A transmission cost optimization method based on quantum bit storage

Abstract

This invention provides a transmission cost optimization method based on qubit storage, belonging to the technical field of transmission cost optimization in distributed quantum computing. It addresses the problems of excessive quantum resource consumption and high transmission cost. The technical solution is as follows: S1, establishing a storage model; S2, constructing a cross-gate merged transmission model; S3, implementing a transmission cost optimization algorithm based on the distributed quantum circuit storage model. The beneficial effects of this invention include: a storage model with wide applicability and low transmission cost, while reducing qubit consumption.

Description

Technical Field

[0001] The present invention relates to the technical field of transmission cost optimization in distributed quantum computing, and in particular to a transmission cost optimization method based on quantum bit storage. Background Art

[0002] Researchers first proposed quantum computing in the 1980s. After nearly 40 years of development, quantum computing has become an emerging discipline with great potential to surpass traditional computing. Due to its ultra-fast parallel computing capabilities, quantum computing offers exponentially faster time-to-solve for some classical problems compared to traditional algorithms. Therefore, quantum computing undoubtedly plays a vital role in solving classical problems. Furthermore, quantum computing is widely used in fields such as quantum communications, quantum chemistry, and quantum finance, providing superior computing power compared to traditional computing. The prospects for quantum computing are vast, and it will be integrated with even more disciplines in the future. Currently, quantum computing is entering an era of rapid development. Companies both domestically and internationally, such as IBM, Google, and Origin Quantum, have released quantum computers with 127, 72, and 64 qubits, and plan to release quantum computers with over 1,000 qubits in the coming years.

[0003] Although the number of qubits in quantum computers continues to increase, current quantum computers still cannot meet the demand for use. This is primarily due to three reasons. First, as the number of qubits increases, crosstalk between qubits becomes severe, leading to quantum decoherence instability and loss of stability across the entire quantum circuit. Second, because quantum circuits have a certain error rate, error correction requires a large number of qubits. Current quantum computers cannot accommodate this large number of error-correcting qubits, making ideal error correction impossible. Third, when the number of qubits in a quantum circuit exceeds the number of qubits in a quantum computer, the circuit cannot be executed on a single quantum computer. To address these issues, efforts are underway to increase the number of qubits in quantum computers, but currently, there are technical bottlenecks in expanding the number of qubits in quantum computers. The paper "Dadkhah D, Zomorodi M, Hosseini SE, et al. Reordering and partitioning of distributed quantum circuits [J]. IEEE Access, 2022, 10:70329-70341" describes distributed quantum computing, where circuits with excessive qubits are distributed across multiple quantum computers for execution. This approach is more direct and effective. In the paper: Wu A, Zhang H, Li G, et al. AutoComm: A Framework for Enabling Efficient Communication in Distributed Quantum Programs [J]. arXiv preprint arXiv: 2207.11674, 2022. It is recorded that to date, most distributed quantum computing uses teleportation as a means of communication between subsystems. Teleportation requires the use of classical channels and quantum channels to complete transmission, transmitting an unknown quantum state to other quantum computing devices through quantum entanglement. In addition, in the paper: Wang MY, Wang XD, Ruan DL, et al. Quantum direct portation, Acta Physica Sinica, 70, 190301 (2021): 21-27. It is recorded that quantum direct teleportation can also be used as a quantum communication protocol.In the paper: Zhang H, Sun Z, Qi R, et al. Realization of quantum secure direct communication over 100km fiber with time-bin and phase quantum states[J]. Light: Science & Applications, 2022, 11(1): 83. Quantum direct transmission directly transmits a large number of quantum states and then purifies the single quantum states to obtain the desired quantum states, avoiding the consumption of entanglement resources. Since the time cost of quantum communication is much greater than the time to execute a single quantum gate, effectively reducing the transmission cost between quantum computing subsystems is a key issue in distributed quantum computers.

[0004] The current transmission model in distributed quantum computing based on teleportation has the following disadvantages:

[0005] (1) Excessive quantum resource consumption

[0006] Currently, most distributed computing uses teleportation as a communication protocol. The basic idea of teleportation is to transfer the state of a quantum bit from one location to another through a third-party medium and then reproduce it. When a large number of quantum bits need to be transmitted in a distributed circuit, a large number of auxiliary quantum bits are required to achieve entanglement, resulting in excessive consumption of quantum resources.

