The Art of Optimizing T-Depth for Quantum Error Correction in Large-Scale Quantum Computing
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916650193780736 |
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| author | Chatterjee, Avimita Ghosh, Archisman Ghosh, Swaroop |
| author_facet | Chatterjee, Avimita Ghosh, Archisman Ghosh, Swaroop |
| contents | Quantum Error Correction (QEC), combined with magic state distillation, ensures fault tolerance in large-scale quantum computation. To apply QEC, a circuit must first be transformed into a non-Clifford (or T) gate set. T-depth, the number of sequential T-gate layers, determines the magic state cost, impacting both spatial and temporal overhead. Minimizing T-depth is crucial for optimizing resource efficiency in fault-tolerant quantum computing. While QEC scalability has been widely studied, T-depth reduction remains an overlooked challenge. We establish that T-depth reduction is an NP-hard problem and systematically evaluate multiple approximation techniques: greedy, divide-and-conquer, Lookahead-based brute force, and graph-based. The Lookahead-based brute-force algorithm (partition size 4) performs best, optimizing 90\% of reducible cases (i.e., circuits where at least one algorithm achieved optimization) with an average T-depth reduction of around 51\%. Additionally, we introduce an expansion factor-based identity gate insertion strategy, leveraging controlled redundancy to achieve deeper reductions in circuits initially classified as non-reducible. With this approach, we successfully convert up to 25\% of non-reducible circuits into reducible ones, while achieving an additional average reduction of up to 11.8\%. Furthermore, we analyze the impact of different expansion factor values and explore how varying the partition size in the Lookahead-based brute-force algorithm influences the quality of T-depth reduction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06045 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Art of Optimizing T-Depth for Quantum Error Correction in Large-Scale Quantum Computing Chatterjee, Avimita Ghosh, Archisman Ghosh, Swaroop Quantum Physics Quantum Error Correction (QEC), combined with magic state distillation, ensures fault tolerance in large-scale quantum computation. To apply QEC, a circuit must first be transformed into a non-Clifford (or T) gate set. T-depth, the number of sequential T-gate layers, determines the magic state cost, impacting both spatial and temporal overhead. Minimizing T-depth is crucial for optimizing resource efficiency in fault-tolerant quantum computing. While QEC scalability has been widely studied, T-depth reduction remains an overlooked challenge. We establish that T-depth reduction is an NP-hard problem and systematically evaluate multiple approximation techniques: greedy, divide-and-conquer, Lookahead-based brute force, and graph-based. The Lookahead-based brute-force algorithm (partition size 4) performs best, optimizing 90\% of reducible cases (i.e., circuits where at least one algorithm achieved optimization) with an average T-depth reduction of around 51\%. Additionally, we introduce an expansion factor-based identity gate insertion strategy, leveraging controlled redundancy to achieve deeper reductions in circuits initially classified as non-reducible. With this approach, we successfully convert up to 25\% of non-reducible circuits into reducible ones, while achieving an additional average reduction of up to 11.8\%. Furthermore, we analyze the impact of different expansion factor values and explore how varying the partition size in the Lookahead-based brute-force algorithm influences the quality of T-depth reduction. |
| title | The Art of Optimizing T-Depth for Quantum Error Correction in Large-Scale Quantum Computing |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2503.06045 |