CN116681139B - Quantum state preparation method and related device - Google Patents
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Abstract
The invention discloses a quantum state preparation method and a related device, wherein the method comprises the following steps: determining hamming weights of the target quantum states to be prepared and a group of quantum bits; determining all first qubit combinations for the action weight distribution module and all second qubit combinations for the action decomposition module according to the hamming weight and the qubit; obtaining a preparation line according to the weight distribution module, the decomposition module, all first quantum bit combinations and all second quantum bit combinations; and driving the preparation line according to the initial quantum state so as to evolve the initial quantum state to the target quantum state. According to the embodiment of the invention, the Hamming weight is firstly distributed into different sub-combinations through the weight distribution module, and then the quantum state is decomposed by the decomposition module, so that Dicke states are prepared.
Description
Technical Field
The invention belongs to the technical field of quanta, in particular to a quantum state preparation method and a related device.
Background
The Dicke (Dike) state is a highly entangled state that is more studied in quantum mechanics, and the Dicke state can be expressed as:
Wherein " "Means quantum stateThe hamming weight of (2) isThe hamming weight can be regarded as the number of "1" s in a string of binary characters, e.g. the hamming weight of "010101" is 3. The Dicke state can be regarded as calculating the underlying hamming weight asAn equiprobable superposition of all quantum states of (a) is provided.
The Dicke state is widely applied to quantum information processing and high-precision measurement, and can complete a quantum communication scheme with powerful functions and can also test the performance of a quantum computer relative to other entangled states. In addition, dicke states are also important in the fields of quantum optics, quantum multi-body simulation and the like, and are also applied to the development of quantum algorithms for many combination optimization problems due to the conservation property of the unique hamming weight. Therefore, in view of the importance of Dicke states, how to prepare Dicke states is one of the issues that need to be resolved in quantum computing.
Disclosure of Invention
The invention aims to provide a quantum state preparation method and a related device, wherein a weight distribution module distributes Hamming weights into different quantum bit sub-combinations, and a decomposition module is utilized to decompose a quantum state to realize Dicke-state preparation.
One embodiment of the application provides a quantum state preparation method, which comprises the following steps:
determining a hamming weight of a target quantum state to be prepared and a group of quantum bits, wherein the target quantum state is Dicke states;
determining all first quantum bit combinations for acting a weight distribution module and all second quantum bit combinations for acting a decomposition module according to the hamming weights and the quantum bits, wherein the weight distribution module is used for distributing hamming weights of initial quantum states to different quantum bit sub-combinations of the first quantum bit combinations, and the decomposition module is used for decomposing intermediate states so that the hamming weights are uniformly distributed on all the quantum bits, and the intermediate states are obtained based on the initial quantum states and the weight distribution module;
Obtaining a preparation line according to the weight distribution module, the decomposition module, all first quantum bit combinations and all second quantum bit combinations;
and driving the preparation line according to the initial quantum state so as to evolve the initial quantum state to the target quantum state.
Optionally, the determining all first qubit combinations for the acting weight distribution module and all second qubit combinations for the acting decomposition module according to the hamming weight and the qubit includes:
constructing a weight distribution binary tree by using the obtained number of quantum bits and hamming weight, wherein the number of quantum bits corresponding to each child node in the weight distribution binary tree is as follows Integer multiple of (2) or withIs equal to the remainder of，For the hamming weight, theA remainder obtained by dividing the number of the obtained qubits by the hamming weight;
Based on the weight distribution binary tree, all first qubit combinations for the active weight distribution module and all second qubit combinations for the active decomposition module are determined.
Optionally, the determining all first qubit combinations for the acting weight distribution module and all second qubit combinations for the acting decomposition module based on the weight distribution binary tree includes:
Taking a quantum bit corresponding to a parent node in the weight distribution binary tree as a first quantum bit combination for acting a weight distribution module;
And using the qubit corresponding to one leaf node of the weight distribution binary tree as a second qubit combination for acting on the decomposition module.
Optionally, the weight distribution module includes:
a first sub-module for adjusting the hamming weight of the quantum state corresponding to the first sub-combination to And front partEach quantum bit isA state wherein the first sub-combination comprises a first qubit combinationThe number of qubits is one,The number of qubits that are one first qubit combination,The number of qubits contained for a second sub-combination corresponding to the first qubit combination;
A second sub-module for adjusting the hamming weight of the quantum state corresponding to the second sub-combination to Wherein, the method comprises the steps of, wherein,For the hamming weight of the initial quantum state,。
Optionally, the first submodule includes a plurality of controlled RY gates;
the second sub-module comprises at least And CNOT gates.
Optionally, the first sub-module includes:
A first weight adjustment unit for adjusting the hamming weight of the quantum state corresponding to the second sub-combination to 1, and a second weight adjustment unit for adjusting the hamming weight of the quantum state corresponding to the second sub-combination to 1 The qubit of the bit is set toA state;
a second weight adjustment unit, configured to adjust the hamming weight of the quantum state corresponding to the first sub-combination to be And front partEach quantum bit isA state;
And the weight reduction unit is used for reducing the hamming weight of the quantum state corresponding to the second sub-combination.
Optionally, the first weight adjustment unit and the weight reduction unit each includeA CNOT gate;
The second sub-module also includes a controlled SWAP gate.
Yet another embodiment of the present application provides a quantum state preparing apparatus, the apparatus comprising:
The first determining module is used for determining the hamming weight of a target quantum state to be prepared and a group of quantum bits, wherein the target quantum state is Dicke states;
A second determining module, configured to determine, according to the hamming weight and the qubits, all first qubit combinations for the action weight distribution module and all second qubit combinations for the action decomposition module, where the weight distribution module is configured to distribute hamming weights of an initial quantum state to different qubit sub-combinations of the first qubit combinations, and the decomposition module is configured to decompose intermediate states such that the hamming weights are uniformly distributed over all the qubits, where the intermediate states are obtained based on the initial quantum state and the weight distribution module;
The obtaining module is used for obtaining a preparation line according to the weight distribution module, the decomposition module, all the first quantum bit combinations and all the second quantum bit combinations;
and the preparation module is used for driving the preparation circuit according to the initial quantum state so as to evolve the initial quantum state to the target quantum state.
