Method and apparatus for detecting quantum pattern states

Abstract

The invention relates to a method and a device for detecting a quantum graph state. The method comprises the following steps: measuring a first expected value of a product of components of quantum bits of all first-class lattice points in a state space along a first direction in a quantum information system; measuring the (v-1) th expected value of the product of each quantum bit and the component of the quantum bit coupled with the quantum bit in the state space along the v-th direction in the quantum information system; and determining whether the quantum information system is in a graph state or not according to the first expected value and all the (v-1) th expected values.

Description

TECHNICAL FIELD

[0001] The present disclosure belongs to the technical field of quantum information, and in particular, relates to a method and device for detecting a quantum graph state. BACKGROUND

[0002] In the field of quantum, a graph state is a multi-component entangled state that can be corresponded to a graph in mathematics, the vertices of the graph represent quantum bits, and the edges represent the interaction or coupling between two quantum bits. Among them, the graph state on a square lattice can be referred to as a cluster state. The cluster state is a commonly used entangled state in quantum mechanics, which has the characteristics of maximum connectivity and persistent entanglement compared with other entangled states, and has great application potential in the fields of quantum computing, quantum communication and quantum information processing.

[0003] For example, in the field of quantum computing, the cluster state is a universal quantum resource and a basic building block for measurement-based quantum computing, which can be used to implement quantum gate operations and quantum algorithms. One of the characteristics of the cluster state is that its construction method is relatively simple, and it has a certain robustness, which makes it have a certain practicality in quantum computing. In addition, in the field of quantum communication, the quantum cluster state can be used for quantum key distribution, quantum remote state transmission and other tasks.

[0004] The quantum cluster state can be realized by different physical systems, such as ion traps, superconducting qubits and photonic systems. SUMMARY

[0005] According to a first aspect of the present disclosure, a method for detecting a quantum graph state is provided, comprising: measuring a first expectation value of a product of components of quantum bits of all first-type lattice points in a quantum information system along a first direction in a state space, wherein the quantum information system comprises first-type lattice points and second-type lattice points, each first-type lattice point is coupled with one or more second-type lattice points, and each second-type lattice point is coupled with an even number of first-type lattice points; measuring a v-1th expectation value of a product of components of each quantum bit and quantum bits coupled with the quantum bit along a vth direction in the state space, wherein v is an integer from 3 to k+4, k is less than or equal to the number of coupled quantum bits, the second direction is perpendicular to the first direction, the second direction is a direction in which a ground state and an excited state of the quantum bit are connected, the vth direction is a direction in which a unit vector of the first direction and a unit vector of the second direction are linearly combined, and the vth direction is different with different values of v; and determining whether the quantum information system is in the quantum graph state according to the first expectation value and all v-1th expectation values.

[0006] In some embodiments, measuring the first expectation value of the product of the components along the first direction comprises rotating the qubits in the state space such that the components originally along the first direction are rotated to the second direction, and measuring the first expectation value along the second direction; measuring the (v-1)th expectation value of the product of the components along the vth direction comprises rotating the qubits in the state space such that the components originally along the vth direction are rotated to the second direction, and measuring the (v-1)th expectation value along the second direction.

[0007] In some embodiments, the rotating comprises at least one of: adjusting at least one of the Rabi frequency and the detuning frequency such that the Rabi frequency and the detuning frequency are equal and greater than the coupling coefficient to rotate the qubits in the state space about a direction in which a unit vector of the first direction and a unit vector of the second direction are located; adjusting the Rabi frequency and the detuning frequency such that the Rabi frequency is greater than the coupling coefficient and the detuning frequency is less than the coupling coefficient to rotate the qubits in the state space about the first direction; adjusting the Rabi frequency and the detuning frequency such that the detuning frequency is greater than the coupling coefficient and the Rabi frequency is less than the coupling coefficient to rotate the qubits in the state space about the second direction.

[0008] In some embodiments, the quantum information system is a cluster state of a chain of N qubits, N being an odd number, the qubits of the first type being the first odd qubits of the chain, wherein each qubit is coupled to the qubits of the neighboring sites.

[0009] In some embodiments, determining whether the quantum information system is in the quantum cluster state according to the first expectation value and all the (v-1)th expectation values comprises: determining whether the quantum information system is in the quantum cluster state according to the difference between the first expectation value and 1, and the difference between the expectation value of the stabilizer of each site and 1; wherein, X u is the component of the qubit of the u-th site along the first direction in the state space, Z u is the component of the qubit of the u-th site along the second direction in the state space, u taking an integer value from 1 to N, the first expectation value M0 satisfies: M0 = <∏X i >, wherein i takes an odd integer value from 1 to N; the second expectation value of the product of the components of the qubit of the i-th site and the qubits coupled to the qubit of the i-th site along the third direction in the state space satisfies: wherein the third direction is the same as the first direction, i takes an integer value from 2 to N-1; the third expectation value of the product of the components of the qubit of the i-th site and the qubits coupled to the qubit of the i-th site along the fourth direction in the state space satisfies: in the case of i = 1, in the case where i is an integer between 2 and N-1 inclusive, in the case where i = N, where the fourth direction is a direction in which a unit vector of the second direction and a unit vector of the first direction are summed; a fourth expectation value of a product of a component of the quantum bit of the i-th lattice site and a component of the quantum bit coupled to the quantum bit of the i-th lattice site in the state space along a fifth direction satisfies: in the case where i = 1, in the case where i is an integer between 2 and N-1 inclusive, in the case where i = N, where the fifth direction is a direction in which a unit vector of the second direction is subtracted from a unit vector of the first direction; an expectation value M of the stabilizer of the i-th lattice site i satisfies: in the case where i = 1, in the case where i is an integer between 2 and N-1 inclusive, in the case where i = N,

[0010] In some embodiments, the quantum information system is a bipartite multidimensional graph state having N quantum bits.

[0011] In some embodiments, determining whether the quantum information system is in the quantum graph state according to the first expectation value and all the v-1-th expectation values includes: determining whether the quantum information system is in the quantum graph state according to a difference between the first expectation value and 1, and a difference between the expectation value of the stabilizer of each lattice site and 1; where X u is a component of the quantum bit of the u-th lattice site in the state space along the first direction, Z u is a component of the quantum bit of the u-th lattice site in the state space along the second direction, u is an integer between 1 and N, and the first expectation value M0 satisfies: M0 = <∏ i X i >, where i is a number of the quantum bit of the first type of lattice site; a v-1-th expectation value of a product of a component of the quantum bit of the i-th lattice site and a component of the quantum bit coupled to the quantum bit of the i-th lattice site in the state space along the v-th direction satisfies: where i is an integer between 1 and N, j is a number of the quantum bit coupled to the quantum bit of the i-th lattice site, and θ is an angle between the v-th direction and the second direction; an expectation value M of the stabilizer of the i-th lattice site i satisfies: wherein i is an integer from 1 to N, θ is an angle between the v direction and the second direction, a θ is a linear combination coefficient corresponding to the v direction.