[0007] (2) Transmission cost is too high

[0008] The combined transmission model has little effect on optimizing distributed circuits, and it fails to consider the impact of the post-transmission qubit storage mode on transmission costs. The combined transmission model imposes specific requirements on the arrangement of quantum gates in the circuit. When global gates do not have the same transmission qubits, the combined transmission model fails, and the optimization effect on the circuit is not significant. Furthermore, without a fixed number of auxiliary qubits to receive and store quantum states sent from other quantum computers, the consumption of auxiliary qubits increases with the number of transmissions. When too many qubits are used for storage, qubits interfere with each other, the transmission cost increases, and the reliability and fidelity of the circuit are affected.

[0009] How to solve the above technical problems is the subject faced by the present invention. Summary of the Invention

[0010] The present invention aims to provide a method for optimizing transmission costs based on qubit storage. This method addresses the issues of excessive quantum resource consumption and transmission costs. The present invention offers a storage mode with broad applicability and low transmission costs, while also reducing qubit consumption.

[0011] In order to achieve the above-mentioned purpose of the invention, the technical solution adopted by the present invention is as follows:

[0012] A transmission cost optimization method based on quantum bit storage includes the following steps:

[0013] S1. Establish storage model;

[0014] Based on the use of quantum direct teleportation as the communication protocol for distributed quantum computing, only the overhead of storage qubits is considered; storage qubits can be divided into direct storage qubits and temporary storage qubits. Direct storage qubits are used to store the qubits of local gates or global gates in a certain partition. The number of direct storage qubits is determined by the size of the circuit. The larger the circuit, the more direct storage qubits are required. After a quantum state is transmitted through direct teleportation, a new qubit is required to receive and store this quantum state. This qubit is temporary and can continue to repeatedly store the qubit of the next direct teleportation. In each partition, one or more qubits are required to temporarily store the qubit transmitted from another partition. This qubit is called a temporary storage qubit. The number of temporary storage qubits directly affects the transmission cost of the distributed circuit. The more temporary storage qubits, the lower the transmission cost of the circuit.

[0015] S2, build a cross-gate merge transmission model;

[0016] Based on the storage model of the temporary storage bit in S1, it can be represented in the logic circuit that each partition has a temporary storage bit; Figure 2 The structure shown is Figure 1 In the circuit storage model, qa0 and qa1 are both temporary storage qubits, where qa0 is the temporary storage qubit of the P1 partition and qa1 is the temporary storage qubit of the P2 partition. There is only one temporary storage bit in each of the P1 and P2 partitions, which can transfer the P1 partition qubit to the P2 partition and store it in the temporary storage qubit qa1, and can also transfer the P2 partition qubit to the P1 partition and store it in the temporary storage qubit qa0.

[0017] S3, based on the transmission cost optimization algorithm under the distributed quantum circuit storage model, includes the following steps:

[0018] Step 1: Based on the transmission queue list of the previous optimization results, the quantum bit of the quantum state transmitted by each transmission queue is obtained;

[0019] Step 2: Starting from the first transmission queue, traverse all transmission queues and determine whether the number of forward transmissions can be reduced based on the state of the transmitted qubits;

[0020] Step 3: Then traverse all the gates of the transmission queue backward to determine whether there are other gates on the qubit. If there are no other gates, the backhaul is allowed to be reduced.

[0021] Step 4: Finally, the forward and return status codes of each transmission queue are returned. 0 means no transmission is required, and 1 means transmission is required. The overall transmission cost of this distributed line is calculated.

[0022] A quantum state is transmitted from partition P1 to partition P2. This process is forward transmission and is called forward transmission.

[0023] A quantum state is transferred from the P1 partition to the P2 partition, and then transferred back to the P1 partition after the P2 operation is completed. This process is called backtransmission.

[0024] In S1, the number of directly stored qubits minimized by each distributed subsystem is shown in the following formula (1):

[0025]

[0026] Here, k represents the number of partitions, and n represents the total number of initial circuit qubits.

