Circuit complexity of quantum access models for encoding classical data

• URL: http://arxiv.org/abs/2311.11365v2
• Date: Mon, 29 Apr 2024 03:20:46 GMT
• Title: Circuit complexity of quantum access models for encoding classical data
• Authors: Xiao-Ming Zhang, Xiao Yuan,
• Abstract summary: We study the Clifford$+T$ complexity of constructing some typical quantum access models. We show that both sparse-access input models and block-encoding require nearly linear circuit complexities. Our protocols are built upon improved quantum state preparation and a selective oracle for Pauli strings.
• Score: 4.727325187683489
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Classical data encoding is usually treated as a black-box in the oracle-based quantum algorithms. On the other hand, their constructions are crucial for practical algorithm implementations. Here, we open the black-boxes of data encoding and study the Clifford$+T$ complexity of constructing some typical quantum access models. For general matrices, we show that both sparse-access input models and block-encoding require nearly linear circuit complexities relative to the matrix dimension, even if matrices are sparse. We also gives construction protocols achieving near-optimal gate complexities. On the other hand, the construction becomes efficient with respect to the data qubit when the matrix is the linear combination polynomial terms of efficient unitaries. As a typical example, we propose improved block encoding when these unitaries are Pauli strings. Our protocols are built upon improved quantum state preparation and a selective oracle for Pauli strings, which hold independent value. Our access model constructions offer considerable flexibility, allowing for tunable ancillary qubit number and offers corresponding space-time trade-offs.

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