CN111401562B - Method and device for operating quantum circuit in terminal interface - Google Patents

Method and device for operating quantum circuit in terminal interface Download PDF

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CN111401562B
CN111401562B CN202010163932.3A CN202010163932A CN111401562B CN 111401562 B CN111401562 B CN 111401562B CN 202010163932 A CN202010163932 A CN 202010163932A CN 111401562 B CN111401562 B CN 111401562B
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quantum circuit
logic gate
terminal interface
circuit
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CN111401562A (en
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吴明玉
徐路
仇惠贤
张敏
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Benyuan Quantum Computing Technology Hefei Co ltd
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Benyuan Quantum Computing Technology Hefei Co ltd
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    • G06N10/00Quantum computing, i.e. information processing based on quantum-mechanical phenomena

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Abstract

The application discloses a method and a device for operating a quantum circuit in a terminal interface, wherein the method comprises the following steps: receiving single-step operation of a user on a quantum circuit at a terminal interface; and responding to the single-step operation, operating the quantum logic gate in the next execution time sequence of the quantum circuit, and displaying an operation result on the terminal interface, wherein the quantum logic gate which is not operated in the quantum circuit is in an editable state. By using the embodiment of the application, when a user builds and operates the quantum circuit, the user can operate the quantum circuit once and once in a single step, observe the intermediate operation result, and reedite the quantum circuit which is not operated, thereby improving the user experience and filling the blank of the related technology.

Description

Method and device for operating quantum circuit in terminal interface
Technical Field
The application belongs to the technical field of quantum computing, and particularly relates to a method and a device for operating a quantum circuit in a terminal interface.
Background
The quantum computer is a kind of physical device which performs high-speed mathematical and logical operation, stores and processes quantum information according to the law of quantum mechanics. When a device processes and calculates quantum information and operates on a quantum algorithm, the device is a quantum computer.
The quantum computing simulation is a simulation computation which simulates and follows the law of quantum mechanics by means of numerical computation and computer science, and is taken as a simulation program, and the high-speed computing capability of a computer is utilized to characterize the space-time evolution of the quantum state according to the basic law of quantum bits of the quantum mechanics.
With the increasing development of modern technology, quantum technology achieves an exponential increase in the digital computing power. The more the number of qubits, the more the computation speed increases, and the more powerful it functions. However, in the aspect of providing quantum computing online demonstration and education department popularization simulation service for users, users cannot experience that when quantum circuits are built and operated on a computer interaction interface, the operation mode is to operate all the quantum circuits at one time, intermediate operation results cannot be interrupted or observed, the quantum circuits cannot be edited again, and the user experience is limited.
Disclosure of Invention
The application aims to provide a method and a device for operating a quantum circuit in a terminal interface, which solve the defects in the prior art, enable a user to operate the quantum circuit once at a single step, observe the intermediate operation result and re-edit the quantum circuit which is not operated.
One embodiment of the present application provides a method for operating a quantum circuit in a terminal interface, including:
receiving single-step operation of a user on a quantum circuit at a terminal interface; the single-step operation refers to an operation of operating a quantum logic gate in an execution time sequence to obtain a state of a quantum circuit after the time sequence;
and responding to the single-step operation, operating the quantum logic gate in the next execution time sequence of the quantum circuit, displaying an operation result on the terminal interface, and distinguishing and displaying the operated quantum logic gate in the quantum circuit on the terminal interface, wherein the quantum logic gate which is not operated in the quantum circuit is in an editable state.
Optionally, after running the quantum logic gate in the next execution timing of the quantum wire, the method further includes:
receiving editing operation for a quantum logic gate which is not operated in the quantum circuit; wherein the editing operation includes: addition, deletion, and substitution;
and responding to the editing operation, and displaying the edited quantum circuit on a terminal interface.
Optionally, the operation result includes: probability and amplitude of quantum states.
Still another embodiment of the present application provides an apparatus for operating a quantum wire in a terminal interface, including:
the first receiving module is used for receiving single-step operation of a user on the quantum circuit at the terminal interface; the single-step operation refers to an operation of operating a quantum logic gate in an execution time sequence to obtain a state of a quantum circuit after the time sequence;
and the response operation module is used for responding to the single-step operation, operating the quantum logic gate in the next execution time sequence of the quantum circuit, displaying an operation result on the terminal interface, and distinguishing and displaying the operated quantum logic gate in the quantum circuit on the terminal interface, wherein the quantum logic gate which is not operated in the quantum circuit is in an editable state.