[0027] In S1, the number of temporary storage qubits of each distributed subsystem is set to 1, which is the minimum. At this time, the qubit overhead of each distributed subsystem is minimized, and the number of qubits occupied by the partition is shown in the following formula (2):

[0028]

[0029] In S3 Figure 3 As shown, in the P1 system, q0, q1, q3, and q4 are directly stored qubits, and q2 is a temporary storage qubit, corresponding to Figure 2 The temporary storage qubit qa0 in the P2 system; q1, q2, q3, q4 are direct storage qubits, and q0 is a temporary storage qubit, corresponding to Figure 2 The temporary storage qubit qa1 in Figure 2 The q0, q1, and q2 qubits in the circuit are mapped to Figure 3 On the quantum bits of the P1 system, q3, q4, and q5 quantum bits are mapped to Figure 3 On the quantum bit of the P2 system.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] (1) Less qubit consumption;

[0032] Qubit overhead includes the cost of both storage qubits and auxiliary entanglement qubits. Because this patent utilizes direct quantum teleportation as the communication protocol for distributed quantum computing, it relies solely on direct quantum channels for communication, eliminating the need for auxiliary qubits to achieve entanglement. Therefore, only the storage qubit overhead is considered. To further enhance the practical application of distributed quantum computing and minimize qubit consumption, this patent minimizes the storage qubit overhead. Compared to existing distributed models, this patent requires fewer qubits.

[0033] (2) A storage mode with wider applicability and lower transmission cost;

[0034] Given a given qubit overhead, the storage model proposed in this patent consumes fewer qubits, better aligning with the original goal of distributed quantum computing—solving the qubit shortage. Therefore, this storage model can accommodate a wider range of distributed quantum circuits and has broader applicability. This storage model can further reduce unnecessary transmissions, thereby lowering transmission costs. Compared to the combined transmission model, transmission cost optimization based on the storage model offers a secondary optimization based on the combined transmission model, further reducing circuit transmission costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0036] Figure 1 This is the distributed quantum circuit division diagram of the present invention.

[0037] Figure 2 This is a diagram of the distributed logic circuit storage model of the present invention.

[0038] Figure 3 This is a diagram of the distributed topology storage model of the present invention.

[0039] Figure 4 It is the circuit diagram after the door of the present invention moves.

[0040] Figure 5 This is the unoptimized combined transmission line diagram of the present invention.

[0041] Figure 6 This is the unoptimized transmission pattern of the present invention.

[0042] Figure 7 This is the optimized transmission pattern of the present invention. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. Of course, the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0044] Example 1

[0045] Please refer to Figure 1-Figure 4 , the technical solution adopted by the present invention is specifically as follows:

[0046] A transmission cost optimization method based on quantum bit storage includes the following steps:

[0047] S1. Establish storage model;

[0048] Based on the use of quantum direct teleportation as the communication protocol for distributed quantum computing, only the overhead of storage qubits is considered; storage qubits can be divided into direct storage qubits and temporary storage qubits. Direct storage qubits are used to store the qubits of local gates or global gates in a certain partition. The number of direct storage qubits is determined by the size of the circuit. The larger the circuit, the more direct storage qubits are required. After a quantum state is transmitted through direct teleportation, a new qubit is required to receive and store this quantum state. This qubit is temporary and can continue to repeatedly store the qubit of the next direct teleportation. In each partition, one or more qubits are required to temporarily store the qubit transmitted from another partition. This qubit is called a temporary storage qubit. The number of temporary storage qubits directly affects the transmission cost of the distributed circuit. The more temporary storage qubits, the lower the transmission cost of the circuit.

[0049] S2, build a cross-gate merge transmission model;

[0050] Based on the storage model of the temporary storage bit in S1, it can be represented in the logic circuit that each partition has a temporary storage bit; Figure 2 The structure shown is Figure 1 In the circuit storage model, qa0 and qa1 are both temporary storage qubits, where qa0 is the temporary storage qubit of the P1 partition and qa1 is the temporary storage qubit of the P2 partition. There is only one temporary storage bit in each of the P1 and P2 partitions, which can transfer the P1 partition qubit to the P2 partition and store it in the temporary storage qubit qa1, and can also transfer the P2 partition qubit to the P1 partition and store it in the temporary storage qubit qa0.

