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

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., π/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.