseudopure state is the method described in any one of claims 1 to 29; and After preparing the pseudopure state, transmitting a third radio frequency pulse to the sample and collecting a detection signal from the sample to perform quantum computing; The third radio frequency pulse is used to change the energy level structure of the quantum bit of the sample.

31. A nuclear magnetic resonance quantum computer, characterized in that: include: A sample having at least two qubits; A radio frequency control unit, used for transmitting radio frequency pulses to the sample and collecting detection signals from the sample; When preparing a pseudopure state, the radio frequency control unit is used to transmit a first radio frequency pulse to the sample, and the first radio frequency pulse is used to perform a first unitary operation on the thermal equilibrium state of the sample to obtain a first transition state having a first density matrix, wherein the sub-diagonal elements in the first density matrix are identical to each other, and non-zero terms appear in the non-diagonal elements of the first density matrix; After performing the first unitary operation on the sample, the RF control unit stops transmitting the first RF pulse to the sample and maintains the stop time of transmitting the RF pulse to the sample for a first preset time to obtain a pseudopure state of the sample.

32. The nuclear magnetic resonance quantum computer according to claim 31, characterized in that: After the pseudopure state is prepared, the radio frequency control unit is used to transmit a third radio frequency pulse to the sample and collect a detection signal from the sample to perform quantum computing; The third radio frequency pulse is used to change the energy level structure of the quantum bit of the sample.

33. The nuclear magnetic resonance quantum computer according to claim 31, characterized in that: During the first preset time, the sample in the first transition state uses a spontaneous relaxation process to convert non-zero items appearing in non-diagonal elements of the first density matrix into zero.

34. The nuclear magnetic resonance quantum computer according to claim 33, characterized in that: During the first preset time, the sample in the first transition state uses a spontaneous dephasing relaxation process to convert non-zero items appearing in non-diagonal elements of the first density matrix into zero.

35. The nuclear magnetic resonance quantum computer according to claim 33, characterized in that: During the first preset time, the sample changes from the first transition state to the pseudopure state by a spontaneous relaxation process.

36. The nuclear magnetic resonance quantum computer according to claim 31, characterized in that: The first preset time is selected from (0, 1] seconds.

37. The nuclear magnetic resonance quantum computer according to claim 36, characterized in that: The first preset time is selected from (0, 200] milliseconds, or (0, 300] milliseconds, or (0, 400] milliseconds, or (0, 500] milliseconds, or [50, 400] milliseconds.

38. The nuclear magnetic resonance quantum computer according to claim 36, characterized in that: The first preset time is 50 milliseconds, or 100 milliseconds, or 150 milliseconds, or 200 milliseconds, or 250 milliseconds, or 300 milliseconds, or 350 milliseconds, or 400 milliseconds, or 450 milliseconds, or 500 milliseconds, or 550 milliseconds, or 600 milliseconds.

39. The nuclear magnetic resonance quantum computer according to claim 33 or 34, characterized in that: The first preset time is the time required for all non-zero items appearing in the non-diagonal elements of the first density matrix to become zero.

40. The nuclear magnetic resonance quantum computer according to claim 31, characterized in that: After waiting for the first preset time, the sample in the first transition state obtains a second transition state having a second density matrix, and the non-diagonal elements of the second density matrix are all zero.

41. The nuclear magnetic resonance quantum computer according to claim 40, characterized in that: When preparing the pseudopure state, after stopping transmitting the radio frequency pulse to the sample for the first preset time, the radio frequency pulse control unit is further used to transmit a second radio frequency pulse to the sample, and perform a second unitary operation on the sample to exchange the relative positions of the sub-diagonal elements in the second density moment; After performing the second unitary operation on the sample, the radio frequency control unit stops transmitting the second radio frequency pulse to the sample, and keeps stopping transmitting the radio frequency pulse to the sample for a second preset time.

42. The nuclear magnetic resonance quantum computer according to claim 41, characterized in that During the second preset time, the sample uses a spontaneous depolarization relaxation process to adjust the size of the sub-diagonal elements in the second density matrix.