[0051] S3, based on the transmission cost optimization algorithm under the distributed quantum circuit storage model, includes the following steps:

[0052] Step 1: Based on the transmission queue list of the previous optimization results, the quantum bit of the quantum state transmitted by each transmission queue is obtained;

[0053] Step 2: Starting from the first transmission queue, traverse all transmission queues and determine whether the number of forward transmissions can be reduced based on the state of the transmitted qubits;

[0054] Step 3: Then traverse all the gates of the transmission queue backward to determine whether there are other gates on the qubit. If there are no other gates, the backhaul is allowed to be reduced.

[0055] Step 4: Finally, the forward and return status codes of each transmission queue are returned. 0 means no transmission is required, and 1 means transmission is required. The overall transmission cost of this distributed line is calculated.

[0056] A quantum state is transmitted from partition P1 to partition P2. This process is forward transmission and is called forward transmission.

[0057] A quantum state is transferred from the P1 partition to the P2 partition, and then transferred back to the P1 partition after the P2 operation is completed. This process is called backtransmission.

[0058] In S1, the number of directly stored qubits minimized by each distributed subsystem is shown in the following formula (1):

[0059]

[0060] Here, k represents the number of partitions, and n represents the total number of initial circuit qubits.

[0061] In S1, the number of temporary storage qubits of each distributed subsystem is set to 1, which is the minimum. At this time, the qubit overhead of each distributed subsystem is minimized, and the number of qubits occupied by the partition is shown in the following formula (2):

[0062]

[0063] In S3 Figure 3 As shown, in the P1 system, q0, q1, q3, and q4 are directly stored qubits, and q2 is a temporary storage qubit, corresponding to Figure 2 The temporary storage qubit qa0 in the P2 system; q1, q2, q3, q4 are direct storage qubits, and q0 is a temporary storage qubit, corresponding to Figure 2 The temporary storage qubit qa1 in; Figure 2 The q0, q1, and q2 qubits in the circuit are mapped to Figure 3 On the quantum bits of the P1 system, q3, q4, and q5 quantum bits are mapped to Figure 3 On the quantum bits of the P2 system.

[0064] Example 2

[0065] On the basis of Example 1, Figure 1 Take the line as an example, and optimize its forward and return times. When forward and return optimization is not performed, the combined transmission model is used, and the movement rule is used to move the G7 gate to the left to the right of the G1 gate. The line after the movement is as follows Figure 4 As shown. G1 and G7 gates are combined to transmit a two-way quantum teleportation once, G2 gate is combined to transmit a two-way quantum teleportation once, G6 and G8 gates are combined to transmit a two-way quantum teleportation once, a total of three two-way quantum teleportations, the transmission cost is 6. Figure 2 After optimizing the line using the combined transmission model, forward and backhaul optimization continued. Gates G1 and G7 had no previous gates on the q4 qubit, so forward transmission was not required. However, since q4 qubit has subsequent gates, backhaul was required. Similarly, gate G2 did not require a forward transmission, but did require a backhaul. Gates G6 and G8 had no previous gates on the q2 qubit, so forward transmission was not required. Since there were no subsequent gates, they were measured directly on the temporary storage qubits in the P2 partition, eliminating the need for backhaul. Therefore, after forward and backhaul optimization, the transmission cost of this line was reduced from 6 to 2, achieving significant optimization results.

[0066] Example 3

[0067] On the basis of embodiments 1 and 2, after optimizing the transmission cost of the line using the combined transmission model, the number of forward transmissions and return transmissions is further optimized based on the storage mode, thereby reducing the overall transmission cost of the line.

[0068] by Figure 5 Take the unoptimized combined transmission line as an example. This line is the 4gt11_82 line in the benchmark test set RevLib. The line contains two combined transmission queues. Queue 1 contains G1, G2, and G10, and queue 2 contains G7, T, G11, and G12. Before optimization, each combined transmission queue requires one forward transmission and one return transmission. Figure 6 As shown, the arrows indicate the reverse direction of transmission. The circuit requires a total of four quantum direct transmissions. P1 first transmits the quantum state of q1 to P2, which then transmits the target bit state after executing gate G10 back to P1. Similarly, P2 transmits the control bit state of gate G7 to P1, which then transmits the control bit state of gate G12 back to P2. Therefore, the circuit transmission cost is 4.

