The design of quantum circuits is often idealized, however, executing these circuits on quantum devices necessitates meeting the connectivity constraints imposed on physical devices by inserting SWAP gates. Various methods based on exact and heuristic solutions have been proposed to address the challenge of minimizing the degradation of quantum circuit performance due to factors such as circuit depth and the number of inserted SWAP gates while solving the qubit mapping problem. However, exact methods suffer from long runtime, lack of flexibility, and difficulty in scaling to larger circuits, while heuristic methods struggle to find the global optimum. Recently, solving the qubit mapping problem using machine learning approaches has emerged as a novel and promising solution. This paper studies qubit mapping optimization techniques based on machine learning, optimizing a model that solves the qubit mapping problem using the Deep Q-Network (DQN) algorithm, resulting in a SA-DQN model with superior performance in terms of circuit depth. The optimization efforts include improving the SWAP insertion strategy during the qubit mapping process and optimizing the model's initial mapping. Our SA-DQN model, tested on the IBM QX5 architecture and Rigetti 19Q Acorn architecture with a set of test circuits, achieved an improvement of 7.62% to 8.51% and 8.37% to 9.17% in circuit depth ratio compared to the original DQN model, respectively.
The design of quantum circuits is often idealized, however, executing these circuits on quantum devices necessitates meeting the connectivity constraints imposed on physical devices by inserting SWAP gates. Various methods based on exact and heuristic solutions have been proposed to address the challenge of minimizing the degradation of quantum circuit performance due to factors such as circuit depth and the number of inserted SWAP gates while solving the qubit mapping problem. However, exact methods suffer from long runtime, lack of flexibility, and difficulty in scaling to larger circuits, while heuristic methods struggle to find the global optimum. Recently, solving the qubit mapping problem using machine learning approaches has emerged as a novel and promising solution. This paper studies qubit mapping optimization techniques based on machine learning, optimizing a model that solves the qubit mapping problem using the Deep Q-Network (DQN) algorithm, resulting in a SA-DQN model with superior performance in terms of circuit depth. The optimization efforts include improving the SWAP insertion strategy during the qubit mapping process and optimizing the model's initial mapping. Our SA-DQN model, tested on the IBM QX5 architecture and Rigetti 19Q Acorn architecture with a set of test circuits, achieved an improvement of 7.62% to 8.51% and 8.37% to 9.17% in circuit depth ratio compared to the original DQN model, respectively.
Quantum circuit placement (QCP) is the process of mapping the synthesized logical quantum programs on physical quantum machines, which introduces additional SWAP gates and affects the performance of quantum circuits. Nevertheless, determining the minimal number of SWAP gates has been demonstrated to be an NP-complete problem. Various heuristic approaches have been proposed to address QCP, but they suffer from suboptimality due to the lack of exploration. Although exact approaches can achieve higher optimality, they are not scalable for large quantum circuits due to the massive design space and expensive runtime. By formulating QCP as a bilevel optimization problem, this paper proposes a novel machine learning (ML)-based framework to tackle this challenge. To address the lower-level combinatorial optimization problem, we adopt a policy-based deep reinforcement learning (DRL) algorithm with knowledge transfer to enable the generalization ability of our framework. An evolutionary algorithm is then deployed to solve the upper-level discrete search problem, which optimizes the initial mapping with a lower SWAP cost. The proposed ML-based approach provides a new paradigm to overcome the drawbacks in both traditional heuristic and exact approaches while enabling the exploration of optimality-runtime trade-off. Compared with the leading heuristic approaches, our ML-based method significantly reduces the SWAP cost by up to 100%. In comparison with the leading exact search, our proposed algorithm achieves the same level of optimality while reducing the runtime cost by up to 40 times.
Rapid progress in the physical implementation of quantum computers gave birth to multiple recent quantum machines implemented with superconducting technology. In these NISQ machines, each qubit is physically connected to a bounded number of neighbors. This limitation prevents most quantum programs from being directly executed on quantum devices. A compiler is required for converting a quantum program to a hardware-compliant circuit, in particular, making each two-qubit gate executable by mapping the two logical qubits to two physical qubits with a link between them. To solve this problem, existing studies focus on inserting SWAP gates to dynamically remap logical qubits to physical qubits. However, most of the schemes lack the consideration of time-optimality of generated quantum circuits, or are achieving time-optimality with certain constraints. In this work, we propose a theoretically time-optimal SWAP insertion scheme for the qubit mapping problem. Our model can also be extended to practical heuristic algorithms. We present exact analysis results by using our model for quantum programs with recurring execution patterns. We have for the first time discovered an optimal qubit mapping pattern for quantum fourier transformation (QFT) on 2D nearest neighbor architecture. We also present a scalable extension of our theoretical model that can be used to solve qubit mapping for large quantum circuits.
