$T$-depth-optimized Quantum Search with Quantum Data-access Machine

• URL: http://arxiv.org/abs/2211.03941v2
• Date: Thu, 2 Nov 2023 23:37:42 GMT
• Title: $T$-depth-optimized Quantum Search with Quantum Data-access Machine
• Authors: Jung Jun Park, Kyunghyun Baek, M. S. Kim, Hyunchul Nha, Jaewan Kim, and Jeongho Bang
• Abstract summary: We introduce an efficient quantum data-access process, dubbed as quantum data-access machine (QDAM) We analyze the runtime of our algorithm in view of the fault-tolerant quantum computation (FTQC) consisting of logical qubits within an effective quantum error correction code.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Quantum search algorithms offer a remarkable advantage of quadratic reduction in query complexity using quantum superposition principle. However, how an actual architecture may access and handle the database in a quantum superposed state has been largely unexplored so far; the quantum state of data was simply assumed to be prepared and accessed by a black-box operation -- so-called oracle, even though this process, if not appropriately designed, may adversely diminish the quantum query advantage. Here, we introduce an efficient quantum data-access process, dubbed as quantum data-access machine (QDAM), and present a general architecture for quantum search algorithm. We analyze the runtime of our algorithm in view of the fault-tolerant quantum computation (FTQC) consisting of logical qubits within an effective quantum error correction code. Specifically, we introduce a measure involving two computational complexities, i.e. quantum query and $T$-depth complexities, which can be critical to assess performance since the logical non-Clifford gates, such as the $T$ (i.e., $\pi/8$ rotation) gate, are known to be costliest to implement in FTQC. Our analysis shows that for $N$ searching data, a QDAM model exhibiting a logarithmic, i.e., $O(\log{N})$, growth of the $T$-depth complexity can be constructed. Further analysis reveals that our QDAM-embedded quantum search requires $O(\sqrt{N} \times \log{N})$ runtime cost. Our study thus demonstrates that the quantum data search algorithm can truly speed up over classical approaches with the logarithmic $T$-depth QDAM as a key component.

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