Fault-tolerant logical measurements via homological measurement

Abstract

We introduce homological measurement, a framework for measuring the logical Pauli operators encoded in CSS stabilizer codes. The framework is based on the algebraic description of such codes as chain complexes. Protocols such as lattice surgery some of its recent generalizations are shown to be special cases of homological measurement. Using this framework, we develop a specific protocol called edge expanded homological measurement for fault-tolerant measurement of arbitrary logical Pauli operators of general qLDPC codes, requiring a number of ancillary qubits growing only linearly with the weight of the logical operator measured, and guaranteed that the distance of the code is preserved. We further benchmark our protocol numerically in a photonic architecture based on GKP qubits, showing that the logical error rate of various codes are on par with other methods requiring more ancilla qubits.

20 pages, 5 figures, 5 tables. Version 2 fixes a mistake in section 3.4 and briefly addresses related recent work

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Cited by in corpus (7)

• Magic tricycles: Efficient magic state generation with finite block-length quantum LDPC codes
• Parallel Logical Measurements via Quantum Code Surgery
• Accelerating Fault-Tolerant Quantum Computation with Good qLDPC Codes
• Color code with a logical control-$S$ gate using transversal $T$ rotations
• Wire Codes
• Universal fault tolerant quantum computation in 2D without getting tied in knots
• Unified Framework for Quantum Code Embedding