[0012] In some embodiments, the quantum information system is determined to be in the quantum graph state when the difference between the first expectation value and the expectation value of the stabilizer of each lattice point and 1 is less than 1 / N 2 .

[0013] In some embodiments, measuring the expectation value along the second direction comprises: operation a. removing the quantum bits in the excited state by using laser; operation b. performing fluorescence imaging on the remaining quantum bits in the ground state to obtain the value of the quantum bits in the position to be measured; repeating operation a and operation b, and taking the average of the obtained quantum bit values as the expectation value.

[0014] In some embodiments, the quantum bits are Rydberg atom systems, and the Hamiltonian of the Rydberg atom system is wherein Ω(t) is a Rabi frequency, Δ(t) is a detuning frequency, C6 is a coupling coefficient of the Rydberg atom inter-van der Waals force, |g> and <g| are ground states, |r> and <r| are Rydberg states, i and j each represent the number of lattice points, and j>i, and n is a Rydberg particle number operator.

[0015] In some embodiments, the method further comprises: in the case of adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Ω=Δ=h>>C6, evolving the Rydberg atom system for In the second direction, measurement is performed to obtain the expectation value of the component along the first direction in the state space; in the case of adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Ω=0, Δ=h>>C6, evolving the Rydberg atom system for Δt3=1 / (4h), and then in the case of adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Δ=0, Ω=h>>C6, evolving the Rydberg atom system for Δt4=1 / (8h), measurement is performed in the second direction to obtain the expectation value of the component along the third direction in the state space, wherein the third direction is the direction in which the sum of the unit vector of the first direction and the unit vector of the second direction is located; in the case of adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Ω=0, -Δ=h>>C6, evolving the Rydberg atom system for Δt3=1 / (4h), and then in the case of adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Δ=0, Ω=h>>C6, evolving the Rydberg atom system for Δt4=1 / (8h), measurement is performed in the second direction to obtain the expectation value of the component along the fourth direction in the state space, wherein the fourth direction is the direction in which the difference between the unit vector of the second direction and the unit vector of the first direction is located.

[0016] In some embodiments, the quantum bits are one of an ion trap, a superconducting quantum bit, and a photon system.

[0017] According to a second aspect of the present disclosure, there is provided an apparatus for detecting a quantum graph state, comprising: a measurement module configured to measure a first expectation value of a product of components of all first-type lattice sites in a quantum information system along a first direction in a state space, wherein the quantum information system comprises first-type lattice sites and second-type lattice sites, each first-type lattice site is coupled with one or more second-type lattice sites, and each second-type lattice site is coupled with an even number of first-type lattice sites; and measure a v-1th expectation value of a product of components of each quantum bit and quantum bits coupled with the quantum bit along a vth direction in the state space, wherein v is an integer from 3 to k+4, k is less than or equal to the number of coupled quantum bits, the second direction is perpendicular to the first direction, the second direction is a direction in which a ground state and an excited state of the quantum bit are connected in the state space, the vth direction is a direction in which a unit vector of the first direction and a unit vector of the second direction are linearly combined, and the vth direction is different as v is different; and a processing module configured to determine whether the quantum information system is in a quantum graph state according to the first expectation value and all v-1th expectation values.

[0018] In some embodiments, the measurement module comprises: a laser configured to generate laser light capable of rotating the quantum bits in the state space and removing the quantum bits in the excited state; and an imaging unit configured to perform fluorescence imaging on the remaining quantum bits in the ground state to obtain the expectation value of the quantum bits in the position to be measured.

[0019] Other features and advantages of the present disclosure will become more apparent from the following detailed description of exemplary embodiments of the present disclosure with reference to the attached drawings. BRIEF DESCRIPTION OF DRAWINGS

[0020] The accompanying drawings, which constitute a part of this specification, illustrate embodiments of the present disclosure and serve to explain the principles of the present disclosure.

[0021] The present disclosure can be understood moreappreciably with reference to the following detailed description when considered in conjunction with the accompanying drawings, in which:

[0022] Figure 1 A flowchart of a method for detecting a quantum graph state according to an exemplary embodiment of the present disclosure is shown;

[0023] Figure 2 A flowchart of step S100 according to a specific embodiment of the present disclosure is shown;

[0024] Figure 3 A flowchart of step S200 according to a specific embodiment of the present disclosure is shown;

[0025] Figure 4 FIG. 17 shows a flow diagram of measuring a desired value in a second direction according to an embodiment of the present disclosure;

[0026] Figure 5 FIG. 18 shows a structural diagram of a quantum cluster state according to an exemplary embodiment of the present disclosure;

[0027] Figure 6 FIG. 19 shows a structural diagram of a quantum graph state according to an exemplary embodiment of the present disclosure;

[0028] Figure 7 FIG. 20 shows an example block diagram of an apparatus for detecting a quantum graph state according to an exemplary embodiment of the present disclosure;

[0029] Figure 8 FIG. 21 shows a diagram of preparing and detecting a quantum cluster state according to an embodiment of the present disclosure.

[0030] Note that, in the following embodiments, the same reference numerals are sometimes used to designate the same parts or parts having the same function among different drawings, and repeated explanation thereof is omitted. In the present specification, similar reference numerals and letters are used to designate similar items, and therefore, once an item is defined in one drawing, it need not be further discussed in subsequent drawings.

[0031] For ease of understanding, the position, size, range, and the like of each structure shown in the drawings and the like are sometimes not actual position, size, range, and the like. Therefore, the disclosed embodiments are not limited to the position, size, range, and the like disclosed in the drawings and the like. In addition, the drawings are not necessarily drawn to scale, and some features can be exaggerated to show details of specific components. DETAILED DESCRIPTION

[0032] Various exemplary embodiments of the present disclosure will now be described in detail below with reference to the accompanying drawings. Note that the relative arrangement, numerical expressions, and numerical values of components and steps set forth in these embodiments are not limiting to the scope of the present disclosure unless specifically stated otherwise.

[0033] The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way limiting to the scope of the disclosure and its applications or uses. Those skilled in the art will recognize that many modifications can be made to the exemplary embodiments and the concepts described herein, and as such are intended to be within the scope of the disclosure.

