Preparation method and device of pseudo-pure state based on radio frequency field inhomogeneity

Abstract

The application discloses a pseudo-pure state preparation method and device based on radio frequency field inhomogeneity. The pseudo-pure state preparation method comprises the following steps: performing a first unitary operation on a thermal equilibrium state of a nuclear magnetic resonance sample to obtain a first quantum state; performing a second unitary operation on the first quantum state, so that diagonal elements corresponding to nuclear spin polarization components in a density matrix of the first quantum state are rotated to a preset direction, and off-diagonal elements corresponding to nuclear spin polarization components are rotated to a direction perpendicular to the preset direction, to obtain a second quantum state; applying a radio frequency field with predetermined parameters to the second quantum state by using a radio frequency coil to perform a non-unitary operation, to obtain a third quantum state; and performing a third unitary operation on the third quantum state to rotate nuclear spin polarization components in the third quantum state to an initial direction, to obtain a pseudo-pure state of the nuclear magnetic resonance sample. The method does not need to use a gradient field, so that the preparation difficulty is reduced, and the preparation time is shortened.

Description

Technical Field

[0001] This invention belongs to the field of quantum computing technology, specifically, it relates to a method and apparatus for preparing pseudopure states based on radio frequency field inhomogeneity. Background Technology

[0002] In nuclear magnetic resonance quantum computing, preparing the initial quantum state—the pseudopure state—is a necessary and indispensable step, as important as initialization in other quantum computing systems. The dynamics and measurement behavior of the pseudopure state are identical to those of the pure state.

[0003] Existing methods for preparing pseudopure states include time averaging (PRA 57, 3348), spatial averaging (PNAS 94, 1634), control transfer (PRA 82, 032315), relaxation (PRA 94, 012312), and line-selective methods (ChemicalPhysics Letters 340, 509). Taking an experiment with n qubits as an example, we will briefly illustrate each method. I. Time Averaging: This method requires repeating the experiment 2^n-1 times, summing the results to obtain the final result. It has high time complexity and requires a nuclear magnetic resonance quantum computer with good time stability. II. Spatial Averaging: This method requires multiple pulsed gradient fields (n gradient fields are needed for an n-qubit experiment), and the efficiency of preparing pseudopure states is low (signal strength decreases on a scale of 1 / 2^n). III. Control Transfer: This method requires multiple pulsed gradient fields. IV. Relaxation Method: Although this method can start from any initial state without using a gradient field, it requires multiple (hundreds) iterations of the same pulse sequence in a single experiment, resulting in a long experiment time. Furthermore, the number of pulse iterations and the waiting time between iterations need to be optimized on a practical NMR quantum computer. V. Line-selective Method: Although this method only requires one gradient field and is highly efficient in preparing pseudopure states, for homonuclear qubits, the gradient field cannot eliminate the zero-order coherence term generated in this method, making it impossible to prepare pseudopure states in homonuclear systems.

[0004] Therefore, existing methods for preparing pseudopure states either require the use of gradient fields, which are difficult to prepare and have high technical barriers, or require long preparation times, which are inefficient and costly. Summary of the Invention

[0005] The technical problem solved by this invention is: how to achieve pseudopure states of nuclear magnetic resonance quantum computing systems without using gradient fields and in a relatively short time.

[0006] This application discloses a method for preparing pseudopure states based on radio frequency field inhomogeneities, the method comprising:

[0007] The first unitary operation is performed on the thermal equilibrium state of the NMR sample to obtain the first quantum state, in which the population of all energy eigenstates except the ground state is the same;

[0008] A second unitary operation is performed on the first quantum state, causing the nuclear spin polarization components corresponding to the diagonal elements in the density matrix of the first quantum state to rotate from the initial direction to be parallel to the preset direction, and causing the nuclear spin polarization components corresponding to the off-diagonal elements to rotate to be perpendicular to the preset direction, thus obtaining the second quantum state;

[0009] A radio frequency field with predetermined parameters is applied to the second quantum state using a radio frequency coil to perform a non-unitary operation, thereby eliminating the nuclear spin polarization component perpendicular to the preset direction and retaining the nuclear spin polarization component parallel to the preset direction, to obtain a third quantum state, wherein the direction of the radio frequency field is perpendicular to the preset direction.