Optionally, the method further comprises:
the second receiving module is used for receiving editing operation for a quantum logic gate which is not operated in the quantum circuit; wherein the editing operation includes: addition, deletion, and substitution;
and the response display module is used for responding to the editing operation and displaying the edited quantum circuit on a terminal interface.
Optionally, the operation result includes: probability and amplitude of quantum states.
A further embodiment of the application provides a storage medium having a computer program stored therein, wherein the computer program is arranged to perform the method of any of the preceding claims when run.
Yet another embodiment of the application provides an electronic device comprising a memory having a computer program stored therein and a processor configured to run the computer program to perform the method described in any of the above.
Compared with the prior art, the method and the device have the advantages that firstly, single-step operation of a user on the quantum circuit is received at the terminal interface, the single-step operation is responded, the quantum logic gate in the next execution time sequence of the quantum circuit is operated, and the operation result is displayed at the terminal interface, wherein the quantum logic gate which is not operated in the quantum circuit is in an editable state, so that the user can operate the quantum circuit once in a single step when constructing and operating the quantum circuit, observe the intermediate operation result, and can reedit the not operated quantum circuit, improve the user experience, and fill the blank of the related technology.
Drawings
Fig. 1 is a hardware block diagram of a computer terminal according to an operation method of a quantum circuit in a terminal interface according to an embodiment of the present application;
fig. 2 is a schematic flow chart of a method for operating a quantum circuit in a terminal interface according to an embodiment of the present application;
fig. 3 is a schematic diagram illustrating the operation of a quantum circuit according to an embodiment of the present application;
fig. 4 is an edit schematic diagram of a quantum circuit according to an embodiment of the present application;
fig. 5 is a schematic structural diagram of an operation device of a quantum circuit in a terminal interface according to an embodiment of the present application.
Detailed Description
The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the application.
At present, quantum computing tends to be expressed in a high level, and primary learning of users with little knowledge about quantum computing is insufficient to clearly demonstrate the whole of the quantum computing from simple to complex computing processes, such as the visual display process of computing evolution and physical realization of quantum circuits. Therefore, the embodiment of the application provides a method and a device for operating a quantum circuit in a terminal interface, a storage medium and an electronic device.
The method for operating the quantum circuit in the terminal interface is described in detail below, and can be applied to electronic equipment such as mobile terminals, particularly mobile phones and tablet computers; such as a computer terminal, in particular a general computer or the like.
The following describes the operation of the computer terminal in detail by taking it as an example. FIG. 1 is a block diagram of a quantum computing analog hardware architecture according to an embodiment of the application. As shown in fig. 1, the computer terminal 10 may include one or more (only one is shown in fig. 1) processors 102 (the processor 102 may include, but is not limited to, a microprocessor MCU or a processing device such as a programmable logic device FPGA) and a memory 104 for storing data, and optionally, a transmission device 106 for communication functions and an input-output device 108. It will be appreciated by those skilled in the art that the configuration shown in fig. 1 is merely illustrative and is not intended to limit the configuration of the computer terminal described above. For example, the computer terminal 10 may also include more or fewer components than shown in FIG. 1, or have a different configuration than shown in FIG. 1.
The memory 104 may be used to store software programs and modules of application software, such as program instructions/modules corresponding to the quantum computing simulation method in the embodiment of the present application, and the processor 102 executes the software programs and modules stored in the memory 104 to perform various functional applications and data processing, i.e., implement the method described above. Memory 104 may include high-speed random access memory, and may also include non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some examples, the memory 104 may further include memory located remotely from the processor 102, which may be connected to the computer terminal 10 via a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.
The transmission means 106 is arranged to receive or transmit data via a network. The specific examples of the network described above may include a wireless network provided by a communication provider of the computer terminal 10. In one example, the transmission device 106 includes a network adapter (Network Interface Controller, NIC) that can connect to other network devices through a base station to communicate with the internet. In one example, the transmission device 106 may be a Radio Frequency (RF) module for communicating with the internet wirelessly.