Quantum computing has already demonstrated great computational potential across multiple domains and has received more and more attention. However, due to the connectivity limitations of Noisy Intermediate-Scale Quantum (NISQ) devices, most of the quantum algorithms cannot be directly executed without the help of inserting SWAP gates. Nevertheless, more SWAP gates lead to a longer execution time and, inevitably, lower fidelity of the algorithm. To this end, this paper proposes an optimized qubit mapping algorithm based on a dynamic look-ahead strategy to minimize the number of SWAP gates inserted. Firstly, a heuristic algorithm is proposed based on maximizing physical qubit connectivity to generate the optimal initial qubit mapping, which reduces the need for logical qubit shifts during subsequent SWAP gate insertion. Secondly, in the form of directed acyclic graphs, we identify quantum gates that violate the constraints of physical coupling and insert SWAP gates to remap qubits, thereby overcoming the limitations of qubit interactions. Finally, the optimal SWAP gate insertion strategy is built by comparing the cost of different SWAP gate insertion strategies through a multi-window look-ahead strategy to reduce the number of SWAP gates inserted. The experimental results show that the strategy in this paper decreases the number of SWAP gate insertions and significantly reduces the depth of quantum circuits when performing qubit mapping compared with state-of-the-art methods.
The design of quantum algorithms typically assumes the availability of an ideal quantum computer, characterized by full connectivity, noiseless operation, and unlimited coherence time. However, Noisy Intermediate-Scale Quantum (NISQ) devices present a stark contrast, with a limited number of qubits, non-negligible quantum operation errors, and stringent constraints on the connectivity of physical qubits within a Quantum Processing Unit (QPU). This necessitates the dynamic remapping of logical qubits to physical qubits within the compiler to facilitate the execution of two-qubit gates in the algorithm. However, this introduces additional operations, consequently reducing the fidelity of the algorithm. Therefore, minimizing the number of added gates becomes crucial. Finding such an optimal routing problem is NP-hard, and the task is conventionally addressed using human-crafted heuristics to search for SWAP sequences, but these lack performance guarantees. In this study, we employ a Seq2Seq machine learning model for the qubit routing task, incorporating a Transformer neural network to learn the routing information in the gate and SWAP sequence. Compared to heuristic search-based algorithms, our approach significantly reduces the overhead of quantum computing resources required to adapt logical circuits to physical circuits executable on specific quantum backend hardware.
The rapid progress of physical implementation of quantum computers paved the way of realising the design of tools to help users write quantum programs for any given quantum devices. The physical constraints inherent to the current NISQ architectures prevent most quantum algorithms from being directly executed on quantum devices. To enable two-qubit gates in the algorithm, existing works focus on inserting SWAP gates to dynamically remap logical qubits to physical qubits. However, their schemes lack the consideration of the depth of generated quantum circuits. In this work, we propose a depth-aware SWAP insertion scheme for qubit mapping problem in the NISQ era.
Quantum circuit mapping is a critical process in quantum computing that involves adapting logical quantum circuits to adhere to hardware constraints, thereby generating physically executable quantum circuits. Current quantum circuit mapping techniques, such as solver-based methods, often encounter challenges related to slow solving speeds due to factors like redundant search iterations. Regarding this issue, we propose a machine learning approach for accelerating optimal qubit mapping (MLQM). First, the method proposes a global search space pruning scheme based on prior knowledge and machine learning, which in turn improves the solution efficiency. Second, to address the limited availability of effective samples in the learning task, MLQM introduces a novel data augmentation and refinement scheme, this scheme enhances the size and diversity of the quantum circuit dataset by exploiting gate allocation and qubit rearrangement. Finally, MLQM also further improves the solution efficiency by pruning the local search space, which is achieved through an adaptive dynamic adjustment mechanism of the solver variables. Compared to state-of-the-art qubit mapping approaches, MLQM achieves optimal qubit mapping with an average solving speed-up ratio of 1.79 and demonstrates an average advantage of 22% in terms of space complexity.