[0010] A third unitary operation is performed on the third quantum state to rotate the nuclear spin polarization component in the third quantum state to the initial direction, thereby obtaining the pseudopure state of the nuclear magnetic resonance sample.

[0011] Preferably, the thermal equilibrium state is a heteronuclear two-qubit quantum state or a multi-qubit quantum state.

[0012] Preferably, when the thermal equilibrium state of the NMR sample is a two-qubit quantum state, the initial direction is the z-direction of a single qubit in the Bloch sphere form, the preset direction is the y-direction of a single qubit in the Bloch sphere form, and the direction of the radio frequency field is the z-direction of a single qubit in the Bloch sphere form. The method for performing the first unitary operation is as follows: a selective excitation pulse is used to perform the first unitary operation U1 to adjust the diagonal elements corresponding to the three eigenstates other than the ground state in the density matrix of the thermal equilibrium state to be the same, thus obtaining the first quantum state. In the density matrix of the first quantum state, some off-diagonal elements have non-zero terms. The first unitary operation U1 is:

[0013]

[0014] in, α1 and α2 are both rotation coefficients.

[0015] Preferably, the operator representation of the second unitary operation is as follows:

[0016]

[0017] in,

[0018] Preferably, the operator representation of the third unitary operation is as follows:

[0019]

[0020] Preferably, the preset parameters include a preset radio frequency field strength and a preset duration of action.

[0021] Preferably, the nuclear magnetic resonance sample is a dimethyl phosphite sample, and the thermal equilibrium state is that of the dimethyl phosphite sample. 1 H nucleus and 31 The two-qubit quantum state of the P-core.

[0022] This application also discloses a pseudopure state preparation device based on radio frequency field inhomogeneity, the pseudopure state preparation device comprising:

[0023] The first unitary operation module is used to perform the first unitary operation on the thermal equilibrium state of the pre-constructed nuclear magnetic resonance sample to obtain the first quantum state, in which the population of other energy eigenstates except the ground state is the same;

[0024] The second unitary operation module performs a second unitary operation on the first quantum state, causing the nuclear spin polarization components corresponding to the diagonal elements in the density matrix of the first quantum state to be parallel to a preset direction and causing the nuclear spin polarization components corresponding to the off-diagonal elements to be perpendicular to the preset direction, thereby obtaining the second quantum state;

[0025] The non-unitary operation module is used to apply a radio frequency field with predetermined parameters to the second quantum state using a radio frequency coil to perform a non-unitary operation, so as to eliminate the nuclear spin polarization component corresponding to the off-diagonal element perpendicular to the preset direction, and retain the nuclear spin polarization component corresponding to the diagonal element parallel to the preset direction, to obtain a third quantum state, wherein the direction of the radio frequency field is perpendicular to the preset direction.

[0026] The third unitary operation module is used to perform a third unitary operation on the third quantum state to rotate the nuclear spin polarization component corresponding to the diagonal element to the initial direction, thereby obtaining the pseudopure state of the nuclear magnetic resonance sample.

[0027] This application also discloses a computer-readable storage medium storing a pseudo-pure state preparation program based on radio frequency field inhomogeneity, wherein the pseudo-pure state preparation program, when executed by a processor, implements the above-described pseudo-pure state preparation method.

[0028] This application also discloses a computer device, which includes a computer-readable storage medium, a processor, and a pseudo-pure state preparation program based on radio frequency field inhomogeneity stored in the computer-readable storage medium, wherein the pseudo-pure state preparation program implements the above-described pseudo-pure state preparation method when executed by the processor.