Optionally, the second determining module includes:
A construction unit, configured to construct a weight distribution binary tree by using the obtained number of qubits and hamming weight, where the number of qubits corresponding to each child node in the weight distribution binary tree is Integer multiple of (2) or withIs equal to the remainder of，For the hamming weight, theA remainder obtained by dividing the obtained number of qubits by the hamming weight;
A determining unit for determining all first qubit combinations for the active weight distribution module and all second qubit combinations for the active decomposition module based on the weight distribution binary tree.
Optionally, the determining unit is specifically configured to:
Taking a quantum bit corresponding to a parent node in the weight distribution binary tree as a first quantum bit combination for acting a weight distribution module;
And using the qubit corresponding to one leaf node of the weight distribution binary tree as a second qubit combination for acting on the decomposition module.
Optionally, the weight distribution module includes:
a first sub-module for adjusting the hamming weight of the quantum state corresponding to the first sub-combination to And front partEach quantum bit isA state wherein the first sub-combination comprises a first qubit combinationThe number of qubits is one,The number of qubits that are one first qubit combination,The number of qubits contained for a second sub-combination corresponding to the first qubit combination;
A second sub-module for adjusting the hamming weight of the quantum state corresponding to the second sub-combination to Wherein, the method comprises the steps of, wherein,For the hamming weight of the initial quantum state,。
Optionally, the first submodule includes a plurality of controlled RY gates;
the second sub-module comprises at least And CNOT gates.
Optionally, the first sub-module includes:
A first weight adjustment unit for adjusting the hamming weight of the quantum state corresponding to the second sub-combination to 1, and a second weight adjustment unit for adjusting the hamming weight of the quantum state corresponding to the second sub-combination to 1 The qubit of the bit is set toA state;
a second weight adjustment unit, configured to adjust the hamming weight of the quantum state corresponding to the first sub-combination to be And front partEach quantum bit isA state;
And the weight reduction unit is used for reducing the hamming weight of the quantum state corresponding to the second sub-combination.
Optionally, the first weight adjustment unit and the weight reduction unit each includeA CNOT gate;
The second sub-module also includes a controlled SWAP gate.
An embodiment of the application provides a storage medium having a computer program stored therein, wherein the computer program is arranged to implement the method of any of the preceding claims when run.
An embodiment of the application provides an electronic device comprising a memory having a computer program stored therein and a processor arranged to run the computer program to implement the method of any of the above.
Compared with the prior art, the quantum state preparation method and the related device provided by the invention have the advantages that firstly, the hamming weight and a group of quantum bits of a target quantum state to be prepared are determined; then determining all first qubit combinations for the action weight distribution module and all second qubit combinations for the action decomposition module according to the hamming weight and the qubit; obtaining a preparation circuit according to the weight distribution module, the decomposition module, all the first quantum bit combinations and all the second quantum bit combinations; and then driving the preparation line according to the initial quantum state so as to evolve the initial quantum state to the target quantum state. The Hamming weight is firstly distributed into different sub-combinations through the weight distribution module, and then the quantum state is decomposed by the decomposition module, so that Dicke states are prepared.
Drawings
FIG. 1 is a network block diagram of a quantum state preparation system according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of a quantum state preparation method according to an embodiment of the present invention;
Fig. 3 is a schematic structural diagram of a weight distribution binary tree according to an embodiment of the present invention;
Fig. 4 is a schematic diagram of a quantum circuit corresponding to a first submodule according to an embodiment of the present invention;
fig. 5 is a schematic diagram of a quantum circuit corresponding to a first weight adjustment unit according to an embodiment of the present invention;
Fig. 6 is a schematic diagram of a quantum circuit corresponding to a second weight adjustment unit according to an embodiment of the present invention;
Fig. 7 is a schematic diagram of a quantum circuit corresponding to a second submodule according to an embodiment of the present invention;
FIG. 8 is a block diagram of a bit operation according to an embodiment of the present invention Schematic diagram of equivalent quantum circuit of (a);
FIG. 9 is a schematic diagram of an equivalent quantum circuit of a controlled SWAP gate provided by an embodiment of the present invention;
fig. 10 is a schematic diagram of a quantum circuit corresponding to a weight distribution module according to an embodiment of the present invention;
fig. 11 is a schematic diagram of a quantum circuit corresponding to a shift module according to an embodiment of the present invention;
FIG. 12 is a schematic diagram of an equivalent quantum circuit of a SWAP turnstile according to an embodiment of the present invention;
fig. 13 is a schematic diagram of an equivalent quantum circuit of a decomposition module according to an embodiment of the present invention;
Fig. 14 is a schematic structural diagram of a quantum state preparation device according to an embodiment of the present invention.
Detailed Description
The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the invention.
Fig. 1 is a network block diagram of a quantum state preparation system according to an embodiment of the present invention. The quantum state preparation system may include a network 110, a server 120, a wireless device 130, a client 140, a storage unit 150, a classical computing unit 160, a quantum computing unit 170, and may also include additional memory, classical processors, quantum processors, and other devices not shown.
Network 110 is a medium used to provide a communication link between various devices and computers connected together within the quantum state manufacturing system, including but not limited to the internet, intranets, local area networks, mobile communication networks, and combinations thereof, by wired, wireless communication links, or fiber optic cables, etc.
Server 120, wireless device 130, and client 140 are conventional data processing systems that may contain data and have applications or software tools that perform conventional computing processes. The client 140 may be a personal computer or a network computer, so the data may also be provided by the server 120. The wireless device 130 may be a smart phone, tablet, notebook, smart wearable device, or the like. The memory unit 150 may include a database 151 that may be configured to store data of qubit parameters, quantum logic gate parameters, quantum wires, quantum programs, and the like.
Classical computing unit 160 (quantum computing unit 170) may include a classical processor 161 (quantum processor 171) for processing classical data (quantum data), which may be boot files, operating system images, and an application 163 (application 173), and a memory 162 (memory 172) for storing classical data (quantum data), which may be a boot file, an operating system image, and an application 163 (application 173), which may be used to implement a quantum algorithm compiled according to a quantum state preparation method provided by an embodiment of the present invention.