[0034] Techniques, methods, and apparatus known to those of ordinary skill in the related art can not be discussed in detail herein, but should be considered as part of the specification, where appropriate.

[0035] Before quantum computing, quantum communication or quantum information processing, etc. is performed, it is usually necessary to first determine whether the quantum state prepared in the quantum information system meets the expected standard. Specifically, for a quantum information system using graph states (including cluster states) as operation resources, it is usually necessary to detect the proportion of graph states in the prepared quantum state. When the proportion of graph states is higher than the expected standard, it is considered that the prepared quantum state meets the use requirements.

[0036] Quantum graph states (including quantum cluster states) are a specific class of stable states. When the expectation value of all stable states is 1, the quantum state is a complete quantum graph state. Therefore, whether the quantum information system is in the expected state can be confirmed by measuring the expectation value of the stable state of the quantum information system.

[0037] However, to detect or authenticate whether the prepared quantum state is a graph state or a cluster state, different operations need to be performed on different quantum bits to obtain the expectation value of the stable state of the quantum information system. On the existing atomic quantum computing platform, this requires moving the atoms to be operated to different operation regions for operation, which requires a large amount of resources, and detection or authentication is relatively difficult.

[0038] To solve the above problems, the present disclosure provides a method for detecting a quantum graph state.

[0039] In an exemplary embodiment of the present disclosure, as shown in Figure 1 The method for detecting a quantum graph state can include: step S100, measuring the first expectation value of the product of the components of all first-type lattice quantum bits in the quantum information system along the first direction in the state space; step S200, measuring the v-1 expectation value of the product of the components of each quantum bit and the quantum bits coupled with the quantum bit along the v direction in the state space; and step S300, determining whether the quantum information system is in a quantum graph state according to the first expectation value and all v-1 expectation values.

[0040] In order to clearly and intuitively describe the content of the present disclosure, the quantum state of a quantum bit is described in the state space in this paper. Specifically, the connection between the excited state and the ground state of a quantum bit can be taken as the second direction in the state space, wherein the second direction is perpendicular to the first direction, and the midpoint of the connection between the point where the excited state is located and the point where the ground state is located is taken as the origin, and the length of the connection between the point where the excited state is located and the point where the ground state is located is taken as the diameter to form a Bloch sphere. The position of a quantum bit in the Bloch sphere or on the sphere surface is the current state of the quantum bit.

[0041] In this disclosure, the X direction is used to represent the first direction, the Z direction is used to represent the second direction, and linear combinations of X and Z, such as Z+X, ZX, etc., are used to represent other directions pointed to by the unit vectors of X and Z under that linear combination. Unless otherwise specified, all first directions, second directions, up to the v-th direction, etc., appearing in this disclosure refer to directions in the state space.

[0042] In this context, the quantum information system is divisible, and at least one subclass of lattice nodes has an even degree, where the degree of a lattice node refers to the number of lattice nodes coupled to that lattice node. Specifically, the quantum information system can include first-class lattice nodes and second-class lattice nodes, with each first-class lattice node coupled to one or more second-class lattice nodes, and each second-class lattice node coupled to an even number of first-class lattice nodes. In graph states or cluster states, coupling refers to an interaction between qubits on two coupled lattice nodes, such that the two qubits are sufficiently strongly entangled to enable the quantum information system to be used for quantum computing, quantum communication, or quantum information processing. In this paper, coupling can also be replaced by adjacency, entanglement, interaction, connection, etc. Furthermore, coupling between lattice nodes and coupling between qubits on lattice nodes have the same meaning in this paper.

[0043] Some examples of quantum information systems, such as Figure 5 and Figure 6 As shown. Among them, Figure 5 The example shown is a qubit chain consisting of 9 qubits 1-9, where even-numbered qubits are coupled to an even number of other qubits and thus can be considered as a second-class lattice point, and odd-numbered qubits are coupled to one or more other qubits and thus can be considered as a first-class lattice point. Figure 5 The nine qubits shown are merely an example; other examples may contain different numbers of qubits. Additionally, Figure 6 The diagram shows an example of a multidimensional qubit pattern, consisting of 10 qubits 1-10. Qubits numbered 2, 4, 7, and 9 are coupled with an even number of other qubits and can therefore be considered as second-class lattice points. Qubits numbered 1, 3, 5, 6, 8, and 10 are coupled with one or more other qubits and can therefore be considered as first-class lattice points. Figure 6 The 10 qubits shown are merely an example; other examples may contain different numbers of qubits. In some other embodiments, where the degree of all lattice points in the system is even (i.e., all lattice points are coupled to an even number of another type of lattice point), either type of lattice point can be designated as the first type and the other as the second type.

[0044] In the system, the expected value of the stabilizer can include: an expected value M0 of the stabilizer of all first-type lattice points and an expected value M of the stabilizer of each lattice point i . Wherein the expected value of the stabilizer of all first-type lattice points is a first expected value M0 of a product of components of quantum bits of all first-type lattice points in a state space along a first direction, satisfying M0 = <Π i X i > where i takes the number of quantum bits of the first-type lattice points. The expected value of each lattice point is an expected value M of a product of a component of quantum bits of each lattice point in a state space along a first direction and a component of quantum bits of all lattice points coupled with the lattice point in a state space along a second direction i , satisfying M i = <X i Π j Z j > where i, j are the numbers of quantum bits of respective lattice points, for example, in N lattice points, i takes an integer between 1 and N, j takes the number of quantum bits coupled with the quantum bits of the i-th lattice point, X i is a component of quantum bits of the i-th lattice point in a state space along a first direction, and Z j is a component of quantum bits of the j-th lattice point in a state space along a second direction.

[0045] In step S100, the first expected value of the product of the components of the quantum bits of all first-type lattice points in a state space along a first direction is measured. In some embodiments, M0 can be directly obtained by measurement.

[0046] In some embodiments, as shown in Figure 2 , step S100 can include: step S110, rotating the quantum bits in a state space so that the original components in the first direction are rotated to the second direction, and step S120, measuring the first expected value along the second direction. Wherein, as shown in Figure 4 , step S120 can include: step S122, operation a. removing quantum bits in an excited state by laser, step S124, operation b. fluorescent imaging of the remaining quantum bits in a ground state to obtain the value of the quantum bits in the position to be measured, step S126, repeating operation a and operation b, and taking the average of the obtained quantum bit values as the expected value.

