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Algorithm-Aware Qubit Mapping

Yanjun Ji, Ilia Polian

Published Sep 11, 2023• 0 citations
Publisher

Abstract

Algorithm-aware (AlgAw) qubit mapping aims at directly providing the solutions to qubit mapping of algorithms with regular structures based on the algorithm’s features. Although exact methods can provide high quality solutions, their compilation time grows exponentially with circuit size. To improve scalability, we propose the AlgAw qubit mapping approach. The main idea is to first identify subcircuits in an algorithm to be mapped, then analyze optimal solutions for small scale subcircuits found by exact methods, extend these solutions to large scale subcircuits, reconstruct the entire circuit and assign parameters, and finally map pretranspiled circuits onto the target quantum devices. Applying AlgAw to the quantum approximate optimization algorithm (QAOA) on linear and T-shaped subtopologies produces optimal and scalable solutions for arbitrary numbers of qubits and depths, which is critical to the algorithm’s performance on near-term quantum devices. Compared to other methods including Qiskit, Tket, and SWAP-network, AlgAw produces the least number of CNOT gates and the lowest circuit depth for the pretranspiled circuits. Furthermore, AlgAw takes only a few seconds to construct a resulting circuit having a hundred qubits. The benchmarking results on IBM quantum devices show that AlgAw qubit mapping yields better performance than others. AlgAw is applicable to other variational quantum algorithms (VQAs) and can also be applied to other algorithms.

DOI
10.36227/techrxiv.21786146.v2

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Algorithm-Aware Qubit Mapping

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Algorithm-aware (AlgAw) qubit mapping aims at directly providing the solutions to qubit mapping of algorithms with regular structures based on the algorithm's features. Although exact methods can provide high quality solutions, their compilation time grows exponentially with circuit size. To improve scalability, we propose the AlgAw qubit mapping approach. The main idea is to first identify subcircuits in an algorithm to be mapped, then analyze optimal solutions for small scale subcircuits found by exact methods, extend these solutions to large scale subcircuits, reconstruct the entire circuit and assign parameters, and finally map pretranspiled circuits onto the target quantum devices. Applying AlgAw to the quantum approximate optimization algorithm (QAOA) on linear and T-shaped subtopologies produces optimal and scalable solutions for arbitrary numbers of qubits and depths, which is critical to the algorithm's performance on near-term quantum devices. Compared to other methods including Qiskit, Tket, and SWAP-network, AlgAw produces the least number of CNOT gates and the lowest circuit depth for the pretranspiled circuits. Furthermore, AlgAw takes only a few seconds to construct a resulting circuit having a hundred qubits. The benchmarking results on IBM quantum devices show that AlgAw qubit mapping yields better performance than others. AlgAw is applicable to other variational quantum algorithms (VQAs) and can also be applied to other algorithms.