[0029] The present invention discloses a method and apparatus for preparing pseudopure states based on radio frequency field inhomogeneity, which have the following technical advantages compared with the prior art:

[0030] This method can prepare pseudopure states without using a gradient field, which effectively reduces the preparation difficulty and significantly shortens the preparation time compared with other pseudopure state preparation methods that do not use a gradient field. Attached Figure Description

[0031] Figure 1 This is a flowchart of a pseudopure state preparation method based on radio frequency field inhomogeneity according to Embodiment 1 of the present invention;

[0032] Figure 2 This is a schematic diagram of the population change after the first unitary operation in Embodiment 1 of the present invention;

[0033] Figure 3 This is a diagram showing the state of the radio frequency coil and sample tube in use according to Embodiment 1 of the present invention;

[0034] Figure 4 This is a diagram showing the field strength distribution of a solenoid in the existing technology.

[0035] Figure 5 This is a diagram showing the change in nuclear spin polarization under simulated radio frequency control pulses in Embodiment 1 of the present invention;

[0036] Figure 6 This is a schematic diagram of the nuclear spin of the nuclear magnetic resonance sample in the Bloch sphere according to Embodiment 1 of the present invention.

[0037] Figure 7 This is a schematic diagram of the pseudopure state preparation device based on radio frequency field inhomogeneity according to Embodiment 2 of the present invention;

[0038] Figure 8 This is a schematic diagram of a computer device according to Embodiment 4 of the present invention. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0040] Before describing the various embodiments of this application in detail, the technical concept of this application is first briefly described: Several existing pseudopure state preparation methods either require the use of a gradient field or multiple cyclic experiments. The former is more difficult and complex to prepare, while the latter is time-consuming and inefficient. Therefore, this application provides a pseudopure state preparation method based on radio frequency field inhomogeneity. First, the nuclear spin polarization components to be retained in the NMR sample are rotated to a direction parallel to a preset direction through two unitary operations, and the nuclear spin polarization components to be eliminated are rotated to a direction perpendicular to the preset direction. Then, a radio frequency field is applied to attenuate the nuclear spin polarization components in the direction perpendicular to the preset direction to zero. After turning off the radio frequency field, a unitary operation is performed again to rotate the retained nuclear spin polarization components to the initial direction, thereby obtaining the pseudopure state of the NMR sample. By utilizing the decrease in nuclear spin polarization caused by the inconsistent nuclear spin precession rate at different locations in a non-uniform radio frequency field, a pseudopure state is obtained by eliminating some nuclear spin polarization components while retaining the required nuclear spin polarization components. This process can be completed in a short time without the need to add a gradient field, resulting in high efficiency.

[0041] Specifically, such as Figure 1 As shown, the pseudopure state preparation method based on radio frequency field inhomogeneity in this embodiment includes the following steps:

[0042] Step S10: Perform the first unitary operation on the thermal equilibrium state of the pre-constructed NMR sample to obtain the first quantum state, in which the population of other energy eigenstates except the ground state is the same;

[0043] Step S20: Perform a second unitary operation on the first quantum state, so that the nuclear spin polarization components corresponding to the diagonal elements in the density matrix of the first quantum state are rotated from the initial direction to be parallel to the preset direction, and the nuclear spin polarization components corresponding to the off-diagonal elements are rotated to be perpendicular to the preset direction, thus obtaining the second quantum state;

[0044] Step S30: Apply a radio frequency field with predetermined parameters to the second quantum state using a radio frequency coil to perform a non-unitary operation, so as to eliminate the nuclear spin polarization component perpendicular to the preset direction and retain the nuclear spin polarization component parallel to the preset direction, thereby obtaining the third quantum state, wherein the direction of the radio frequency field is perpendicular to the preset direction.

[0045] Step S40: Perform a third unitary operation on the third quantum state to rotate the nuclear spin polarization component in the third quantum state to the direction perpendicular to the preset direction, thereby obtaining the pseudopure state of the nuclear magnetic resonance sample.

[0046] Before proceeding to step S10, it is necessary to first obtain the thermal equilibrium state.