[0069] like Figure 7As shown, since the state of the quantum bit q1 transmitted by the first transmission queue is the ground state, there is no need to transmit the quantum state of q1. The ground state of the quantum bit temporarily stored in the P2 partition is directly used to reconstruct the gates in the queue, so the forward transmission to the P2 partition is omitted. After P2 executes the seven quantum gates G1, G2, G3, G4, G5, G6, and G10, since the control bit state of the subsequent G7 gate on q1 is determined by the target bit of the G10 gate on q1, it is necessary to transmit the target bit state of the G10 gate back to the P1 partition in the P2 partition, consuming a transmission cost. Similarly, the forward transmission and return transmission of the second transmission queue are optimized. Since the state of the transmitted quantum bit q4 is determined by the control bit of the G9 gate, the P2 partition needs to forward the control bit state of the G9 gate to the P1 partition. After the P1 partition executes the four gates G7, T, G11, and G12, no other gates need to use the quantum state of q4, so there is no need to return it, and it can be measured directly in the P1 partition. So far, Figure 7 The distributed line shown in the figure is executed, requiring a total of one forward transmission and one return transmission, with a transmission cost of 2.

[0070] Based on the quantum bit storage model, the transmission cost of this line was optimized, reducing it from 4 times to 2 times, a significant improvement. Subsequently, genetic algorithms will be used to change the distributed line partitioning method, striving to find a transmission strategy with the lowest transmission cost.

[0071] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A transmission cost optimization method based on quantum bit storage, characterized in that: The following steps are involved: S1. Establish storage model: Based on the use of quantum direct transmission as the communication protocol for distributed quantum computing, the overhead of storing qubits is considered; storage qubits are divided into direct storage qubits and temporary storage qubits. Direct storage qubits are used to store the qubits of local gates or global gates in a certain partition. The number of direct storage qubits is determined by the size of the circuit. The larger the circuit, the more direct storage qubits are required. After a quantum state is transmitted through direct transmission, a new qubit is required to receive and store this quantum state. This qubit is temporary and continues to repeatedly store the qubit of the next direct transmission. In each partition, one or more qubits are required to temporarily store the qubit transmitted from another partition. This qubit is called a temporary storage qubit. The number of temporary storage qubits directly affects the transmission cost of the distributed circuit. The more temporary storage qubits, the lower the transmission cost of the circuit. S2. Build a cross-gate merge transmission model: Based on the storage model of temporary storage bits in S1, it is represented in the logic circuit that each partition has a temporary storage bit, qa0 and qa1 are both temporary storage qubits, where qa0 is the temporary storage qubit of the P1 partition, and qa1 is the temporary storage qubit of the P2 partition; there is only one temporary storage bit in each of the P1 and P2 partitions, the P1 partition qubit is transmitted to the P2 partition and stored in the temporary storage qubit qa1, and the P2 partition qubit is transmitted to the P1 partition and stored in the temporary storage qubit qa0; S3. Transmission cost optimization algorithm based on distributed quantum circuit storage model: including the following steps: Step 1: Based on the transmission queue list of the previous optimization results, the quantum bit of the quantum state transmitted by each transmission queue is obtained; Step 2: Starting from the first transmission queue, traverse all transmission queues and determine whether the number of forward transmissions can be reduced based on the state of the transmitted qubits; Step 3: Then traverse all the gates of the transmission queue backward to determine whether there are other gates on the qubit. If there are no other gates, the backhaul is allowed to be reduced. Step 4: Finally, the forward and return status codes of each transmission queue are returned. 0 indicates no transmission is required, and 1 indicates transmission is required. The total transmission cost of this distributed line is calculated. The quantum state is transmitted from the P1 partition to the P2 partition. This process is forward transmission, called forward transmission. The quantum state is transferred from the P1 partition to the P2 partition, and then transferred back to the P1 partition after the P2 operation is completed. This process is called backtransmission.

2. The transmission cost optimization method based on quantum bit storage according to claim 1, characterized in that: In S1, the number of directly stored qubits minimized by each distributed subsystem is shown in the following formula (1): Here, k represents the number of partitions, and n represents the total number of initial circuit qubits.

3. The transmission cost optimization method based on quantum bit storage according to claim 1, characterized in that: In S1, the number of temporarily stored qubits of each distributed subsystem is set to 1, which is the minimum. At this time, the qubit overhead of each distributed subsystem is minimized, and the number of qubits occupied by the partition is shown in the following formula (2):

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