[0047] In step S200, the expected value of the product of each qubit and the component coupled to that qubit along the v-th direction in the state space is measured in the quantum information system. Here, v is an integer from 3 to k+4, and the v-th direction varies with the value of v. Specifically, to avoid the difficulty of operating on a single qubit, the expected value M of the stabilizer at the i-th lattice point is obtained more easily. i It is possible to measure the (v-1)th desired value along the v-th direction in state space by operating multiple qubits together as a whole. satisfy Then we can rely on linear combinations Eliminate those that do not have <X i ∏ j Z j +Z i ∑ j X j ∏ g Z g Terms of the form > and the coefficients of the remaining terms are set to 1, i.e., linear combinations yield the following: According to the Cauchy-Schwarz inequality or the anti-commutation relation, we can obtain... <Z i ∑ j X j ∏ g Z g >=0, that is Thus, the stabilizer M of the lattice point is obtained. i Where i is the lattice node number corresponding to the stabilizer, j is the qubit number coupled to the qubit at the lattice node containing the stabilizer, and ∑ is calculated for all j. j Accumulation or finding π j Multiply by g, where g is the number of the qubit coupled to the lattice point where the stabilizer resides, and g is the number of the qubit that is not the same as j. Calculate π over all g. g Multiplication, where i is coupled to only one j and g does not exist, ∏ g Z g =1. X i X is the component of the qubit at the i-th lattice point along the first direction in the state space. j Z is the component of the qubit at the j-th lattice point along the first direction in the state space. i Z is the component of the qubit at the i-th lattice point along the second direction in the state space. j Z is the component of the qubit at the j-th lattice point along the second direction in the state space. g Let be the component of the qubit at the g-th lattice point along the second direction in the state space. Here, θ is the angle between the v-th direction and the second direction, and a... θLet M be the linear combination coefficients corresponding to the v-th direction, and let M be the summation of M with respect to θ. i It is the sum of multiple products obtained by multiplying a component along the first direction with multiple components along the second direction, i.e., satisfying Where k is less than or equal to the number of qubits coupled to the qubit, the v-th direction is the direction of the linear combination of the unit vector of the first direction and the unit vector of the second direction, one of the v-th directions can be the same as the first direction, and one of the v-th directions can be the same as the second direction.

[0048] In some embodiments, such as Figure 3 As shown, step S200 may include: step S210, rotating the qubit in the state space so that the component originally in the v-th direction rotates to the second direction; and step S220, measuring the (v-1)-th desired value along the second direction. The specific operation process of step S220 may be similar to or the same as the specific operation process of step S120. Figure 4 As shown, step S220 may include: step S122, operation a. using a laser to remove the qubits in the excited state; step S124, operation b. performing fluorescence imaging on the remaining qubits in the ground state to obtain the value of the qubit at the position to be measured; step S126, repeating operation a and operation b, and taking the average of the obtained qubit values ​​as the expected value.

[0049] As mentioned above, Figure 2 The specific process of step S100 is shown, which may include: step S110, rotating the qubit in the state space so that the component originally in the first direction is rotated to the second direction; step S120, measuring along the second direction to obtain the first expected value. Figure 3 The specific process of step S200 is shown, which may include: S210, rotating the qubit in the state space so that the component originally in the v-th direction is rotated to the second direction; step S220, measuring the expected value of the v-1-th direction along the second direction.

[0050] The rotation in steps S110 and S210 can include at least one of the following: adjusting at least one of the Rabi frequency and the detuning frequency such that the Rabi frequency and the detuning frequency are equal and much larger than the coupling coefficient, so as to make the quantum bit rotate in the state space around a direction of a unit vector of the first direction and a unit vector of the second direction; adjusting the Rabi frequency and the detuning frequency of the system such that the Rabi frequency is much larger than the coupling coefficient and the detuning frequency is much smaller than the coupling coefficient, so as to make the quantum bit rotate in the state space around the first direction; or adjusting the Rabi frequency and the detuning frequency of the system such that the detuning frequency is much larger than the coupling coefficient and the Rabi frequency is much smaller than the coupling coefficient, so as to make the quantum bit rotate in the state space around the second direction. The Rabi frequency is a frequency at which the quantum bit changes between the ground state and the excited state under the action of the external optical field, and is embodied on the Bloch sphere as rotation around the X axis. The size of the Rabi frequency can be adjusted by changing the laser intensity, such as the power of the laser. The detuning frequency is a frequency at which the quantum bit has a phase change under the action of the external optical field, and is embodied on the Bloch sphere as rotation around the Z axis. The size of the detuning frequency can be adjusted by changing the difference between the laser frequency and the inherent frequency of the atom, such as using an acousto-optic modulator. The coupling coefficient represents the strength of the interaction between multiple quantum bits. The Rabi frequency and / or the detuning frequency being much larger than the coupling coefficient means that the corresponding frequency is large enough to exclude the influence of the coupling coefficient in the operation and make the quantum bit rotate in the state space. The Rabi frequency or the detuning frequency being much smaller than the coupling coefficient means that the frequency is small enough to exclude the influence of the quantum bit rotating in the state space due to the small frequency.

[0051] As described above, with reference to Figure 4 Steps S120 and S220 can include: step S122, operation a. removing the quantum bits in the excited state by using laser light, step S124, operation b. performing fluorescence imaging on the remaining quantum bits in the ground state to obtain the value of the quantum bits in the position to be measured, step S126, repeating operation a and operation b, and taking the average of the obtained quantum bit values as the expected value.

[0052] In step S122, specifically, laser light with a photon energy between the excited state and the ground state can be inputted, so that the excited state quantum bits are ionized and the ground state quantum bits remain unchanged. Under the action of the environmental electric field, the ionized excited state quantum bits leave the system, and only the ground state quantum bits remain.

[0053] At step S124, specifically, after the excited state qubits leave the system, only the ground state qubits remain, and fluorescence imaging can be performed on the system. According to the positions and number of the remaining qubits obtained by fluorescence imaging, the result of the measurement can be determined. For example, if there is a qubit at the position when imaging, it indicates that the qubit is in the ground state, and if there is no qubit at the position when imaging, it indicates that the qubit is in the excited state. After the fluorescence imaging determines the remaining qubits, the measurement value of the qubit in the ground state is 1, and the measurement value of the qubit in the excited state is -1.

[0054] At step S126, specifically, since quantum mechanical measurement is probabilistic, the result obtained by a single measurement of a quantum state can only be one of the ground state or the excited state. Specifically, only the value of the Z-direction endpoint position in the Bloch sphere can be obtained with the probability of the proportion of the state, and the actual expected value in the Z-direction cannot be directly obtained. Therefore, the values of the qubits obtained after multiple measurements are averaged as the actual expected value in the Z-direction. In addition, in the case of obtaining the expectation value of the product of multiple quantum state components, the multiple quantum state components are first measured and the product is calculated, and then the product obtained by multiple measurements is averaged as the expectation value of the product of the components.