[0047] The initial spin state in a nuclear magnetic resonance system is generally in thermal equilibrium:

[0048]

[0049] For multispin systems, the population density matrix of their thermal equilibrium states follows a Boltzmann distribution:

[0050]

[0051] in, Let ω0 be the Hamiltonian of the nuclear spin in a static magnetic field, ω0 be the Larmor frequency of the nuclear spin, and K be the value of ω0. B is Boltzmann's constant, and T is the temperature of the system at thermal equilibrium.

[0052] For example, the NMR sample in this embodiment 1 is a dimethyl phosphite sample in thermal equilibrium state. 1 H nucleus and 31 The density matrix of the two-qubit quantum state in thermal equilibrium, constructed using the P-core, is as follows:

[0053]

[0054] in, They are respectively 1 H nucleus and 31 The resonance frequency of the P nucleus in the same static magnetic field. For convenience, the letters a, b, c, and d represent the populations of the four energy eigenstates |00><00|, |01><01|, |10><10|, and |11><11|. In the density matrix of the thermal equilibrium state, each diagonal element is distinct, and all off-diagonal elements are zero. It should be noted that other samples capable of constructing multi-qubit quantum states can also be used for NMR samples.

[0055] In thermal equilibrium, spins exist in a mixed state with classical probabilistic superposition. Quantum computing typically requires initializing all nuclear spin quantum states to a pure state like |00…0>. Liquid NMR quantum computing samples cannot suppress all nuclear spins to the ground state by cooling; therefore, room-temperature NMR quantum computing requires the preparation of a so-called pseudo-pure state (PPS). A pseudo-pure state is a quantum state that is not truly pure |00…0>, but exhibits dynamic behavior completely consistent with the truly pure state |00…0>.

[0056]

[0057] Where n is the number of nuclear spins and α is a coefficient. The significance of pseudopure states lies in the fact that in nuclear magnetic resonance quantum computing, the maximally mixed state I has no readout signal. If the thermal equilibrium state can be prepared into a quantum state that can be expanded into the sum of an identity matrix I and pure states |00…0><00…0|, then the observable dynamical behavior of this quantum state is completely consistent with that of the truly pure state |00…0><00…0|.

[0058] Since the transition from thermal equilibrium to a pseudopure state is a non-unitary process, the preparation of the pseudopure state requires not only radio frequency pulses but also the introduction of a non-unitary process. For example, the time-averaging method or the phase-cycle method introduces a non-unitary process by summing multiple experimental results, while the spatial averaging method and the relaxation method introduce a non-unitary process using a gradient field and free relaxation, respectively. This embodiment utilizes the non-uniformity of the radio frequency field caused by the radio frequency coil to introduce a non-unitary process.

[0059] Specifically, in step S10, a selective excitation pulse is used to adjust the thermal equilibrium state so that the populations of the other intrinsic states |01><01|, |10><10|, and |11><11|, excluding the ground state |00><00|, are equal. For example... Figure 2 As shown, the first unitary operation of selective excitation A transition can occur between the |10> and |11> states; a transition can occur between the |11> and |10> states. This can be achieved by adjusting the rotation coefficients α1 and α2 to appropriate values. 1 H and 31 The quantum state density matrix composed of P has all populations equal except for the ground state |00><00|, that is:

[0060]

[0061] Because selective excitation operations introduce coherent terms into the quantum state, i.e., off-diagonal elements of the first quantum state density matrix. At this point, the first quantum state ρ and the pseudopure state ρ we want to prepare... PPS The only difference is the existence of off-diagonal elements Δ, so non-unitary operations are needed to remove the non-zero off-diagonal elements in these density matrices.

