Binary Tree Block Encoding of Classical Matrix

doi:10.1109/TQE.2025.3624699

Binary Tree Block Encoding of Classical Matrix

2026-01-01

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张国锋 (Guofeng Zhang) *

DOI：10.1109/TQE.2025.3624699

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State preparation and block encoding are essential subroutines in quantum computing. The former provides basic encoding of quantum states, while the latter transforms classical data into a matrix representation within a quantum circuit. Some quantum advantages are built on the assumption that the block-encoding subroutine has been compiled in the quantum circuit, and this derives a problem of how to efficiently compile a block encoding. The resource tradeoffs of block encoding, such as circuit size, subnormalization factor, compilation complexity (both time and space), and robustness against errors, are central to its efficiency. In this work, the binary tree block-encoding (BIT-BLE) protocol is introduced, which optimizes these tradeoffs. For a classical matrix in C-2nx2n, our approach reduces the compilation time to O(n2(2n)) using n ancilla qubits, achieving superior resource tradeoffs compared to existing methods. Numerical experiments further reveal that the approach outlined in BITBLE enhances compilation efficiency, resource scalability, and robustness against singlequbit gate errors in various standard data encoding tasks. Moreover, all algorithms are available as open source.

Keywords:

Encoding

Protocols

Logic gates

Binary trees

Sparse matrices

Multiplexing

Qubit

Quantum circuit

Quantum state

Measurement

Circuit size

quantum circuit

quantum compiling

state preparation

unitary synthesis

Binary Tree Block Encoding of Classical Matrix

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