[0055] Returning to Figure 1 At step S300, whether the quantum information system is in a quantum cluster state is determined according to the first expectation value and all the v-1 expectation values. Specifically, according to the method of the foregoing embodiments, the expectation value of the stabilizer M0 and the expectation value of the plurality of stabilizers M i In some embodiments, when the difference between the expectation value of all stabilizers and 1 is less than 1 / N 2 , i.e., the difference between the first expectation value and the expectation value of the stabilizer of each lattice point and 1 is less than 1 / N 2 , it is determined that the quantum information system is in a quantum graph state, where N is the number of qubits in the quantum information system.

[0056] Next, the value of each v-th direction and the linear combination method in the cluster state of the qubit chain are specifically described in combination with embodiments similar to the embodiments of the present disclosure Figure 5

[0057] As described above, the quantum information system can be a cluster state of a qubit chain with N qubits, N is an odd number, one of the endpoints is numbered as 1, each qubit is coupled with the qubit adjacent to the number, the qubit of the first type of lattice point is the odd number point of the qubit chain, and the qubit of the second type of lattice point is the even number point of the qubit chain.

[0058] The first expectation value M0 satisfies: M0 = <∏X i ​where i takes on odd integers from 1 to N, X i is the component of the quantum bit at the ith lattice site in state space along the first direction.

[0059] is the second expectation value of the product of the component of the quantum bit at the ith lattice site in state space along the third direction and the component of the quantum bit coupled to the quantum bit at the ith lattice site in state space along the third direction satisfies: where i takes on integers from 2 to N-1, the third direction is the same as the first direction, X i is the component of the quantum bit at the ith lattice site in state space along the first direction, X i-1 is the component of the quantum bit at the i-1th lattice site in state space along the first direction, X i+1 is the component of the quantum bit at the i+1th lattice site in state space along the first direction.

[0060] is the third expectation value of the product of the component of the quantum bit at the ith lattice site in state space along the fourth direction and the component of the quantum bit coupled to the quantum bit at the ith lattice site in state space along the fourth direction satisfies: in the case where i = 1, and in the case where i = N, the fourth direction is the direction in which the unit vector of the second direction and the unit vector of the first direction sum, X i is the component of the quantum bit at the ith lattice site in state space along the first direction, X i-1 is the component of the quantum bit at the i-1th lattice site in state space along the first direction, X i+1 is the component of the quantum bit at the i+1th lattice site in state space along the first direction, Z i is the component of the quantum bit at the ith lattice site in state space along the second direction, Z i-1 is the component of the quantum bit at the i-1th lattice site in state space along the second direction, Z i+1 is the component of the quantum bit at the i+1th lattice site in state space along the second direction, X1 is the component of the quantum bit at the 1st lattice site in state space along the first direction, X2 is the component of the quantum bit at the 2nd lattice site in state space along the first direction, X N is the component of the quantum bit at the Nth lattice site in state space along the first direction, X N-1 is the component of the quantum bit at the N-1th lattice site in state space along the first direction, Z1 is the component of the quantum bit at the 1st lattice site in state space along the second direction, Z2 is the component of the quantum bit at the 2nd lattice site in state space along the second direction, Z Nis a component of the quantum bit at the Nth lattice point in the state space along the second direction, Z N-1 is a component of the quantum bit at the N-1th lattice point in the state space along the second direction.

[0061] is a fourth expectation value of a product of a component of the quantum bit at the ith lattice point in the state space along the fifth direction and a component of the quantum bit coupled to the quantum bit at the ith lattice point in the state space along the fifth direction satisfies: in a case where i takes an integer value between 2 and N-1 inclusive, in a case where i = 1, and in a case where i = N, the fifth direction is a direction in which a difference between a unit vector of the second direction and a unit vector of the first direction is located, X i is a component of the quantum bit at the ith lattice point in the state space along the first direction, X i-1 is a component of the quantum bit at the i-1th lattice point in the state space along the first direction, X i+1 is a component of the quantum bit at the i+1th lattice point in the state space along the first direction, Z i is a component of the quantum bit at the ith lattice point in the state space along the second direction, Z i-1 is a component of the quantum bit at the i-1th lattice point in the state space along the second direction, Z i+1 is a component of the quantum bit at the i+1th lattice point in the state space along the second direction, X1 is a component of the quantum bit at the 1st lattice point in the state space along the first direction, X2 is a component of the quantum bit at the 2nd lattice point in the state space along the first direction, X N is a component of the quantum bit at the Nth lattice point in the state space along the first direction, X N-1 is a component of the quantum bit at the N-1th lattice point in the state space along the first direction, Z1 is a component of the quantum bit at the 1st lattice point in the state space along the second direction, Z2 is a component of the quantum bit at the 2nd lattice point in the state space along the second direction, Z N is a component of the quantum bit at the Nth lattice point in the state space along the second direction, Z N-1 is a component of the quantum bit at the N-1th lattice point in the state space along the second direction.

[0062] an expectation value of the stabilizer at the ith lattice point satisfies: in a case where i = 1, in a case where i takes an integer value between 2 and N-1 inclusive, and in a case where i = N,

[0063] In the above embodiments, θ in the third direction is taken as 90°, which is the same as the first direction. θ in the fourth direction is taken as 45°, which is the direction where the sum of the unit vectors of the second direction and the first direction lies. θ in the fifth direction is taken as -45°, which is the direction where the difference between the unit vector of the second direction and the unit vector of the first direction lies.

[0064] In some other embodiments, as Figure 6 shown, the quantum information system can be a bipartite multi-dimensional graph state. In the case where there are w coupled qubits for a certain qubit, it is in the form of Each term in contains a total of w + 1 Z or X direction component operators. It can be divided into w + 2 classes according to the number of Z direction component operators and X direction component operators in each term. Then, w + 2 different θs can be obtained through linear combination to get the required M that only contains 1 X direction operator i = <X i ∏ j Z j + Z i ∑ j X j ∏ g Z g >. By choosing some θs, the number of θs that need to be measured can be further reduced. For example, by simultaneously choosing θ and -θ and then taking the difference, the terms with an even number of X direction component operators can be eliminated together. For example, as shown in the previous Figure 5 embodiment of the cluster state of the one-dimensional qubit chain, when w is 1, that is, at the endpoints, such a choice only requires 2 θs. And when w is 2, one group is in the form of θ and -θ, then a total of only 3 θs are required. Similarly, for any w, θ can be chosen in this form, so that only w + 1 θs are needed to implement this method.