[0062] Furthermore, the first quantum state obtained in step S10 can be represented by a Pauli basis vector expansion as follows:

[0063]

[0064] in, Let ε be a Pauli basis vector. i,j Let be the coefficients of each expansion term. The diagonal elements of the density matrix ρ of the first quantum state are... Since the diagonal elements have been balanced to the desired pseudopure population form, the nuclear spin polarization components corresponding to the diagonal elements need to be protected by rotating them to the parallel direction of a predetermined direction (see the description below; the polarization of nuclear spin in the predetermined direction is not affected by radio frequency field inhomogeneities). The nuclear spin polarization components corresponding to the off-diagonal elements Δ in the density matrix of the first quantum state are those that we want to eliminate using radio frequency field inhomogeneities, including... item.

[0065] For example, the second unitary operation of the rotation operation is performed in step S20. The first quantum state may contain only I z The spin polarization of the component rotates to a direction parallel to the preset direction (the y-direction in the Bloch sphere), and all components containing I... x ,I y The spin polarization of the component rotates to the direction perpendicular to the preset direction (on the xz plane in the Bloch sphere), resulting in the second quantum state. In this embodiment, the initial direction is the z-direction of a single qubit in the Bloch sphere form, the preset direction is the y-direction of a single qubit in the Bloch sphere form, and the direction of the radio frequency field is the z-direction of a single qubit in the Bloch sphere form.

[0066] Specifically, in step S30, a radio frequency field with predetermined parameters is applied to the second quantum state using a radio frequency coil to perform a non-unitary operation, thereby eliminating the nuclear spin polarization component perpendicular to the preset direction and retaining the nuclear spin polarization component parallel to the preset direction, thus obtaining the third quantum state, wherein the direction of the radio frequency field is perpendicular to the preset direction. The principle of step S30 is described below in two parts.

[0067] First, the radio frequency field generated by the radio frequency coil is non-uniform. For example... Figure 3 As shown, an RF coil is wound around the outside of a sample tube, which contains an NMR sample on the order of Avogadro's constant. Ideally, the RF field should be uniform for all nuclear spins in the NMR sample. However, in reality, a coil of finite length will always result in inhomogeneities in the RF field. Figure 3 The black dashed line in the middle represents the spatial distribution of the radio frequency field strength emitted by the radio frequency coil. It can be seen that the radio frequency field strength experienced by the nuclear spins at both ends of the sample tube is weaker than that experienced by the nuclear spins at the center of the coil.

[0068] Furthermore, to more intuitively demonstrate the magnetic field strength of the radio frequency coil, please refer to... Figure 4The field strength distribution diagram of the solenoid shown (cited in: Ren Jungang, Zhao Chunwang. Full field distribution of magnetic field of finite-length solenoid [J]. Physics Bulletin, 2010(10):3) shows that the field strength distribution inside the solenoid is relatively uniform, the field strength is stronger near the solenoid end, and the field strength outside the solenoid decreases significantly. This results in the radio frequency field strength received by the part of the sample liquid column located outside the coil not reaching the expected intensity.

[0069] Second, radio frequency field inhomogeneities lead to inconsistent nuclear spin behavior. This inconsistency in nuclear spin dynamics manifests in the ensemble as a decrease in nuclear spin polarization, and the NMR readout signal depends precisely on the net magnetic moment contributed by the nuclear spin ensemble polarization. For example... Figure 5 As shown, a series of radio frequency (RF) control pulses of increasing duration were applied to the nuclear spins in the |0> state, causing the nuclear spins to rotate around the y-axis. The signal intensity of the nuclear spin ensemble was observed after applying the RF control pulses in each experiment. The projection of the nuclear spin polarization onto the xy-plane exhibits a sinusoidal variation, while the magnitude of the nuclear spin polarization decays significantly with increasing RF control field duration. At scales much smaller than the decoherence time, this decay effect is due to the inhomogeneity of the RF field.