Any data or information stored or generated in classical computing unit 160 (quantum computing unit 170) may also be configured to be stored or generated in another classical (quantum) processing system in a similar manner, as may any application program that it executes.
It should be noted that, the real quantum computer is a hybrid structure, and it includes at least two major parts in fig. 1: a classical calculation unit 160 responsible for performing classical calculations and controls; the quantum computing unit 170 is responsible for running a quantum program to realize quantum computing.
The classical computing unit 160 and the quantum computing unit 170 may be integrated in one device or may be distributed among two different devices. A first device, for example, comprising a classical computing unit 160 runs a classical computer operating system on which quantum application development tools and services are provided, and also the storage and network services required for quantum applications. The user develops the quantum program through a quantum application development tool and service thereon, and transmits the quantum program to a second device including the quantum computing unit 170 through a web service thereon. The second device runs a quantum computer operating system, the code of the quantum program is analyzed and compiled into an instruction which can be identified and executed by the quantum processor 170 through the quantum computer operating system, and the quantum processor 170 realizes a quantum algorithm corresponding to the quantum program according to the instruction.
The computation unit of the classical processor 161 in the classical computation unit 160 is a CMOS tube based on silicon chips, which is not limited by time and coherence, i.e. which is not limited by the time of use, which is available at any time. Furthermore, the number of such computational units is also sufficient in silicon chips, the number of computational units in a classical processor 161 is now thousands of, the number of computational units is sufficient and the CMOS pipe selectable computational logic is fixed, e.g. and logic. When the CMOS tube is used for operation, a large number of CMOS tubes are combined with limited logic functions, so that the operation effect is realized.
The basic computational unit of quantum processor 171 in quantum computational unit 170 is a qubit, the input of which is limited by coherence and also by coherence time, i.e., the qubit is limited in terms of time of use and is not readily available. Full use of qubits within the usable lifetime of the qubits is a critical challenge for quantum computing. In addition, the number of qubits in a quantum computer is one of the representative indicators of the performance of the quantum computer, and each qubit realizes a calculation function through a logic function configured as required. In view of the limited number of qubits, the logic functions in the quantum computing field are diversified, such as Hadamard gates (Hadamard gates, H gates), bery-X gates (X gates), bery-Y gates (Y gates), bery-Z gates (Z gates), X gates, RY gates, RZ gates, CNOT gates, CR gates, iSWAP gates, toffoli gates, and the like. In quantum computation, the operation effect is realized by combining limited quantum bits with various logic function combinations.
Based on these differences, the design of classical logic functions acting on CMOS transistors and the design of quantum logic functions acting on qubits are significantly and essentially different; the classical logic function acts on the design of the CMOS tube without considering the individuality of the CMOS tube, such as the individuality identification and the position of the CMOS tube in the silicon chip, and the usable time length of each CMOS tube, so the classical algorithm formed by the classical logic function only expresses the operation relation of the algorithm, and does not express the dependence of the algorithm on the individuals of the CMOS tube.
The quantum logic function acts on the qubit, and the individuality of the qubit needs to be considered, such as the individuality identification, the position and the relation with surrounding qubits of the number of the qubit in the quantum chip, and the usable duration of each qubit. Therefore, the quantum algorithm formed by the quantum logic functions not only expresses the operation relation of the algorithm, but also expresses the dependence of the algorithm on quantum bit individuals.
Exemplary:
quantum algorithm one: h1, H2, CNOT (1, 3), H3, CNOT (2, 3);
and a quantum algorithm II: h1, H2, CNOT (1, 2), H3, CNOT (2, 3);
Wherein 1/2/3 respectively represents three sequentially connected qubits q1, q2, q3 or mutually connected qubits q1, q2, q3;
an exemplary explanation of the quantum algorithm's influence by the quantum bit coherence time is as follows:
defining the execution time of a single-quantum bit logic gate as t, and 1 two single-quantum bit logic gates acting on adjacent bits as 2t; then:
When the three q1, q2 and q3 are mutually connected, the calculation of the quantum algorithm I needs 6t and is carried out in 4 time periods, the time duration needed by each time period is respectively t,2t, t and 2t, and the calculation executed in each time period is as follows: h1 and H2; CNOT (1, 3); h3; CNOT (2, 3);
the first quantum algorithm is calculated by 5t and is carried out in 3 time periods, the time duration required by each time period is t,2t and 2t respectively, and the operation executed in each time period is as follows: h1, H2, H3; CNOT (1, 2); CNOT (2, 3);
When q1, q2 and q3 are connected in sequence, the quantum algorithm one needs to be equivalent to: h1 and H2; swap (1, 2), CNOT (2, 3), swap (1, 2); h3; CNOT (2, 3); the equivalent quantum algorithm I needs 10t to be calculated, and 4 time periods are divided, and the time duration needed by each time period is t,6t, t and 2t respectively. The operations performed in each time period are: h1 and H2; swap (1, 2), CNOT (2, 3), swap (1, 2); h3; CNOT (2, 3).
Therefore, the design of the quantum logic function acting on the quantum bit (including the design of whether the quantum bit is used or not and the design of the use efficiency of each quantum bit) is the key for improving the operation performance of the quantum computer, and special design is required, which is the uniqueness of the quantum algorithm realized based on the quantum logic function and is different from the nature and the significance of the classical algorithm realized based on the classical logic function. The above design for qubits is a technical problem that is not considered nor faced by common computing devices. Based on the above, the invention provides a quantum state preparation method and a related device aiming at how to prepare Dicke states in quantum computation, aiming at realizing Dicke state preparation.
Referring to fig. 2, fig. 2 is a schematic flow chart of a quantum state preparation method according to an embodiment of the present invention, which may include the following steps:
s201: and determining the hamming weight of a target quantum state to be prepared and a group of quantum bits, wherein the target quantum state is Dicke states.
