Optimal compression with quantum retrieval

2026-10-05

AI Summary

This study addresses the problem of achieving optimal lossless compression and efficient bit retrieval for high Hamming weight strings within the quantum query model. To balance storage space and retrieval efficiency, this work proposes adaptive and non-adaptive quantum query mechanisms built upon Quantum Random Access Codes (QRACs) and standard oracle encodings. The adaptive scheme attains an optimal compression rate up to a logarithmic factor, while the non-adaptive scheme achieves near-optimality with respect to parameter m, degrading by at most a quadratic factor in n. By realizing compression rates that approach theoretical limits, this research significantly optimizes both the space complexity and query performance of quantum data retrieval.

Abstract

We consider the following data compression problem. Given a string $x \in \{0,1\}^m$ of Hamming weight at most $n$, compress it into a shorter string $y \in \{0,1\}^s$ so that any bit $x_i$ of $x$ can be retrieved without any error using at most $t$ quantum queries to the standard oracle encoding of $y$. If queries are allowed to be adaptive we show how optimal compression up to a logarithmic factor can be achieved. If the queries are required to be made non-adaptively, we show schemes whose space is optimal in its dependence on $m$ except for a logarithmic factor, and is at most quadratically worse when compared to the optimum in its dependence on $n$.

Problem

• data compression
• quantum retrieval
• quantum queries
• Hamming weight

Innovation

• quantum retrieval
• data compression
• adaptive queries
• non-adaptive queries
• Hamming weight