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Algorithm-aware (AlgAw) qubit mapping aims at directly providing the solutions to qubit mapping of algorithms with regular structures based on the algorithm’s features. Although exact methods can provide high quality solutions, their compilation time grows exponentially with circuit size. To improve scalability, we propose the AlgAw qubit mapping approach. The main idea is to first identify subcircuits in an algorithm to be mapped, then analyze optimal solutions for small scale subcircuits found by exact methods, extend these solutions to large scale subcircuits, reconstruct the entire circuit and assign parameters, and finally map pretranspiled circuits onto the target quantum devices. Applying AlgAw to the quantum approximate optimization algorithm (QAOA) on linear and T-shaped subtopologies produces optimal and scalable solutions for arbitrary numbers of qubits and depths, which is critical to the algorithm’s performance on near-term quantum devices. Compared to other methods including Qiskit, Tket, and SWAP-network, AlgAw produces the least number of CNOT gates and the lowest circuit depth for the pretranspiled circuits. Furthermore, AlgAw takes only a few seconds to construct a resulting circuit having a hundred qubits. The benchmarking results on IBM quantum devices show that AlgAw qubit mapping yields better performance than others. AlgAw is applicable to other variational quantum algorithms (VQAs) and can also be applied to other algorithms.
Algorithm-aware (AlgAw) qubit mapping aims at directly providing the solutions to qubit mapping of algorithms with regular structures based on the algorithm's features. Although exact methods can provide high quality solutions, their compilation time grows exponentially with circuit size. To improve scalability, we propose the AlgAw qubit mapping approach. The main idea is to first identify subcircuits in an algorithm to be mapped, then analyze optimal solutions for small scale subcircuits found by exact methods, extend these solutions to large scale subcircuits, reconstruct the entire circuit and assign parameters, and finally map pretranspiled circuits onto the target quantum devices. Applying AlgAw to the quantum approximate optimization algorithm (QAOA) on linear and T-shaped subtopologies produces optimal and scalable solutions for arbitrary numbers of qubits and depths, which is critical to the algorithm's performance on near-term quantum devices. Compared to other methods including Qiskit, Tket, and SWAP-network, AlgAw produces the least number of CNOT gates and the lowest circuit depth for the pretranspiled circuits. Furthermore, AlgAw takes only a few seconds to construct a resulting circuit having a hundred qubits. The benchmarking results on IBM quantum devices show that AlgAw qubit mapping yields better performance than others. AlgAw is applicable to other variational quantum algorithms (VQAs) and can also be applied to other algorithms.
Algorithm-Aware (AlgAw) qubit mapping aims at directly providing the solutions to qubit mapping of algorithms with regular structures based on the algorithm’s features. Although the exact method provides a high-quality solution, its compilation time grows exponentially with the circuit size. To improve its scalability, we propose the AlgAw qubit mapping. The main idea is to first determine the subcircuits in an algorithm to be mapped, then analyze the optimal solutions of small-scale subcircuits found by exact methods to obtain solutions of large-scale subcircuits, and finally reconstruct the entire circuit and assign parameters. Applying AlgAw to the Quantum Approximate Optimization Algorithm (QAOA) on linear and T-shaped subtopologies produces optimal and scalable solutions for arbitrary numbers of qubits and depths, which is critical to the algorithm’s performance on Noisy Intermediate-Scale Quantum (NISQ) computers. Compared to Qiskit, Tket, and SWAP-Network, AlgAw produces the least number of CNOT gates and the lowest circuit depth. Furthermore, AlgAw takes only a few seconds to obtain a circuit with a hundred qubits that satisfies the connectivity constraints. The benchmarking results on Quantum Processing Units (QPUs) show that AlgAw qubit mapping yields higher values of approximation ratio than others. AlgAw can also be applied to other algorithms such as the Variational Quantum Eigensolver (VQE).
We propose a scalable, hierarchical qubit mapping and routing algorithm that harnesses the power of circuit synthesis. First, we decompose large circuits into subcircuits small enough to be directly resynthesized. For each block, we pre-synthesize them for all permutations of its input and output qubits. Following this offline step, we employ a permutation-aware, block-based generalization of the popular SABRE mapping algorithm. This mapping step stitches together blocks by choosing an input-output permutation that minimizes intrablock gate count and required inter-block communication (SWAP and bridge gates). Our approach has a twofold advantage: 1) circuit synthesis may eliminate more two-qubit gates than other optimizing compilers; 2) considering all permutations of input and output qubits eliminates communication operations transparently. In contrast, other mapping algorithms can only introduce communication operations. We show that we can produce better-quality circuits than commercial compilers: shorter by up to 68% (18% on average) fewer gates than Qiskit, up to 36% (9% on average) fewer gates than Tket. We outperform BQSkit, a permutation-unaware, synthesis-based compiler, by up to 67% (21% on average) fewer gates. We also exceed experimental optimal mappers such as OLSQ in quality (10.7% shorter circuits) and time to solution. Our scalable, heuristic approach can be seamlessly integrated into any quantum circuit compiler or optimization infrastructure, and it applies well to any qubit technology, such as superconducting and trapped ions.
Variational algorithms are among the first practical applications of quantum computing, but their performance is limited by today's noisy intermediate-scale quantum (NISQ) devices. The authors propose scalable, depth-optimal solutions to overcome these limitations by integrating optimal mapping algorithms applied to small submodules of a given NISQ computer (focusing on popular linear and T- and H-shaped subtopologies). Identification of the best qubits combined with postselection keeps the error rate in check. The team reports up to 82% reduction in circuit depth and an average of 138% better success probability, thus paving the way for reliable quantum computing ecosystems of tomorrow.
Quantum Approximation Optimization Algorithm (QAOA) is a highly advocated variational algorithm for solving the combinatorial optimization problem. One critical feature in the quantum circuit of QAOA algorithm is that it consists of two-qubit operators that commute. The flexibility in reordering the two-qubit gates allows compiler optimizations to generate circuits with better depths, gate count, and fidelity. However, it also imposes significant challenges due to additional freedom exposed in the compilation. Prior studies lack the following: (1) Performance guarantee, (2) Scalability, and (3) Awareness of regularity in scalable hardware. We propose a structured method that ensures linear depth for any compiled QAOA circuit on multi-dimensional quantum architectures. We also demonstrate how our method runs on Google Sycamore and IBM Non-linear architectures in a scalable manner and in linear time. Overall, we can compile a circuit with up to 1024 qubits in 10 seconds with a 3.8X speedup in depth, 17% reduction in gate count, and 18X improvement for circuit ESP.
Effective qubit mapping facilitates quantum algorithm implementations in physical quantum computing architectures. Recent work reported promising qubit mapping on one-dimensional trapped-ion systems. Due to manufacturing complexity, however, it is insufficient to map all logical qubits into one single qubit array in a large-scale quantum circuit; instead, we shall divide a quantum circuit into subcircuits for extending to two-dimensional trapped-ion systems. Nevertheless, operating a two-qubit gate between different subcircuits reduces the circuit fidelity. As a result, it is desirable to develop an effective partitioning algorithm that can maintain fidelity and minimize the execution time. This paper develops an effective divide-and-conquer algorithm for each array. Unlike traditional min-cut partitioning to balance the qubit number on each array, we propose a depth-aware partitioning algorithm to expand the solution space for all mapping solutions and optimize the execution time on each array. Besides, we develop a satisfiability modulo theories-based algorithm to optimize the mapping solution for each array. Experimental results show that our algorithm can averagely achieve a 14% total time step reduction and a 30% total fidelity improvement for commonly used benchmarks.