[0070] To illustrate the attenuation effect more vividly, let's combine... Figure 6 The Bloch sphere shown is used for further description. The dynamics of a single qubit can be represented by vectors on the Bloch sphere, with the static magnetic field oriented in the positive z-axis direction, and the |0> and |1> states generated by the Zeeman split of the nuclear spin oriented in the +z and -z directions, respectively. The unitary operation of the radio frequency control pulse that causes the nuclear spin to rotate around the y-axis can be written as... This means that, ideally, all controlled nuclear spins in the sample tube should precess around the y-axis at the same rate. However, a non-uniform radio frequency field causes the precession rates of nuclear spins at different locations in the sample tube to be inconsistent. This inconsistency in dynamics manifests in the NMR signal as a decrease in the polarization of the nuclear spin ensemble. It is noteworthy that this effect of decreasing nuclear spin polarization only affects the nuclear spin polarization components (x, z components) perpendicular to the y-axis (a predetermined direction), while the nuclear spin polarization components (y components) parallel to the rotation axis (y-axis) are not affected. This first embodiment utilizes this selective non-unitary process to prepare the pseudopure state required for NMR quantum computing.

[0071] Specifically, in step S30, a radio frequency field with a preset radio frequency field strength and a preset duration is generated using a radio frequency coil. This radio frequency field acts on the second quantum state, generating a non-unitary process. Ideally, the density matrix evolution is expressed as... However, the U experienced by nuclear spins at different spatial locations is actually different. (Definition located at...) The unitary operation sensed by the nuclear spin at that location is The evolution of the density matrix of the entire NMR sample can be written as a non-unitary process. In this first embodiment, under ideal conditions, assuming the radio frequency field is uniform, a unitary operation can be generated on the second quantum state. Where γ H and γ P They are respectively 1 H nucleus and 31 The gyromagnetic ratio of the P nucleus and They are respectively 1 H and 31 The standard radio frequency field strength of the P-channel, where t is the duration of action. However, as the above analysis shows, the radio frequency field generated by the radio frequency coil is non-uniform. Therefore, the non-unitary process actually generated after the radio frequency field acts on the second quantum state will, after the duration of action, result in the radio frequency field non-uniformity causing... 1 H and 31 In the second quantum state composed of P, all those containing I x ,I z All Pauli terms decay to 0, with the second quantum state containing I. x ,I z The Pauli term is the first quantum state containing I. x ,I y The Pauli terms are obtained through a second unitary operation U2, and the sum of these terms is also the off-diagonal element Δ in the density matrix of the first quantum state. The third quantum state, obtained after the non-unitary action of the radio frequency field, retains only the nuclear spin polarization components in the direction parallel to the preset direction; that is, the third quantum state contains population information for four energy eigenstates |00><00|,|01><01|,|10><10|,|11><11|. The term (equivalent to the first quantum state containing only I) z (The Pauli item of the quantity).

[0072] In step S40, the operator representation of the third unitary operation is as follows: The third unitary operation rotates the nuclear spin polarization component in the direction parallel to the preset direction back to the direction perpendicular to the preset direction (z direction), thus obtaining... Return That is, the populations a and e that satisfy the pseudopure state relation return to the diagonal elements of the density matrix, thus obtaining the pseudopure state:

[0073]

[0074] This pseudopure state can be represented as:

[0075]

[0076] Among them, unit array In nuclear magnetic resonance quantum computing, there is no readout signal, ρ PPS It is a pseudopure state with a signal intensity of (ae), thus completing the preparation of the pseudopure state.

[0077] The pseudopure state preparation method based on radio frequency field inhomogeneity provided in this embodiment can prepare pseudopure states without using a gradient field, effectively reducing the preparation difficulty, and significantly shortening the preparation time compared with other pseudopure state preparation methods that do not use a gradient field.