The target quantum state may be Dicke states, and when the target quantum state is determined, the hamming weight and the corresponding number of qubits are also determined, so that a set of qubits may be determined. Exemplary, if the target quantum state comprisesThe state, the hamming weight of the target quantum state is 6, and the number of qubits is 14, then the determined set of qubits may be q0-q13.
S202: determining all first quantum bit combinations for acting a weight distribution module and all second quantum bit combinations for acting a decomposition module according to the hamming weights and the quantum bits, wherein the weight distribution module is used for distributing hamming weights of initial quantum states to different quantum bit sub-combinations of the first quantum bit combinations, and the decomposition module is used for decomposing intermediate states so that the hamming weights are uniformly distributed on all the quantum bits, and the intermediate states are obtained based on the initial quantum states and the weight distribution module.
In the embodiment of the invention, all first quantum bit combinations and all second quantum bit combinations can be determined by utilizing the hamming weight and the obtained quantum bits, specifically the number of the quantum bits according to a preset rule or a calculation mode. It should be noted that different first qubit combinations may contain the same qubit, the first qubit combination and the second qubit combination may contain the same qubit, the number of qubits contained in different first qubit combinations may be different, and the number of qubits contained in different second qubit combinations may be different. The function of the decomposition module is to "wipe" the hamming weights evenly across all qubits. The initial quantum state can be evolved into a target quantum state through the weight distribution module and the decomposition module, and a desired Dicke state is obtained.
The quantum states corresponding to different quantum bit sub-combinations are initial quantum states or quantum states of the initial quantum states after the initial quantum states are evolved by other weight distribution modules. When the initial quantum state passes through all weight distribution modules, an intermediate state is obtained, and the intermediate state is decomposed by a decomposition module to obtain the target quantum state. The weight distribution module and the decomposition module both comprise quantum logic gates or quantum logic gate combinations for realizing corresponding functions.
S203: and obtaining a preparation circuit according to the weight distribution module, the decomposition module, all the first qubit combinations and all the second qubit combinations.
The weight distribution module is respectively acted on each first quantum bit combination, and then the decomposition module is acted on each second quantum bit combination, so that a preparation line is obtained. It should be noted that, there may be weight distribution modules that may be parallel to each other, and similarly, there may be parallel distribution modules to each other, which act on different first qubit combinations.
S204: and driving the preparation line according to the initial quantum state so as to evolve the initial quantum state to the target quantum state.
In quantum computing, quantum logic gates are applied to corresponding qubits through their corresponding control waveforms, driving the evolution of the quantum states of the qubits. Specifically, according to the quantum logic gate in the preparation line, the quantum bit acted by the quantum logic gate, action time sequence and other information, a corresponding control waveform is applied to the corresponding quantum bit, so that the preparation line is driven to evolve the initial quantum state to the target quantum state.
It can be seen that, in the embodiment of the present invention, hamming weights of target quantum states to be prepared and a set of quantum bits are first determined; then determining all first qubit combinations for the action weight distribution module and all second qubit combinations for the action decomposition module according to the hamming weight and the qubit; obtaining a preparation circuit according to the weight distribution module, the decomposition module, all the first quantum bit combinations and all the second quantum bit combinations; and then driving the preparation line according to the initial quantum state so as to evolve the initial quantum state to the target quantum state. The Hamming weight is firstly distributed into different sub-combinations through the weight distribution module, and then the quantum state is decomposed by the decomposition module, so that Dicke states are prepared.
In some possible embodiments of the present invention, the determining all first qubit combinations for the action weight allocation module and all second qubit combinations for the action decomposition module according to the hamming weights and the qubits may include:
constructing a weight distribution binary tree by using the obtained number of quantum bits and hamming weight, wherein the number of quantum bits corresponding to each child node in the weight distribution binary tree is as follows Integer multiple of (2) or withIs equal to the remainder of，For the hamming weight, theA remainder obtained by dividing the number of the obtained qubits by the hamming weight;
Based on the weight distribution binary tree, all first qubit combinations for the active weight distribution module and all second qubit combinations for the active decomposition module are determined.
In the process of preparing Dicke states, for the first quantum bit combination and the second quantum bit combination, the corresponding quantum states can be superposition states of quantum states with different hamming weights, so that the hamming weight of the quantum state corresponding to each first quantum bit combination must be consistent with the hamming weight corresponding to the previous first quantum bit combination, and the hamming weight of the result allocated by the first quantum bit combination can be kept unchanged. This is required in view ofThe weight distribution module used in the divide-and-conquer process must be such that this acts before the first qubit is combinedSum and back ofFront in qubitOn each qubit, hamming weights of the quantum states are assigned to different regions in the first qubit combination. When this condition is not met, the divide-and-conquer process must be terminated. The goal of the divide-and-conquer strategy is therefore to generate as many weight distribution modules as possible in parallel under this precondition.
In the embodiment of the invention, the divide-and-conquer strategy can be determined by adopting a binary tree mode, so that the generated weight distribution binary tree is balanced as much as possible, the weight distribution binary tree is a binary tree for realizing the hamming weight distribution to different sub-combinations of sub-bits, the nodes of the weight distribution binary tree represent the number of the quantum bits acted by the weight distribution module, and according to the above objective, the sub-node generation strategy thereof is to ensure that the number of the quantum bits acted by the left and right sub-branches is close and is thatInteger multiples or remainders of，. In order not to lose generality, the number of qubits of the left branch of the generated subtree is generally made always larger. When the number of qubits acting on a node is greater thanIt must be able to generate child nodes. If the node is dividedThe quotient of (1) is even, then it is withThe remainder of (2) is allocated to the left branch; otherwise the remainder is assigned to the right branch. According to this rule, a weight distribution binary tree is constructed, and a first quantum bit combination and a second quantum bit combination are determined based on the nature of the nodes of the weight distribution binary tree.
According to the generated weight distribution binary tree, if the child node of a node exists, the left child node and the right child node are needed to exist, and the two child nodes of the node form a first quantum bit combination, because the number of leaf nodes of the weight distribution binary tree is necessarily thatPlus a remainder leaf node that may be present, the depth of the binary tree is. Line depth and weight of each weight distribution moduleIn a linear relationship, the line depth required for the overall weight distribution process is therefore。
In some possible embodiments of the present invention, the determining all first qubit combinations for the active weight distribution module and all second qubit combinations for the active decomposition module based on the weight distribution binary tree may include:
Taking a quantum bit corresponding to a parent node in the weight distribution binary tree as a first quantum bit combination for acting a weight distribution module;
And using the qubit corresponding to one leaf node of the weight distribution binary tree as a second qubit combination for acting on the decomposition module.