[0065] Next, in combination with the specific embodiments of the present disclosure, steps S110 and step S210 in the method for detecting a quantum graph state according to the present disclosure are implemented in the specific quantum system of the cluster state of the one-dimensional qubit chain, as [[ID=3-2]] Figure 8 shown.

[0066] According to a specific embodiment of the present disclosure, the qubit is a Rydberg atom system, and the Hamiltonian of the Rydberg atom system is where Ω(t) is the Rabi frequency, Δ(t) is the detuning frequency, C6 is the coupling coefficient of the van der Waals force between Rydberg atoms, |g> and <g| are the ground states, |r> and <r| are the Rydberg states, n is the Rydberg particle number operator, i and j each represent the lattice point number, ∑ i is the sum over all i, and ∑ i＜j is the sum over all i and j that satisfy j > i. For example, for the case of a total of 3 lattice points, ∑i＜j The summation of i and j is required: i = 1, j = 2; i = 1, j = 3; i = 2, j = 3.

[0067] The cluster state can be prepared by evolving the Rydberg atomic system with the adjusted Rabi frequency Ω and detuning frequency Δ to satisfy Ω = Δ = h >> C6, i.e., making the Rydberg atomic system rotate counterclockwise around the Z+X axis in the state space with an angular frequency of 2πh, evolving the Rydberg atomic system for Δt1 = 1 / (2h), i.e., rotating counterclockwise around the Z+X axis in the state space by 90°. Then, the Rydberg atomic system is evolved with the adjusted Rabi frequency Ω and detuning frequency Δ to satisfy Ω = Δ = 0, i.e., making the Rydberg atomic system rotate counterclockwise around the X axis in the state space with an angular frequency of 2πh, evolving the Rydberg atomic system for Δt2 = 1 / (2C6), i.e., rotating counterclockwise around the X axis in the state space by 45°. Figure 8 As shown in the middle state preparation part. h is an arbitrary frequency value satisfying the formula condition, and h >> C6 means that h is large enough to ignore the influence of coupling in the rotation process, so h can be selected as large as possible. In other embodiments according to the present disclosure, the cluster state or graph state can also be prepared in other ways.

[0068] After the cluster state is prepared, steps S110 and S210 of the present method can be implemented in the following way.

[0069] In the case of adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Ω = Δ = h >> C6, i.e., making the Rydberg atomic system rotate counterclockwise around the Z+X axis in the state space with an angular frequency of 2πh, evolving the Rydberg atomic system for Δt1 = 1 / (2h), i.e., rotating counterclockwise around the Z+X axis in the state space by 90°. In the case of adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Ω = Δ = h >> C6, i.e., making the Rydberg atomic system rotate counterclockwise around the Z+X axis in the state space with an angular frequency of 2πh, evolving the Rydberg atomic system for Δt1 = 1 / (2h), i.e., rotating counterclockwise around the Z+X axis in the state space by 90°. In the case of adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Ω = Δ = h >> C6, i.e., making the Rydberg atomic system rotate counterclockwise around the Z+X axis in the state space with an angular frequency of 2πh, evolving the Rydberg atomic system for Δt1 = 1 / (2h), i.e., rotating counterclockwise around the Z+X axis in the state space by 90°. Figure 8 As shown in the middle state preparation part. h is an arbitrary frequency value satisfying the formula condition, and h >> C6 means that h is large enough to ignore the influence of coupling in the rotation process, so h can be selected as large as possible.

[0070] In the case of adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Ω = 0, Δ = h >> C6, i.e., making the Rydberg atomic system rotate counterclockwise around the Z axis in the state space with an angular frequency of 2πh, evolving the Rydberg atomic system for Δt3 = 1 / (4h), i.e., rotating counterclockwise around the Z axis in the state space by 90°; and then adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Δ = 0, Ω = h >> C6, i.e., making the Rydberg atomic system rotate counterclockwise around the X axis in the state space with an angular frequency of 2πh, evolving the Rydberg atomic system for Δt4 = 1 / (8h), i.e., rotating counterclockwise around the X axis in the state space by 45°. Figure 8 In the case of adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Ω = 0, Δ = h >> C6, i.e., making the Rydberg atomic system rotate counterclockwise around the Z axis in the state space with an angular frequency of 2πh, evolving the Rydberg atomic system for Δt3 = 1 / (4h), i.e., rotating counterclockwise around the Z axis in the state space by 90°; and then adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Δ = 0, Ω = h >> C6, i.e., making the Rydberg atomic system rotate counterclockwise around the X axis in the state space with an angular frequency of 2πh, evolving the Rydberg atomic system for Δt4 = 1 / (8h), i.e., rotating counterclockwise around the X axis in the state space by 45°.

[0071] In the case of adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Ω = 0, -Δ = h >> C6, that is, making the Rydberg atomic system rotate clockwise around the Z axis in the state space at an angular frequency of 2πh, the Rydberg atomic system is evolved for Δt3 = 1 / (4h), that is, the system rotates clockwise around the Z axis in the state space by 90°. Then in the case of adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Δ = 0, Ω = h >> C6, that is, making the Rydberg atomic system rotate counterclockwise around the X axis in the state space at an angular frequency of 2πh, the Rydberg atomic system is evolved for Δt4 = 1 / (8h), that is, the system rotates counterclockwise around the X axis in the state space by 45°, and the expectation value of the Z-X direction can be measured in the Z direction, as shown in the Z-X direction measurement part in Figure 8 h is an arbitrary frequency value satisfying the formula condition, and h >> C6 means that h is large enough to ignore the influence of coupling in the rotation process, so h can be selected as a value as large as possible.

[0072] More expectation values of other directions in the Z direction can also be measured by combining other different Rabi frequencies and detuning frequencies and different action times.

[0073] In other specific embodiments according to the present disclosure, the quantum bit can also be a system such as an ion trap, a superconducting quantum bit, or a photon system.

[0074] In embodiments according to the present disclosure, the quantum information system can be a quantum computing system, a quantum communication system, or a quantum information processing system.