[0078] like Figure 7 As shown in the second embodiment, a pseudopure state preparation device based on radio frequency field inhomogeneity is also disclosed. This pseudopure state preparation device includes a first unitary operation module 100, a second unitary operation module 200, a non-unitary operation module 300, and a third unitary operation module 400. The first unitary operation module 100 performs a first unitary operation on the thermal equilibrium state of a pre-constructed NMR sample to obtain a first quantum state, in which the population of all energy eigenstates except the ground state is the same. The second unitary operation module 200 performs a second unitary operation on the first quantum state, causing the nuclear spin polarization components corresponding to the diagonal elements in the density matrix of the first quantum state to rotate from the initial direction to a direction parallel to a preset direction, and the nuclear spin polarization components corresponding to the non-diagonal elements to rotate to a direction perpendicular to the preset direction, thus obtaining a second quantum state. The non-unitary operation module 300 is used to apply a radio frequency field of predetermined parameters to the second quantum state using a radio frequency coil to perform a non-unitary operation, thereby eliminating the nuclear spin polarization components corresponding to the off-diagonal elements perpendicular to the preset direction and retaining the nuclear spin polarization components corresponding to the diagonal elements parallel to the preset direction, to obtain the third quantum state, wherein the direction of the radio frequency field is perpendicular to the preset direction. The third unitary operation module 400 is used to perform a third unitary operation on the third quantum state to rotate the nuclear spin polarization components corresponding to the diagonal elements to the initial direction, thereby obtaining a pseudopure state of the NMR sample.

[0079] Furthermore, the more detailed working process of each module, such as the first unitary operation module 100, the second unitary operation module 200, the non-unitary operation module 300, and the third unitary operation module 400, can be found in the corresponding description in Embodiment 1, and will not be repeated here.

[0080] This embodiment also discloses a computer-readable storage medium storing a pseudo-pure state preparation program based on radio frequency field inhomogeneity. When the pseudo-pure state preparation program based on radio frequency field inhomogeneity is executed by a processor, it implements the pseudo-pure state preparation method based on radio frequency field inhomogeneity of the above embodiment.

[0081] This third embodiment also discloses a computer device, at the hardware level, such as... Figure 8 As shown, the computer device includes a processor 12, an internal bus 13, a network interface 14, and a computer-readable storage medium 11. The processor 12 reads the corresponding computer program from the computer-readable storage medium and runs it, forming a request processing device at the logical level. Of course, in addition to the software implementation, one or more embodiments of this specification do not exclude other implementation methods, such as logic devices or a combination of hardware and software, etc. That is to say, the execution subject of the following processing flow is not limited to each logic unit, but can also be hardware or logic devices. The computer-readable storage medium 11 stores a pseudopure state preparation program based on radio frequency field inhomogeneity. When the processor executes the pseudopure state preparation program based on radio frequency field inhomogeneity, it implements the above-described pseudopure state preparation method based on radio frequency field inhomogeneity.

[0082] Computer-readable storage media include both permanent and non-permanent, removable and non-removable media that can store information by any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer-readable storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, disk storage, quantum memory, graphene-based storage media or other magnetic storage devices, or any other non-transfer medium that can be used to store information accessible by a computing device.

[0083] The specific embodiments of the present invention have been described in detail above. Although some embodiments have been shown and described, those skilled in the art should understand that modifications and improvements can be made to these embodiments without departing from the principles and spirit of the present invention as defined by the claims and their equivalents, and such modifications and improvements should also be within the protection scope of the present invention.

Claims

1. A method for preparing pseudopure states based on radio frequency field inhomogeneities, characterized in that, The method for preparing the pseudopure state includes: A first unitary operation is performed on the thermal equilibrium state of the nuclear magnetic resonance sample to obtain a first quantum state. In the first quantum state, the population of other energy eigenstates except the ground state is the same. The thermal equilibrium state is a heteronuclear two-qubit quantum state or a multi-qubit quantum state. A second unitary operation is performed on the first quantum state, causing the nuclear spin polarization components corresponding to the diagonal elements in the density matrix of the first quantum state to rotate from the initial direction to be parallel to the preset direction, and causing the nuclear spin polarization components corresponding to the off-diagonal elements to rotate to be perpendicular to the preset direction, thus obtaining the second quantum state; A radio frequency field with predetermined parameters is applied to the second quantum state using a radio frequency coil to perform a non-unitary operation, thereby eliminating the nuclear spin polarization component perpendicular to the predetermined direction and retaining the nuclear spin polarization component parallel to the predetermined direction, to obtain a third quantum state, wherein the direction of the radio frequency field is perpendicular to the predetermined direction, and the predetermined parameters include a predetermined radio frequency field strength and a predetermined duration. A third unitary operation is performed on the third quantum state to rotate the nuclear spin polarization component in the third quantum state to the initial direction, thereby obtaining the pseudopure state of the nuclear magnetic resonance sample.