In the embodiment of the invention, the parent node and the child node are relatively speaking, one parent node may be a child node of another parent node, and one child node may be a parent node of other child nodes. The number of first qubit combinations is the number of parent nodes and the number of second qubit combinations is the number of leaf nodes. Taking the hamming weight corresponding to the target quantum state as 18 and the quantum bit as 170 as an example, the weight distribution binary tree is shown in fig. 3, the numbers in the binary tree represent the quantum bit number corresponding to each node, and the nodes 170, 90, 80, 54, 44, 36 and 26 are mother nodes, and the nodes corresponding to 18 and 8 are leaf nodes. The quantum bit corresponding to each parent node corresponds to a first quantum bit combination, different first quantum bit combinations may have a mutual inclusion relationship, one leaf node corresponds to a second quantum bit combination, and the sum of the quantum bits corresponding to all the second quantum bit combinations is the quantum bit corresponding to the target quantum state, namely, the number of a group of quantum bits is determined. The weight distribution module acts on the qubits corresponding to each parent node in turn based on the order of the weight distribution binary tree from top to bottom, and may act on the qubits corresponding to the parent nodes at the same level of the binary tree in parallel, and the exemplary weight distribution module corresponding to 54, the weight distribution module corresponding to 44, and the weight distribution module corresponding to 36 at the same level as 54 may be executed in parallel.
In some possible embodiments of the present invention, the weight allocation module may include:
a first sub-module for adjusting the hamming weight of the quantum state corresponding to the first sub-combination to And front partEach quantum bit isA state wherein the first sub-combination comprises a first qubit combinationThe number of qubits is one,The number of qubits that are one first qubit combination,The number of qubits contained for a second sub-combination corresponding to the first qubit combination;
A second sub-module for adjusting the hamming weight of the quantum state corresponding to the second sub-combination to Wherein, the method comprises the steps of, wherein,For the hamming weight of the initial quantum state,。
The weight distribution module can be used for front partThe hamming weights of the quantum states whose individual qubits are 1 are assigned to the first sub-combination and the second sub-combination, realizing the following quantum state transformation:
It should be noted that, the quantum state corresponding to one sub-combination is an initial quantum state or an initial quantum state after being evolved by the weight distribution module corresponding to other sub-combinations. The first sub-combination and the second sub-combination respectively correspond to left and right 2 sub-nodes of the same parent node of the weight distribution binary tree. The first sub-combination may correspond to a right node of one parent node of the weight distribution binary tree and the second sub-combination may correspond to a left node of one parent node of the weight distribution binary tree. Taking fig. 3 as an example, 90 corresponds to a parent node, 54 corresponds to a second sub-combination, 36 is a first sub-combination, that is, the first 90 qubits of 170 qubits correspond to the parent node of 90, the first 54 qubits of 90 qubits correspond to the second sub-combination, and the last 36 qubits correspond to the first sub-combination.
The first sub-module is used for adjusting the hamming weight corresponding to the first sub-combination, so that the hamming weight can be increased, and the quantum state can be converted intoThe second sub-module is configured to adjust the hamming weight of the second sub-combination, and may be configured to reduce the hamming weight, so that the sum of hamming weights of the quantum states corresponding to the first quantum bit combination remains unchanged, and the second sub-module reconverts into a state after transformation based on the first sub-module。
In some possible embodiments of the invention, the first sub-module may comprise a plurality of controlled RY gates;
The second sub-module may include And CNOT gates.
In order to make the Hamming weight of each component of the target quantum state in the first sub-combination beAnd just forwardThe respective qubit is 1 and the corresponding amplitude phase is. By successive controlled processes using a seriatim control methodThe gates in turn control the neighboring qubits, the rotation angle of each controlled RY gate is calculated, and the number of controlled gates is consistent with the number of bits to be controlled. The rotation angle parameter of the controlled RY gate can be calculated using the following equation:
Wherein, ，。
The controlled RY gate may determine a control bit of the controlled RY gate based on whether the initial quantum state is an overlap state. When the initial quantum state is the superposition state, the first RY gate is a single control gate, the other RY gates are multiple control gates, taking the first sub-combination with 3 quantum bits as an example, the quantum circuit corresponding to the first sub-module can be as shown in FIG. 4, and the quantum bits in the first sub-combination are all currentlyState, the second sub-combinationBit qubit isThe RY gate is subject to the immediate vicinity of the qubit and the thBit qubit control, for the first RY gate, the immediate qubit is the thThe bit is qubit, so the first RY gate is a single control gate. When the initial quantum state is one state under the calculation basis, namely, is not the superposition state, only the quantum bit of the RY gate in the second sub-combination is controlled to be in a non-zero state, the controlled RY gate can really work, and therefore, the controlled RY gate on other quantum bits can be omitted. In addition, if the qubit controlling the RY gate in the second sub-combination isThe first control bit of all controlled RY gates can be omitted, the first controlled RY gate is a single-qubit rotary gate, and the other controlled RY gates become single-qubit controlled RY gates.
When the hamming weight corresponding to the first sub-combination isWhen the hamming weight corresponding to the second sub-combination isSo that the hamming weight sum remains unchanged. Passing the two sub-combinations one by one of the qubits requiring lifting hamming weightThe CNOT gate connections can precisely control the hamming weight of the second sub-combination. Because the connected qubits are independent, the two-bit gates of the method can be used in parallel, and the corresponding quantum circuit depth is 1.
In some possible embodiments of the present invention, the first sub-module may include:
A first weight adjustment unit for adjusting the hamming weight of the quantum state corresponding to the second sub-combination to 1, and a second weight adjustment unit for adjusting the hamming weight of the quantum state corresponding to the second sub-combination to 1 The qubit of the bit is set toA state;
a second weight adjustment unit, configured to adjust the hamming weight of the quantum state corresponding to the first sub-combination to be And front partEach quantum bit isA state;
And the weight reduction unit is used for reducing the hamming weight of the quantum state corresponding to the second sub-combination.