[0075] According to another aspect of the present disclosure, an apparatus for detecting a quantum state is also provided. As Figure 7As shown, the device 400 for detecting a quantum graph state can include a measurement module 402 and a processing module 404. The measurement module 402 can be configured to measure a first expectation value of a product of components of quantum bits of all first-type lattice sites in a quantum information system along a first direction in a state space, wherein the quantum information system includes first-type lattice sites and second-type lattice sites, each first-type lattice site is coupled to one or more second-type lattice sites, and each second-type lattice site is coupled to an even number of first-type lattice sites; and measure a v-1th expectation value of a product of components of each quantum bit and quantum bits coupled to the quantum bit along a vth direction in the state space, wherein v is an integer from 3 to k+4, k is less than or equal to a number of coupled quantum bits, a second direction is perpendicular to the first direction, and the second direction is a direction in which a ground state and an excited state of the quantum bit are connected in the state space, and the vth direction is a direction in which a unit vector of the first direction and a unit vector of the second direction are linearly combined. The processing module 404 can be configured to determine whether the quantum information system is in the quantum graph state according to the first expectation value and all v-1th expectation values. Specifically, the measurement module 402 can include a laser and an imaging unit. The laser is configured to generate laser light capable of rotating the quantum bit in the state space and removing the quantum bit in the excited state. The imaging unit is configured to perform fluorescence imaging on the remaining quantum bit in the ground state to obtain an expectation value of the quantum bit in a position to be measured. The device 400 for detecting a quantum graph state can be configured to perform the method described in any of the above method embodiments of the present disclosure.

[0076] In the technical solution of the present disclosure, the first expectation value of the product of components of quantum bits of all first-type lattice sites in a quantum information system along a first direction in a state space can be measured; the v-1th expectation value of the product of components of each quantum bit and quantum bits coupled to the quantum bit along a vth direction in the state space can be measured; and whether the quantum information system is in a quantum graph state can be determined according to the first expectation value and all vth expectation values. In this way, by changing the expectation value of the stabilizer from the expectation value of the product of components of a single quantum bit along a first direction and components of multiple quantum bits along a second direction to the expectation value of the product of components of multiple quantum bits along multiple single directions, the problem of individually adjusting a single quantum bit is avoided, the resource requirement of measurement is reduced, and the difficulty of detecting or authenticating a quantum graph state (including a quantum cluster state, etc.) is reduced.

[0077] The above-described one or more exemplary embodiments of the present disclosure are described. Other embodiments are within the scope of the following claims. In some cases, the actions or steps recited in the claims can be performed in a different order than the order described in the embodiments and still achieve the desired result. In addition, the processes depicted in the figures do not necessarily require the particular order shown, or sequential order to achieve the desired results. In certain implementations, multitasking and parallel processing can be advantageous.

[0078] The terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, the exclusion of additional identical or equivalent elements does not apply to a process, method, article, or apparatus that comprises the recited elements. For example, the use of "first", "second", or the like, does not necessarily indicate any particular order but is used to name elements.

[0079] For the convenience of description, the above apparatus is described in various modules respectively described in functions. Of course, in the implementation of one or more embodiments of the present disclosure, the functions of each module can be implemented in the same or more software and / or hardware, or the modules implementing the same function can be implemented by a combination of multiple sub-modules or sub-units. The above-described apparatus embodiments are only illustrative, for example, the division of the units is only a logical functional division, and in actual implementation, there can be another division manner, for example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point, the coupling or direct coupling or communication coupling between the displayed or discussed each other can be indirect coupling or communication coupling through some interface, device or unit, which can be electrical, mechanical or other form.

[0080] The same parts and / or features of the various embodiments of the present disclosure can be referred to with the same or similar reference numerals. Each embodiment described herein is intended to serve as a representative example only, and is not intended in any way to limit the overall scope of the present disclosure. Furthermore, the various embodiments of the present disclosure can be used together or in various combinations, as would be understood by one of ordinary skill in the art. In the description of the present disclosure, the terms "one embodiment," "some embodiments," "an example," "a specific example," or "some examples" are intended to mean that a particular feature, structure, material, or characteristic is included in at least one embodiment or example of the present disclosure, and is used in certain instances to

[0081] In addition, the words "herein," "above," "below," "nowhere," "above-mentioned," and words of similar meaning, when used in this disclosure, shall not

[0082] The above description is merely illustrative of the embodiments of the present disclosure and is not intended to limit the scope of the present disclosure. Various modifications and changes can be made by persons of ordinary skill in the art to the embodiments of the present disclosure without departing from the spirit and the scope of the present disclosure. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present disclosure shall be included in the scope of the claims.

Claims

1. A method for detecting a quantum state, comprising: measuring a first expectation value of a product of components of all first-type sites in a quantum information system along a first direction in state space, wherein the quantum information system comprises first-type sites and second-type sites, each first-type site is coupled to one or more second-type sites, and each second-type site is coupled to an even number of first-type sites; measuring a v-1th expectation value of a product of components of each qubit and qubits coupled to the qubit along a vth direction in state space, wherein v is an integer from 3 to k+4, k is less than or equal to the number of the coupled qubits, a second direction is perpendicular to the first direction, the second direction is a direction in state space along which a ground state and an excited state of a qubit are connected, a vth direction is a direction along which a unit vector of the first direction and a unit vector of the second direction are linearly combined, and the vth direction is different for different values of v; and determining whether the quantum information system is in a quantum state according to the first expectation value and all v-1th expectation values. 2.The method of claim 1, wherein measuring the first expectation value of the product of components along the first direction comprises rotating the qubits in state space such that components originally along the first direction are rotated to the second direction, and measuring the first expectation value along the second direction; measuring the v-1th expectation value of the product of components along the vth direction comprises rotating the qubits in state space such that components originally along the vth direction are rotated to the second direction, and measuring the v-1th expectation value along the second direction.

3. The method of claim 2, wherein, the rotating comprises at least one of: adjusting at least one of a Rabi frequency and a detuning frequency such that the Rabi frequency and the detuning frequency are equal and greater than a coupling coefficient to rotate the qubits in state space around a direction along which a unit vector of the first direction and a unit vector of the second direction are summed; adjusting the Rabi frequency and the detuning frequency such that the Rabi frequency is greater than the coupling coefficient and the detuning frequency is less than the coupling coefficient to rotate the qubits in state space around the first direction; adjusting the Rabi frequency and the detuning frequency such that the detuning frequency is greater than the coupling coefficient and the Rabi frequency is less than the coupling coefficient to rotate the qubits in state space around the second direction.

4. The method of claim 1, wherein, the quantum information system is a cluster state of a chain of N qubits, N is an odd number, and the qubits of the first-type sites are odd-numbered sites of the chain of qubits, wherein each qubit is coupled to qubits of adjacent sites.