It should be noted that a real quantum computer is a hybrid structure, which includes two major parts: part of the computers are classical computers and are responsible for performing classical computation and control; the other part is quantum equipment, which is responsible for running quantum programs so as to realize quantum computation. The quantum program is a series of instruction sequences written by a quantum language such as the qlunes language and capable of running on a quantum computer, so that the support of quantum logic gate operation is realized, and finally, quantum computing is realized. Specifically, the quantum program is a series of instruction sequences for operating the quantum logic gate according to a certain time sequence.
In practical applications, quantum computing simulations are often required to verify quantum algorithms, quantum applications, etc., due to the development of quantum device hardware. Quantum computing simulation is a process of realizing simulated operation of a quantum program corresponding to a specific problem by means of a virtual architecture (namely a quantum virtual machine) built by resources of a common computer. In general, it is necessary to construct a quantum program corresponding to a specific problem. The quantum program, namely the program for representing the quantum bit and the evolution thereof written in the classical language, wherein the quantum bit, the quantum logic gate and the like related to quantum computation are all represented by corresponding classical codes.
Quantum circuits, which are one embodiment of quantum programs, also weigh sub-logic circuits, are the most commonly used general quantum computing models, representing circuits that operate on qubits under an abstract concept, the composition of which includes qubits, circuits (timelines), and various quantum logic gates, and finally the results often need to be read out by quantum measurement operations.
Unlike conventional circuits, which are connected by metal lines to carry voltage or current signals, in a quantum circuit, the circuit can be seen as being connected by time, i.e., the state of the qubit naturally evolves over time, as indicated by the hamiltonian operator, during which it is operated until a logic gate is encountered.
One quantum program is corresponding to one total quantum circuit, and the quantum program refers to the total quantum circuit, wherein the total number of quantum bits in the total quantum circuit is the same as the total number of quantum bits of the quantum program. It can be understood that: one quantum program may consist of a quantum circuit, a measurement operation for the quantum bits in the quantum circuit, a register to hold the measurement results, and a control flow node (jump instruction), and one quantum circuit may contain several tens to hundreds or even thousands of quantum logic gate operations. The execution process of the quantum program is a process of executing all quantum logic gates according to a certain time sequence. Note that the timing is the time sequence in which a single quantum logic gate is executed.
It should be noted that in classical computation, the most basic unit is a bit, and the most basic control mode is a logic gate, and the purpose of the control circuit can be achieved by a combination of logic gates. Similarly, the way in which the qubits are handled is a quantum logic gate. Quantum logic gates are used, which are the basis for forming quantum circuits, and comprise single-bit quantum logic gates, such as Hadamard gates (H gates, aldar Ma Men), brix gates, brix-Y gates, brix-Z gates, RX gates, RY gates and RZ gates; multi-bit quantum logic gates such as CNOT gate, CR gate, iSWAP gate, toffoli gate. Quantum logic gates are typically represented using unitary matrices, which are not only in matrix form, but also an operation and transformation. The effect of a general quantum logic gate on a quantum state is calculated by multiplying the unitary matrix by the matrix corresponding to the right vector of the quantum state.
Referring to fig. 2, fig. 2 is a flow chart of a method for operating a quantum circuit in a terminal interface according to an embodiment of the present application, which may include the following steps:
s201, receiving single-step operation of a user on a quantum circuit at a terminal interface;
specifically, a click trigger operation of a user on an operation function item of the quantum circuit may be received, where the operation function item includes, but is not limited to: single step operation, single step return, full operation and initialization.
The terminal interface may display each operation function item button that the user can click:
the single-step operation is to operate a quantum logic gate operation in an execution time sequence to obtain a state of a quantum circuit after the time sequence;
single step return refers to returning to the state of the quantum wire before an execution time sequence;
all the operations refer to the operation of quantum logic gates in all execution time sequences, namely, the whole quantum circuit is operated at one time, so that the state of the quantum circuit after all the quantum logic gates are executed is obtained;
initialization refers to returning to a default initial state when the entire quantum wire is not running.