When the initial quantum state is the superposition state, the first sub-module may include a first weight adjustment unit, a second weight adjustment unit, and a weight reduction unit. A first weight adjusting unit for adjusting the hamming weight in the second sub-combination to 1 to form one-hot code and making the second sub-combinationBit qubit isThe state, the quantum state becomes. The single thermal coding is used for separating the weight distribution process of each superposition state in the next step. The first weight adjusting unit may be capable ofThe implementation of the CNOT gate takes 4 qubits as an example, and the quantum circuit corresponding to the first weight adjustment unit may be as shown in fig. 5. The weight reduction unit is used for reducing the hamming weight of the second sub-combination after the second weight adjustment unit acts, and is the inverse operation of the first weight adjustment unit, and in some cases, the corresponding quantum circuit can be the same as the quantum circuit structure of the first weight adjustment unit or can beAnd CNOT gates.
The second weight adjustment unit may use one-hot encoding to boost hamming weight of the first sub-combination. After the first weight adjusting unit, the second sub-combination only leaves one quantum bit in a non-zero state under the calculation base and is just arranged at the first positionBits, therefore the process of weight allocation can be regarded as being subject to the firstControlled by a single qubit acting before the first sub-combinationA small module on a qubit. Specifically, the rest of the inactive qubits may be omitted, and the quantum state transformation process of the second weight adjustment unit may be:
。
For example, to As an example, the quantum wires corresponding to the second weight adjusting unit may be as shown in fig. 6,The corresponding RY gates are the first control bits different.
In some possible embodiments of the invention, the second sub-module may further comprise a controlled SWAP gate.
When the quantum state corresponding to the second sub-combination is the superposition state, the hamming weight of the input state cannot be determined, so that interference between states with different hamming weights can be caused by simply using the CNOT gate, and the quantum bit position acted by the CNOT gate cannot be determined, and therefore, a more complex quantum circuit is required to be adopted. Since all hamming weights corresponding to the second sub-combination are located beforeOf quantum bits, and due toThe uppermost qubit can be shifted to the end of the non-0 bits with a bit operation (thBits) and then the last bit weight is reduced with the first sub-combination of the corresponding qubit controlled CNOT gates. The quantum circuit corresponding to the second sub-module can be formed from the front of the two sub-combinations as shown in FIG. 7The last bit of the individual qubits starts and the last bit of the second sub-combination is controlled with the qubits of the first sub-combination. When the qubit of the first sub-combination is in a non-zero state, the CNOT gate will adjust the Hamming weight corresponding to the second sub-combination. The control bits are then shifted up by one bit, and the active bit operation is performed in the second sub-combinationThe Hamming weight is moved down to the last quantum bit, then the CNOT gate is used to reduce the Hamming weight, and so on until the effectAnd twice. Bit operation module usedAs shown in fig. 8, its basic elements are controlled SWAP gates, which can be broken down into CNOT gates and Toffoli gates, as shown in particular in fig. 9. In the embodiment of the present invention, the weight distribution module acts on the first qubit combination, so that a quantum circuit as shown in fig. 10 can be obtained,For the first weight adjustment unit,For the second weight adjustment unit,As the weight reduction unit, a weight reduction unit,In the case of the second sub-module,Sequentially acts on the first qubit combination.
Since the weight distribution module is nowThe conditions of (2) are limited, the weight distribution module can not be used for division treatment, and the decomposition module can be used for decomposing Dicke states one qubit by one qubit. The decomposition principle of the decomposition module is as follows:
First, if Then Dicke states can be considered as a superposition of two Dicke states with the total hamming weight being proportionally distributed to any one of the qubits and the remaining qubits, in the form of:
Wherein, Is the number of permutation and combination. Namely:
The recursive formula decomposes the object Dicke states bit by bit. According to the recurrence formula, the original can be processed Dicke states on a qubit are assigned to the frontOn the quantum bits (second sub-combination) and the rest of the quantum bits (first sub-combination), the decomposition forms are:
in accordance with the above decomposition form, it is assumed that there is a unitary transformation It can be used for connectingThe individual qubits areIn the state ofThe quantum state of the individual qubits becomes Dicke states:
Equivalent to uniformly "decomposing" the hamming weights located only on the first few qubits onto all qubits. The following division can be performed by using the decomposition module. Will be original The quantum bits are divided into two parts according to a recurrence formula, and two parts can be used only by reasonably distributing the weights of the two partsThe Dicke state was obtained. According to the generation strategy of the weight distribution binary tree, the original weight is distributed through a series of weight distribution modulesDividing the quantum bit intoEach comprisesCombinations of individual qubits, plus one containingCombinations of the qubits, which are second qubit combinations. Each of the sizes isThe combined hamming weights of (a) are allThus, the distribution module actually needed is. If it is to be fromObtainingSince:
Will be arbitrary The initial state of the form is transformed into the same form:
At the rear Utilization on individual qubitsConstructing two components, and taking the line capable of completing the initial state transformation as a moving module. By passing throughSeparating the first quantum bit, and then acting a first decomposition module on the remaining quantum bits, and repeating the process continuously to obtain the target Dicke state.
In the embodiment of the invention, the characteristic of Dicke states is utilized, and the quantum bits are segmented through the weight distribution binary tree, so that the modules corresponding to each node can fully utilize the device advantages on the device with the full-connection architecture by utilizing the result of the parent node, and the overall line depth is reduced from the original linear complexity to the logarithmic complexity.
For a pair ofState ofNone of the states is active, andThe basic constituent unit of (a) has the characteristic of SWAP revolving door, and only acts onState ofIn the subspace of state composition. If the initial quantum state is not an overlap state,In practice only at the firstState qubit and firstThe state qubit acts as a SWAP rotator gate. When (when)The action position of the SWAP turnstile is necessarily the first two quantum bits, so the SWAP turnstile is directly acted on the two quantum bits; when (when)From the firstThe control of the individual qubits (specifying the first bit as 0 th) acts on the first and second bitsSWAP rotator gate on each qubit. Since the SWAP turnstile only acts onState ofIn the subspace formed by states, if and only if the first qubit isState and the firstThe quantum bit isThe controlled RY door is actually operated and is differentThe corresponding initial quantum states do not interfere with each other.
