Automatic Depth-Optimized Quantum Circuit Synthesis for Diagonal Unitary Matrices with Asymptotically Optimal Gate Count
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arXiv
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| Format: | Preprint |
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2022
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| author | Zhang, Shihao Huang, Kai Li, Lvzhou |
| author_facet | Zhang, Shihao Huang, Kai Li, Lvzhou |
| contents | Current noisy intermediate-scale quantum (NISQ) devices can only execute small circuits with shallow depth, as they are still constrained by the presence of noise: quantum gates have error rates and quantum states are fragile due to decoherence. Hence, it is of great importance to optimize the depth/gate-count when designing quantum circuits for specific tasks. Diagonal unitary matrices are well-known to be key building blocks of many quantum algorithms or quantum computing procedures. Prior work has discussed the synthesis of diagonal unitary matrices over the primitive gate set $\{\text{CNOT}, R_Z\}$. However, the problem has not yet been fully understood, since the existing synthesis methods have not optimized the circuit depth.
In this paper, we propose a depth-optimized synthesis algorithm that automatically produces a quantum circuit for any given diagonal unitary matrix. Specially, it not only ensures the asymptotically optimal gate-count, but also nearly halves the total circuit depth compared with the previous method. Technically, we discover a uniform circuit rewriting rule well-suited for reducing the circuit depth. The performance of our synthesis algorithm is both theoretically analyzed and experimentally validated by evaluations on two examples. First, we achieve a nearly 50\% depth reduction over Welch's method for synthesizing random diagonal unitary matrices with up to 16 qubits. Second, we achieve an average of 22.05\% depth reduction for resynthesizing the diagonal part of specific quantum approximate optimization algorithm (QAOA) circuits with up to 14 qubits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_01002 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Automatic Depth-Optimized Quantum Circuit Synthesis for Diagonal Unitary Matrices with Asymptotically Optimal Gate Count Zhang, Shihao Huang, Kai Li, Lvzhou Quantum Physics Current noisy intermediate-scale quantum (NISQ) devices can only execute small circuits with shallow depth, as they are still constrained by the presence of noise: quantum gates have error rates and quantum states are fragile due to decoherence. Hence, it is of great importance to optimize the depth/gate-count when designing quantum circuits for specific tasks. Diagonal unitary matrices are well-known to be key building blocks of many quantum algorithms or quantum computing procedures. Prior work has discussed the synthesis of diagonal unitary matrices over the primitive gate set $\{\text{CNOT}, R_Z\}$. However, the problem has not yet been fully understood, since the existing synthesis methods have not optimized the circuit depth. In this paper, we propose a depth-optimized synthesis algorithm that automatically produces a quantum circuit for any given diagonal unitary matrix. Specially, it not only ensures the asymptotically optimal gate-count, but also nearly halves the total circuit depth compared with the previous method. Technically, we discover a uniform circuit rewriting rule well-suited for reducing the circuit depth. The performance of our synthesis algorithm is both theoretically analyzed and experimentally validated by evaluations on two examples. First, we achieve a nearly 50\% depth reduction over Welch's method for synthesizing random diagonal unitary matrices with up to 16 qubits. Second, we achieve an average of 22.05\% depth reduction for resynthesizing the diagonal part of specific quantum approximate optimization algorithm (QAOA) circuits with up to 14 qubits. |
| title | Automatic Depth-Optimized Quantum Circuit Synthesis for Diagonal Unitary Matrices with Asymptotically Optimal Gate Count |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2212.01002 |