S202, responding to the single-step operation, operating a quantum logic gate in the next execution time sequence of the quantum circuit, and displaying an operation result on the terminal interface, wherein the quantum logic gate which is not operated in the quantum circuit is in an editable state.
And the terminal interface responds after receiving the single-step operation, namely, the quantum logic gate in the next execution time sequence of the operation quantum line, and the operation result is displayed in the other area of the terminal interface. Wherein, the operation result may include: probability and amplitude values of quantum states. Quantum bits of quantum logic gate operations at the same execution timing are different and may be executed simultaneously.
Specifically, after the quantum logic gate in the next execution time sequence of the quantum circuit is operated, the operated quantum logic gate in the quantum circuit can be also displayed in a terminal interface in a distinguishing mode.
Illustratively, as shown in fig. 3, the quantum wires may be represented as:
first timing: h q [0];
second timing: x q [0];
third timing: y q [1];
fourth timing: z q [0], NOT q [1];
wherein H represents an H gate, X represents a Brix-X gate, Y represents a Brix-Y gate, Z represents a Brix-Z gate, and NOT represents a NOT gate.
At this time, when the user clicks on the single step operation function item, H q [0] is operated, and the amplitude and probability (not shown) of the quantum state after operation are displayed, wherein the vertical line between H and X in the figure represents the breakpoint position, i.e., the quantum line is currently operated to the position. And clicking the single-step operation function item again, continuing to operate X q [0] in the next time sequence from the current position, and updating and displaying the amplitude and probability of the quantum state after the operation, so that the intermediate evolution process of the quantum state is observed, and the learning understanding of the quantum computing principle is facilitated for a user.
Similarly, the single-click operation may be continued, Y q [1] may be operated, and the last single-click operation may be operated Z q [0] and NOT q [1]. After each run is completed, the running quantum logic gate icon can be displayed differently (not shown in the figure), for example, the original quantum logic gate icon is blue, and the running quantum logic gate icon is gray.
Specifically, after the quantum logic gate in the next execution timing of the quantum circuit is operated, an editing operation for a quantum logic gate that is not operated in the quantum circuit may also be received; wherein the editing operation includes: addition, deletion, and substitution; and responding to the editing operation, and displaying the edited quantum circuit on a terminal interface.
And before receiving the single-step operation of the user on the quantum circuit, the editing operation of the user on the quantum circuit can be received at the terminal interface.
Specifically, the quantum circuit is edited, mainly comprising quantum bits and quantum logic gates for operating the quantum bits, each quantum bit corresponds to a time line, and the quantum logic gates are arranged on the time lines according to the construction requirements of users.
Among them, quantum circuits, also called sub-logic circuits, are the most commonly used general quantum computing model, representing circuits that operate on qubits under an abstract concept, whose composition includes qubits, circuits (timelines), and various quantum logic gates, and finally the result is often required to be read out through quantum measurement operations.
Unlike conventional circuits, which are connected by metal lines to carry voltage or current signals, in a quantum circuit, the circuit can be seen as being connected by time, i.e., the state of the qubit naturally evolves over time, as indicated by the hamiltonian operator, during which it is operated until a logic gate is encountered.
In one implementation, the editing operation may include, but is not limited to: setting a qubit: increasing or decreasing the qubit; setting a quantum logic gate: the single quantum logic gate is not arranged, and then a single quantum logic gate or a preset set of quantum logic gates can be selectively increased by clicking; the quantum logic gate exists, the quantum logic gate can be clicked to carry out selective replacement, deletion or parameter setting, the quantum logic gate can be double-clicked to realize quick deletion, and the icon of the quantum logic gate can be pressed to carry out operations such as dragging.
The terminal is a computer, and the terminal interface displays at least a representation of a qubit, an initial qustate and a time line, and a time sequence number is displayed above the time line.