FIG. 11 is a schematic diagram of a quantum circuit corresponding to a shift module according to an embodiment of the present invention, one of whichComprisingThe SWAP revolving door comprises 1 uncontrolled SWAP revolving door andA controlled SWAP gates, the rotation angle parameter of each SWAP gate may be: . The SWAP turngates may be decomposed into basic quantum logic gate combinations, and the equivalent quantum circuit resulting from the SWAP turngate decomposition may be as shown in fig. 12, with one SWAP turngate decomposed into 4 CNOT gates and two RY gates.
At the position ofThe unit matrix is formed, namely the decomposition module does not change the result of the weight distribution module; at the position ofIn the form of a SWAP turnstile. According to the above-mentioned divide-and-conquer strategy,From the following components、、…、The construction, in particular, as shown in FIG. 13, is a decomposition moduleComprisingAnd a moving module.
Referring to fig. 14, fig. 14 is a schematic structural diagram of a quantum state preparation device according to an embodiment of the present invention, corresponding to the flow shown in fig. 2, where the device includes:
A first determining module 1401, configured to determine a hamming weight of a target quantum state to be prepared and a set of quantum bits, where the target quantum state is Dicke states;
A second determining module 1402, configured to determine, according to the hamming weight and the qubits, all first qubit combinations for an action weight distribution module and all second qubit combinations for an action decomposition module, where the weight distribution module is configured to distribute hamming weights of an initial quantum state to different qubit sub-combinations of the first qubit combinations, and the decomposition module is configured to decompose intermediate states such that the hamming weights are uniformly distributed over all the qubits, the intermediate states being obtained based on the initial quantum state and the weight distribution module;
An obtaining module 1403, configured to obtain a preparation line according to the weight distribution module, the decomposition module, all first qubit combinations, and all second qubit combinations;
a preparation module 1404 is configured to drive the preparation line according to the initial quantum state, so as to evolve the initial quantum state to the target quantum state.
In some possible embodiments of the present invention, the second determining module 1402 may include:
a construction unit, configured to construct a weight distribution binary tree by using the obtained number of qubits and hamming weight, where the number of qubits corresponding to each child node in the weight distribution binary tree is Integer multiple of (2) or withIs equal to the remainder of，For the hamming weight, theA remainder obtained by dividing the number of the obtained qubits by the hamming weight;
A determining unit for determining all first qubit combinations for the active weight distribution module and all second qubit combinations for the active decomposition module based on the weight distribution binary tree.
In some possible embodiments of the present invention, the determining unit is specifically configured to:
Taking a quantum bit corresponding to a parent node in the weight distribution binary tree as a first quantum bit combination for acting a weight distribution module;
And using the qubit corresponding to one leaf node of the weight distribution binary tree as a second qubit combination for acting on the decomposition module.
In some possible embodiments of the present invention, the weight allocation module may include:
a first sub-module for adjusting the hamming weight of the quantum state corresponding to the first sub-combination to And front partEach quantum bit isA state wherein the first sub-combination comprises a first qubit combinationThe number of qubits is one,The number of qubits that are one first qubit combination,The number of qubits contained for a second sub-combination corresponding to the first qubit combination;
A second sub-module for adjusting the hamming weight of the quantum state corresponding to the second sub-combination to Wherein, the method comprises the steps of, wherein,For the hamming weight of the initial quantum state,。
In some possible embodiments of the invention, the first sub-module may comprise a plurality of controlled RY gates;
the second sub-module may include at least And CNOT gates.
In some possible embodiments of the present invention, the first sub-module may include:
A first weight adjustment unit for adjusting the hamming weight of the quantum state corresponding to the second sub-combination to 1, and a second weight adjustment unit for adjusting the hamming weight of the quantum state corresponding to the second sub-combination to 1 The qubit of the bit is set toA state;
a second weight adjustment unit, configured to adjust the hamming weight of the quantum state corresponding to the first sub-combination to be And front partEach quantum bit isA state;
And the weight reduction unit is used for reducing the hamming weight of the quantum state corresponding to the second sub-combination.
In some possible embodiments of the present invention, the first weight adjustment unit and the weight reduction unit may each includeA CNOT gate;
the second sub-module may also include a controlled SWAP gate.
It can be seen that, in the embodiment of the present invention, hamming weights of target quantum states to be prepared and a set of quantum bits are first determined; then determining all first qubit combinations for the action weight distribution module and all second qubit combinations for the action decomposition module according to the hamming weight and the qubit; obtaining a preparation circuit according to the weight distribution module, the decomposition module, all the first quantum bit combinations and all the second quantum bit combinations; and then driving the preparation line according to the initial quantum state so as to evolve the initial quantum state to the target quantum state. The Hamming weight is firstly distributed into different sub-combinations through the weight distribution module, and then the quantum state is decomposed by the decomposition module, so that Dicke states are prepared.
The embodiment of the invention also provides a storage medium, in which a computer program is stored, wherein the computer program is configured to implement the steps in any of the method embodiments described above when run.
Specifically, in the present embodiment, the above-described storage medium may be configured to store a computer program for realizing the steps of:
S201: determining a hamming weight of a target quantum state to be prepared and a group of quantum bits, wherein the target quantum state is Dicke states;
S202: determining all first quantum bit combinations for acting a weight distribution module and all second quantum bit combinations for acting a decomposition module according to the hamming weights and the quantum bits, wherein the weight distribution module is used for distributing hamming weights of initial quantum states to different quantum bit sub-combinations of the first quantum bit combinations, and the decomposition module is used for decomposing intermediate states so that the hamming weights are uniformly distributed on all the quantum bits, and the intermediate states are obtained based on the initial quantum states and the weight distribution module;
s203: obtaining a preparation line according to the weight distribution module, the decomposition module, all first quantum bit combinations and all second quantum bit combinations;
s204: and driving the preparation line according to the initial quantum state so as to evolve the initial quantum state to the target quantum state.