2. The method for preparing pseudopure states based on radio frequency field inhomogeneity according to claim 1, characterized in that, When the thermal equilibrium state of the NMR sample is a two-qubit quantum state, the initial direction is the z-direction of a single qubit in the Bloch sphere form, the preset direction is the y-direction of a single qubit in the Bloch sphere form, and the direction of the radio frequency field is the z-direction of a single qubit in the Bloch sphere form. The method for performing the first unitary operation is as follows: a selective excitation pulse is used to perform the first unitary operation U1 to adjust the diagonal elements corresponding to the three eigenstates (excluding the ground state) in the density matrix of the thermal equilibrium state to be the same, thus obtaining the first quantum state. In the density matrix of the first quantum state, some off-diagonal elements have non-zero terms. The first unitary operation U1 is: ， in, , and All are rotation coefficients.

3. The method for preparing pseudopure states based on radio frequency field inhomogeneity according to claim 2, characterized in that, The operator representation for the second unitary operation is as follows: ， in, .

4. The method for preparing pseudopure states based on radio frequency field inhomogeneity according to claim 3, characterized in that, The operator representation for the third unitary operation is as follows: 。 5. The method for preparing a pseudopure state based on radio frequency field inhomogeneity according to claim 1, characterized in that, The nuclear magnetic resonance sample is a dimethyl phosphite sample, and the thermal equilibrium state is that of the dimethyl phosphite sample. 1 H nucleus and 31 The two-qubit quantum state of the P-core.

6. A pseudopure state preparation device based on radio frequency field inhomogeneity, characterized in that, The pseudo-pure state preparation apparatus includes: The first unitary operation module is used to perform the first unitary operation on the thermal equilibrium state of the pre-constructed nuclear magnetic resonance sample to obtain the first quantum state. The population of the other energy eigenstates in the first quantum state is the same except for the ground state. The thermal equilibrium state is a heteronuclear two-qubit quantum state or a multi-qubit quantum state. The second unitary operation module performs a second unitary operation on the first quantum state, causing the nuclear spin polarization components corresponding to the diagonal elements in the density matrix of the first quantum state to rotate from the initial direction to be parallel to the preset direction, and causing the nuclear spin polarization components corresponding to the off-diagonal elements to rotate to be perpendicular to the preset direction, thereby obtaining the second quantum state; The non-unitary operation module is used to apply a radio frequency field with predetermined parameters to the second quantum state using a radio frequency coil to perform a non-unitary operation, so as to eliminate the nuclear spin polarization component corresponding to the off-diagonal element perpendicular to the preset direction, and retain the nuclear spin polarization component corresponding to the diagonal element parallel to the preset direction, to obtain a third quantum state, wherein the direction of the radio frequency field is perpendicular to the preset direction, and the predetermined parameters include a preset radio frequency field strength and a preset duration of action; The third unitary operation module is used to perform a third unitary operation on the third quantum state to rotate the nuclear spin polarization component corresponding to the diagonal element in the initial direction to obtain the pseudopure state of the nuclear magnetic resonance sample.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a pseudo-pure state preparation program based on radio frequency field inhomogeneity, which, when executed by a processor, implements the pseudo-pure state preparation method according to any one of claims 1 to 5.

8. A computer device, characterized in that, The computer device includes a computer-readable storage medium, a processor, and a pseudo-pure state preparation program based on radio frequency field inhomogeneity stored in the computer-readable storage medium, wherein the pseudo-pure state preparation program, when executed by the processor, implements the pseudo-pure state preparation method according to any one of claims 1 to 5.

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