Referring to FIG. 4, as shown in FIG. 4a, the 0 th qubit is denoted as q [0],0 is the number of bits, the initial qustate is 0, denoted as the qustate right vector |0>, the time line is a horizontal line, and the numbers 1, 2, and 3 above the time line are the time sequence numbers, and represent the first, second, and third time sequences. The user clicks the function item (invisible) at the time line corresponding to q [0] and right below the time sequence 1, a first floating frame comprising quantum logic gates is popped up, the quantum logic gates NOT in the floating frame are clicked, the floating frame disappears, an icon representing the NOT gate is correspondingly displayed at the position on the time line, and similarly, an X gate can be added at the time line right below the time sequence 2. Clicking a functional item "+" for setting the number of the quantum bits, adding one quantum bit, and adding an icon q [1], an initial quantum state right vector |0> and a time line for displaying one quantum bit on the basis of displaying an original quantum circuit by a terminal interface, wherein the final display effect is shown in fig. 4b, and the other functional item "-" for setting the number of the quantum bit is used for reducing one quantum bit, and is opposite to the effect of the functional item "+".
Continuing at q [1]]And adding a Y gate and an H gate on the corresponding time line, wherein the adding mode is the same as that of the NOT gate, and the figure 4c is obtained. Clicking on the NOT icon in FIG. 4c displays a second hover frame containing the designation "NOT" and matrix form of the quantum logic gate represented by the icon as shown in FIG. 4dAnd the operation function items of replacement and deletion are also included: clicking "replace" to display a first hover frame for selecting a quantum logic gate to replace the NOT gate; clicking "delete" deletes the NOT gate. In addition, if the NOT icon is directly double-clicked, the NOT icon can be quickly deleted; if the NOT gate icon is held, it can be dragged, e.g., dragged and dropped to q [0] below timing 3]At the corresponding timeline location.
The terminal responds after receiving the editing operation of the user, and then displays the edited quantum circuit in the interface in real time. Wherein, available prior art realizes: and responding to the editing operation, displaying the edited quantum circuit on the terminal interface, and not being described herein.
For example, by clicking a functional item for setting a qubit, a user adds a qubit, and then the terminal interface adds an icon for displaying a qubit, an initial quantum state and a time line on the basis of displaying an original quantum line, that is, after the terminal interface responds, the edited quantum line is displayed.
Therefore, by receiving a single-step operation of a user on the quantum circuit at the terminal interface, responding the single-step operation, operating the quantum logic gate in the next execution time sequence of the quantum circuit, and displaying an operation result at the terminal interface, wherein the quantum logic gate which is not operated in the quantum circuit is in an editable state, so that the user can operate the quantum circuit once at a single step when constructing and operating the quantum circuit, observe the intermediate operation result, and can reedit the quantum circuit which is not operated, thereby improving the user experience and filling the blank of the related technology.
Referring to fig. 5, fig. 5 is a schematic structural diagram of an operation device of a quantum circuit in a terminal interface according to an embodiment of the present application, where the operation device corresponds to the flow shown in fig. 2, and the operation device may include:
a first receiving module 501, configured to receive, at a terminal interface, a single-step operation of a user on a quantum wire; the single-step operation refers to an operation of operating a quantum logic gate in an execution time sequence to obtain a state of a quantum circuit after the time sequence;
and the response operation module 502 is configured to respond to the single-step operation, operate a quantum logic gate in a next execution time sequence of the quantum circuit, display an operation result on the terminal interface, and display the quantum logic gate operated in the quantum circuit in a distinguishing manner on the terminal interface, where a quantum logic gate not operated in the quantum circuit is in an editable state.
Specifically, the method further comprises the following steps:
the second receiving module is used for receiving editing operation for a quantum logic gate which is not operated in the quantum circuit; wherein the editing operation includes: addition, deletion, and substitution;
and the response display module is used for responding to the editing operation and displaying the edited quantum circuit on a terminal interface.
Specifically, the operation result includes: probability and amplitude of quantum states.
Therefore, by receiving a single-step operation of a user on the quantum circuit at the terminal interface, responding the single-step operation, operating the quantum logic gate in the next execution time sequence of the quantum circuit, and displaying an operation result at the terminal interface, wherein the quantum logic gate which is not operated in the quantum circuit is in an editable state, so that the user can operate the quantum circuit once at a single step when constructing and operating the quantum circuit, observe the intermediate operation result, and can reedit the quantum circuit which is not operated, thereby improving the user experience and filling the blank of the related technology.
