Reducing Depth and Measurement Weights in Pauli-based Computation

• URL: http://arxiv.org/abs/2408.04007v1
• Date: Wed, 7 Aug 2024 18:00:11 GMT
• Title: Reducing Depth and Measurement Weights in Pauli-based Computation
• Authors: Filipa C. R. Peres, Ernesto F. Galvão,
• Abstract summary: Pauli-based computation (PBC) is a universal measurement-based quantum computation model steered by an adaptive sequence of independent and compatible Pauli measurements on magic-state qubits. Here, we propose several new ways of decreasing the weight of the Pauli measurements and their associated textsccnot complexity. We also demonstrate how to reduce this model's computational depth.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Pauli-based computation (PBC) is a universal measurement-based quantum computation model steered by an adaptive sequence of independent and compatible Pauli measurements on separable magic-state qubits. Here, we propose several new ways of decreasing the weight of the Pauli measurements and their associated \textsc{cnot} complexity; we also demonstrate how to reduce this model's computational depth. Inspired by known state-transfer methods, we introduce incPBC, a universal model for quantum computation requiring a larger number of (now incompatible) Pauli measurements of weight at most 2. For usual PBC, we prove new upper bounds on the required weights and computational depth, obtained via a pre-compilation step. We also propose a heuristic algorithm that can contribute reductions of over 30\% to the average weight of Pauli measurements (and associated \textsc{cnot} count) when simulating and compiling Clifford-dominated random quantum circuits with up to 22 $T$ gates and over 20\% for instances with larger $T$ counts.

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