An embodiment of the invention also provides an electronic device comprising a memory and a processor, characterized in that the memory has stored therein a computer program, the processor being arranged to run the computer program to carry out the steps of any of the method embodiments described above.
Specifically, the electronic apparatus may further include a transmission device and an input/output device, where the transmission device is connected to the processor, and the input/output device is connected to the processor.
Specifically, in this embodiment, the above-mentioned processor may be configured to implement the following steps by a computer program:
S201: determining a hamming weight of a target quantum state to be prepared and a group of quantum bits, wherein the target quantum state is Dicke states;
S202: determining all first quantum bit combinations for acting a weight distribution module and all second quantum bit combinations for acting a decomposition module according to the hamming weights and the quantum bits, wherein the weight distribution module is used for distributing hamming weights of initial quantum states to different quantum bit sub-combinations of the first quantum bit combinations, and the decomposition module is used for decomposing intermediate states so that the hamming weights are uniformly distributed on all the quantum bits, and the intermediate states are obtained based on the initial quantum states and the weight distribution module;
s203: obtaining a preparation line according to the weight distribution module, the decomposition module, all first quantum bit combinations and all second quantum bit combinations;
s204: and driving the preparation line according to the initial quantum state so as to evolve the initial quantum state to the target quantum state.
While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.
Claims (8)
1. A method of preparing a quantum state, the method comprising:
determining a hamming weight of a target quantum state to be prepared and a group of quantum bits, wherein the target quantum state is Dicke states;
Determining all first qubit combinations for the action weight distribution module and all second qubit combinations for the action decomposition module according to the hamming weights and the qubits, wherein the method comprises the following steps of: constructing a weight distribution binary tree by using the obtained number of quantum bits and hamming weight, wherein the number of quantum bits corresponding to each child node in the weight distribution binary tree is as follows Integer multiple of (2) or withIs equal to the remainder of，For the hamming weight, theA remainder obtained by dividing the number of the obtained qubits by the hamming weight; taking a quantum bit corresponding to a parent node in the weight distribution binary tree as a first quantum bit combination for acting a weight distribution module; the quantum bit corresponding to one leaf node of the weight distribution binary tree is used as a second quantum bit combination for acting on the decomposition module; the weight distribution module is used for distributing hamming weights of initial quantum states to different quantum bit sub-combinations of the first quantum bit combination, and the decomposition module is used for decomposing intermediate states, so that the hamming weights are uniformly distributed on all the quantum bits, and the intermediate states are obtained based on the initial quantum states and the weight distribution module;
Obtaining a preparation line according to the weight distribution module, the decomposition module, all first quantum bit combinations and all second quantum bit combinations;
and driving the preparation line according to the initial quantum state so as to evolve the initial quantum state to the target quantum state.
2. The method of claim 1, wherein the weight distribution module comprises:
a first sub-module for adjusting the hamming weight of the quantum state corresponding to the first sub-combination to And front partEach quantum bit isA state wherein the first sub-combination comprises a first qubit combinationThe number of qubits is one,The number of qubits that are one first qubit combination,The number of qubits contained for a second sub-combination corresponding to the first qubit combination;
A second sub-module for adjusting the hamming weight of the quantum state corresponding to the second sub-combination to Wherein, the method comprises the steps of, wherein,For the hamming weight of the initial quantum state,。
3. The method of claim 2, wherein the first submodule includes a plurality of controlled RY gates;
the second sub-module comprises at least And CNOT gates.
4. A method according to claim 3, wherein the first sub-module comprises:
A first weight adjustment unit for adjusting the hamming weight of the quantum state corresponding to the second sub-combination to 1, and a second weight adjustment unit for adjusting the hamming weight of the quantum state corresponding to the second sub-combination to 1 The qubit of the bit is set toA state;
a second weight adjustment unit, configured to adjust the hamming weight of the quantum state corresponding to the first sub-combination to be And front partEach quantum bit isA state;
And the weight reduction unit is used for reducing the hamming weight of the quantum state corresponding to the second sub-combination.
5. The method of claim 4, wherein the first weight adjustment unit and the weight reduction unit each compriseA CNOT gate;
The second sub-module also includes a controlled SWAP gate.
6. A quantum state preparation device, the device comprising:
The first determining module is used for determining the hamming weight of the target quantum state to be prepared and a group of quantum bits;
A second determining module, configured to determine, according to the hamming weight and the qubits, all first qubit combinations for the action weight allocation module and all second qubit combinations for the action decomposition module, including: constructing a weight distribution binary tree by using the obtained number of quantum bits and hamming weight, wherein the number of quantum bits corresponding to each child node in the weight distribution binary tree is as follows Integer multiple of (2) or withIs equal to the remainder of，For the hamming weight, theA remainder obtained by dividing the number of the obtained qubits by the hamming weight; taking a quantum bit corresponding to a parent node in the weight distribution binary tree as a first quantum bit combination for acting a weight distribution module; the quantum bit corresponding to one leaf node of the weight distribution binary tree is used as a second quantum bit combination for acting on the decomposition module; the weight distribution module is used for distributing hamming weights of initial quantum states to different quantum bit sub-combinations of the first quantum bit combination, and the decomposition module is used for decomposing intermediate states, so that the hamming weights are uniformly distributed on all the quantum bits, and the intermediate states are obtained based on the initial quantum states and the weight distribution module;
The obtaining module is used for obtaining a preparation line according to the weight distribution module, the decomposition module, all the first quantum bit combinations and all the second quantum bit combinations;
And the preparation module is used for driving the preparation circuit according to the initial quantum state so as to evolve the initial quantum state to the target quantum state, wherein the target quantum state is Dicke states.
7. A storage medium having a computer program stored therein, wherein the computer program is arranged to implement the method of any of claims 1 to 5 when run.
8. An electronic device comprising a memory and a processor, characterized in that the memory has stored therein a computer program, the processor being arranged to run the computer program to implement the method of any of the claims 1 to 5.
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