5. The method of claim 4, wherein, determining whether the quantum information system is in a quantum state according to the first expectation value and all v-1th expectation values comprises: determining whether the quantum information system is in a quantum cluster state according to a difference between the first expectation value and 1 and a difference between an expectation value of a stabilizer of each site and 1; wherein X u is a component of the quantum bit of the u-th lattice site in the state space along a first direction, Z u is a component of the quantum bit of the u-th lattice site in the state space along a second direction, u taking integer values from 1 to N, The first expected value M0 satisfies: M0 = <∏X i >, wherein i takes odd values from 1 to N; a second expected value of a product of components of the quantum bit of the i-th lattice point and the quantum bit coupled with the quantum bit of the i-th lattice point in the state space along a third direction satisfies: wherein the third direction is the same as the first direction, and i is an integer between 2 and N-1. a third expected value of a product of components of the state of the quantum bit of the i-th lattice site and the quantum bit coupled to the quantum bit of the i-th lattice site in the state space along a fourth direction satisfies: In the case of i = 1, in the case where i takes an integer value between 2 and N-1 inclusive, In the case of i = N, wherein the fourth direction is a direction along which a unit vector of the second direction and a unit vector of the first direction are summed. a fourth expectation value of a product of components of the state of the quantum bit of the i-th lattice site and the quantum bit coupled to the quantum bit of the i-th lattice site in the state space along a fifth direction satisfies: In the case of i = 1, in the case where i takes an integer value between 2 and N-1 inclusive, In the case of i = N, The fifth direction is a direction in which a difference between a unit vector of the second direction and a unit vector of the first direction is located. The expected value M of the stabilizer of the i-th lattice i satisfies: In the case of i = 1, in the case where i takes an integer value between 2 and N-1 inclusive, In the case of i = N, 6. The method of claim 1, wherein, The quantum information system is a bipartite multidimensional graph state with N qubits.

7. The method of claim 6, wherein, Determining whether the quantum information system is in the quantum graph state according to the first expectation value and all v-1 expectation values comprises: Determining whether the quantum information system is in the quantum graph state according to a difference between the first expectation value and 1 and a difference between an expectation value of the stabilizer of each lattice point and 1. wherein X u is a component of the quantum bit of the u-th lattice site in the state space along a first direction, Z u is a component of the quantum bit of the u-th lattice site in the state space along a second direction, u being an integer from 1 to N, The first expected value M0 satisfies: M0 = <∏ i X i >, wherein the value of i is the number of the qubit of the first type of lattice point; a v−1th expectation value of a product of components of the quantum bit of the ith lattice site and the quantum bit coupled with the quantum bit of the ith lattice site in the state space along a vth direction satisfies: wherein i is an integer from 1 to N, j is the number of the quantum bit coupled with the quantum bit of the ith lattice site, and θ is an angle between the vth direction and the second direction. The expected value M of the stabilizer of the i-th lattice i satisfies: where i is an integer from 1 to N, θ is the included angle between the v-th direction and the second direction, a θ is the linear combination coefficient corresponding to the v-th direction.

8. The method of claim 5 or 7, wherein, In the case where the difference between the first desired value and the desired value of the stabilizer of each lattice point is less than 1 / N 2 , it is determined that the quantum information system is in a quantum graph state.

9. The method of claim 2, wherein measuring the expectation value along the second direction comprises: Operation a. removing the qubits in the excited state by using a laser; Operation b. performing fluorescence imaging on the remaining qubits in the ground state to obtain the value of the qubit in the position to be measured; Repeating the operation a and the operation b, and taking an average of the obtained values of the qubits as the expectation value.

10. The method of claim 1, wherein, The qubit is a Rydberg atom system, the Hamiltonian of which is Wherein, Ω(t) is the Rabi frequency, Δ(t) is the detuning frequency, C6 is the coupling coefficient of the Van der Waals force between Rydberg atoms, |g> and <g| are the ground state, |r> and <r| are the Rydberg state, i and j each represent the number of lattice points, and j>i, n is the Rydberg particle number operator.

11. The method of claim 10, further comprising: evolving the Rydberg atom system with adjusted Rabi frequency Ω and detuning frequency Δ to satisfy Ω = Δ = h » C6 measuring in the second direction to obtain an expected value of a component in the first direction in state space; In the case of adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Ω=0, Δ=h>>C6, let the Rydberg atomic system evolve Δt3=1 / (4h), and then in the case of adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Δ=0, Ω=h>>C6, let the Rydberg atomic system evolve Δt4=1 / (8h), and measure in the second direction to obtain the expectation value of the component along the third direction in the state space, wherein the third direction is a direction in which the sum of the unit vector of the first direction and the unit vector of the second direction is located; In the case of adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Ω=0, -Δ=h>>C6, let the Rydberg atomic system evolve Δt3=1 / (4h), and then in the case of adjusting the Rabi frequency Ω and the detuning frequency Δ to satisfy Δ=0, Ω=h>>C6, let the Rydberg atomic system evolve Δt4=1 / (8h), and measure in the second direction to obtain the expectation value of the component along the fourth direction in the state space, wherein the fourth direction is a direction in which the difference between the unit vector of the second direction and the unit vector of the first direction is located.

12. The method of claim 1, wherein, The qubit is one of an ion trap, a superconducting qubit, and a photon system.

13. An apparatus for detecting a quantum graph state, comprising: a measurement module configured to: measure a first expectation value of a product of components along a first direction in a state space of qubits of all first-type lattice points in a quantum information system, wherein the quantum information system comprises first-type lattice points and second-type lattice points, each first-type lattice point is coupled to one or more second-type lattice points, and each second-type lattice point is coupled to an even number of first-type lattice points; and measuring a (v-1)-th expectation value of a product of a component of each qubit in the quantum information system along a v-th direction in state space and a component of a qubit coupled with the qubit along the v-th direction in state space, where v is an integer from 3 to k+4, k is less than or equal to a number of the coupled qubits, a second direction is perpendicular to the first direction, the second direction is a direction in which a ground state and an excited state of the qubit are connected, and the v-th direction is a direction in which a linear combination of a unit vector of the first direction and a unit vector of the second direction is located, and the v-th direction is different with different values of v; and a processing module configured to determine whether the quantum information system is in a quantum graph state according to the first expectation value and all (v-1)-th expectation values.

14. The apparatus of claim 13, wherein, The measurement module comprises: a laser configured to generate laser light capable of rotating the qubit in the state space and removing the qubit in the excited state; an imaging unit configured to perform fluorescence imaging on the remaining qubit in the ground state to obtain an expectation value of the qubit in a position to be measured.

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