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.
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.
The rapid progress of physical implementation of quantum computers paved the way for the design of tools to help users write quantum programs for any given quantum device. The physical constraints inherent in 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 consideration of the execution time of generated quantum circuits. In this work, we propose a slack-aware SWAP insertion scheme for the qubit mapping problem in the NISQ era. Our experiments show performance improvement by up to 2.36X at maximum, by 1.62X on average, over 106 representative benchmarks from RevLib, IBM Qiskit , and ScaffCC.
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.
Due to little considerations in the hardware constraints, e.g., limited connections between physical qubits to enable two-qubit gates, most quantum algorithms cannot be directly executed on the Noisy Intermediate-Scale Quantum (NISQ) devices. Dynamically remapping logical qubits to physical qubits in the compiler is needed to enable the two-qubit gates in the algorithm, which introduces additional operations and inevitably reduces the fidelity of the algorithm. Previous solutions in finding such remapping suffer from high complexity, poor initial mapping quality, and limited flexibility and control. To address these drawbacks mentioned above, this paper proposes a SWAP-based Bidirectional heuristic search algorithm (SABRE), which is applicable to NISQ devices with arbitrary connections between qubits. By optimizing every search attempt, globally optimizing the initial mapping using a novel reverse traversal technique, introducing the decay effect to enable the trade-off between the depth and the number of gates of the entire algorithm, SABRE outperforms the best known algorithm with exponential speedup and comparable or better results on various benchmarks.
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.
In recent years, the emergence of the Noisy Intermediate-Scale Quantum (NISQ) era has led to the development of a wide variety of quantum devices, marking a dynamic phase in the field of quantum computing. Despite these advancements, practical applications of quantum computers still face significant challenges, one of the most prominent being the limited connectivity between physical quantum bits (qubits). This limitation requires quantum circuits to be recompiled through layout synthesis before they can be executed on quantum devices. Layout synthesis determines the specific placement of quantum gates within the circuit on the physical hardware. When gates do not align with the connectivity constraints of the device, additional quantum gates must be inserted to remap the qubits, which can negatively affect the circuit’s efficiency and performance. To address this issue, the primary goal of this paper is to enhance the mapping process within layout synthesis, aiming to optimize both the layout and the circuit depth. Experimental results demonstrate that the proposed method effectively reduces the quantum circuit depth, outperforming other existing approaches in terms of efficiency.