43. The nuclear magnetic resonance quantum computer according to claim 41, characterized in that The radio frequency control unit transmits the second radio frequency pulse to the sample multiple times at intervals, and after each second unitary operation, stops transmitting the radio frequency pulse for the second preset time.

44. The nuclear magnetic resonance quantum computer according to claim 41 or 43, characterized in that: When the radio frequency control unit performs the second unitary operation on the sample once and stops transmitting radio frequency pulses to the sample for the second preset time, the sample changes from the second transition state to a pseudo-pure state; or When the RF control unit performs the second unitary operation on the sample multiple times at intervals and after each second unitary operation, stops transmitting RF pulses to the sample for the second preset time, the sample changes from the second transition state to a pseudopure state.

45. The nuclear magnetic resonance quantum computer according to claim 41 or 43, characterized in that: The second transition state is a pseudopure state, and the RF control unit transmits the second RF pulse to the sample and stops transmitting the RF pulse to the sample for the second preset time, so as to improve the fidelity of the pseudopure state.

46. ​​The nuclear magnetic resonance quantum computer of claim 41, wherein: The second preset time is the same as or different from the first preset time.

47. The nuclear magnetic resonance quantum computer of claim 43, wherein: The second preset times are all the same, or different, or not completely the same.

48. The nuclear magnetic resonance quantum computer of claim 31, wherein: The non-diagonal elements in the density matrix of the pseudopure state are zero, and the sub-diagonal elements in the density matrix of the pseudopure state are identical to each other.

49. The nuclear magnetic resonance quantum computer of claim 48, wherein: The size of the sub-diagonal elements in the density matrix of the pseudopure state satisfies the formula: Among them, x i It is used to represent the secondary diagonal elements, m is used to represent the number of secondary diagonal elements, and m is a natural number greater than or equal to 3, 1≤i≤m and i is a natural number, and X is used to represent the main diagonal elements.

50. The nuclear magnetic resonance quantum computer according to claim 48 or 49, characterized in that: The module values ​​of the off-diagonal elements in the density matrix of the pseudopure state satisfy the formula: Where D is used to represent any off-diagonal element, |D| represents the modulus, and x i It is used to represent the secondary diagonal elements, m is used to represent the number of secondary diagonal elements, and m is a natural number greater than or equal to 3, 1≤i≤m and i is a natural number, and X is used to represent the main diagonal elements.

51. The nuclear magnetic resonance quantum computer of claim 31, wherein: The sample is a sample having at least two quantum bits.

52. The nuclear magnetic resonance quantum computer of claim 31, wherein: The pseudopure state is a pseudopure state of a nuclear magnetic resonance quantum computing system.

53. The nuclear magnetic resonance quantum computer according to claim 31 or 51, characterized in that: The sample is a liquid sample.

54. The nuclear magnetic resonance quantum computer of claim 31, wherein: When the sample is a nuclear magnetic resonance sample having two quantum bits, the first unitary operation is: in, β1 and β2 are both rotation coefficients.

55. The nuclear magnetic resonance quantum computer of claim 41, wherein: When the sample is a nuclear magnetic resonance sample having two quantum bits, the second unitary operation is:

56. The nuclear magnetic resonance quantum computer according to claim 54 or 55, characterized in that: The NMR sample includes dimethyl phosphite.

57. The nuclear magnetic resonance quantum computer of claim 41, wherein: When the sample is a nuclear magnetic resonance sample with three quantum bits, the first unitary operation is: in, β1, β2, β3, β4, β5, and β6 are all rotation coefficients.

58. The nuclear magnetic resonance quantum computer of claim 41, wherein: When the sample is a nuclear magnetic resonance sample with three quantum bits, the second unitary operation is:

59. The nuclear magnetic resonance quantum computer according to claim 57 or 58, characterized in that: The NMR sample includes trifluoroiodoethylene.

60. The nuclear magnetic resonance quantum computer of claim 31, wherein: The nuclear magnetic resonance quantum computer also includes a magnet, which is used to generate a constant magnetic field, and the constant magnetic field is used to control and operate the magnetic moment of the spin nuclei in the sample.

61. The nuclear magnetic resonance quantum computer of claim 33, wherein: During the first preset time, the sample changes from the first transition state to the pseudopure state by a spontaneous dephasing relaxation process.

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