An embodiment of the application is also a storage medium having a computer program stored therein, wherein the computer program is arranged to perform the steps of 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 executing the steps of:
s1, receiving single-step operation of a user on a quantum circuit at a terminal interface;
s2, responding to the single-step operation, operating a quantum logic gate in the next execution time sequence of the quantum circuit, and displaying an operation result on the terminal interface.
Specifically, in the present embodiment, the storage medium may include, but is not limited to: a usb disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), a removable hard disk, a magnetic disk, or an optical disk, or other various media capable of storing a computer program.
Therefore, by receiving a single-step operation of a user on the quantum circuit at the terminal interface, responding the single-step operation, operating the quantum logic gate in the next execution time sequence of the quantum circuit, and displaying an operation result at the terminal interface, wherein the quantum logic gate which is not operated in the quantum circuit is in an editable state, so that the user can operate the quantum circuit once at a single step when constructing and operating the quantum circuit, observe the intermediate operation result, and can reedit the quantum circuit which is not operated, thereby improving the user experience and filling the blank of the related technology.
The present application also provides an electronic device comprising a memory having a computer program stored therein and a processor arranged to run the computer program to perform 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 the present embodiment, the above-described processor may be configured to execute the following steps by a computer program:
s1, receiving single-step operation of a user on a quantum circuit at a terminal interface;
s2, responding to the single-step operation, operating a quantum logic gate in the next execution time sequence of the quantum circuit, and displaying an operation result on the terminal interface.
Therefore, by receiving a single-step operation of a user on the quantum circuit at the terminal interface, responding the single-step operation, operating the quantum logic gate in the next execution time sequence of the quantum circuit, and displaying an operation result at the terminal interface, wherein the quantum logic gate which is not operated in the quantum circuit is in an editable state, so that the user can operate the quantum circuit once at a single step when constructing and operating the quantum circuit, observe the intermediate operation result, and can reedit the quantum circuit which is not operated, thereby improving the user experience and filling the blank of the related technology.
While the foregoing is directed to embodiments of the present application, other and further embodiments of the application may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.

Claims (8)

1. The method for operating the quantum circuit in the terminal interface is characterized by comprising the following steps:
receiving single-step operation of a user on a quantum circuit at a terminal interface; the single-step operation refers to an operation of operating a quantum logic gate in an execution time sequence to obtain a state of a quantum circuit after the time sequence;
and responding to the single-step operation, operating the quantum logic gate in the next execution time sequence of the quantum circuit, displaying an operation result on the terminal interface, and distinguishing and displaying the operated quantum logic gate in the quantum circuit on the terminal interface, wherein the quantum logic gate which is not operated in the quantum circuit is in an editable state.
2. The method of claim 1, further comprising, after running a quantum logic gate in a next execution timing of the quantum wire:
receiving editing operation for a quantum logic gate which is not operated in the quantum circuit; wherein the editing operation includes: addition, deletion, and substitution;
and responding to the editing operation, and displaying the edited quantum circuit on a terminal interface.
3. The method of claim 1, wherein the operation result comprises:
probability and amplitude of quantum states.
4. An apparatus for operating a quantum circuit in a terminal interface, comprising:
the first receiving module is used for receiving single-step operation of a user on the quantum circuit at the terminal interface; the single-step operation refers to an operation of operating a quantum logic gate in an execution time sequence to obtain a state of a quantum circuit after the time sequence;
and the response operation module is used for responding to the single-step operation, operating the quantum logic gate in the next execution time sequence of the quantum circuit, displaying an operation result on the terminal interface, and distinguishing and displaying the operated quantum logic gate in the quantum circuit on the terminal interface, wherein the quantum logic gate which is not operated in the quantum circuit is in an editable state.
5. The apparatus as recited in claim 4, further comprising:
the second receiving module is used for receiving editing operation for a quantum logic gate which is not operated in the quantum circuit; wherein the editing operation includes: addition, deletion, and substitution;
and the response display module is used for responding to the editing operation and displaying the edited quantum circuit on a terminal interface.
6. The apparatus of claim 4, wherein the operation result comprises:
probability and amplitude of quantum states.
7. A storage medium having a computer program stored therein, wherein the computer program is arranged to perform the method of any of claims 1 to 3 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 perform the method of any of the claims 1 to 3.
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