Quantum circuit synthesis using Householder transformations
arXiv:2004.07710 · doi:10.1016/j.cpc.2019.107001
Abstract
The synthesis of a quantum circuit consists in decomposing a unitary matrix into a series of elementary operations. In this paper, we propose a circuit synthesis method based on the QR factorization via Householder transformations. We provide a two-step algorithm: during the first step we exploit the specific structure of a quantum operator to compute its QR factorization, then the factorized matrix is used to produce a quantum circuit. We analyze several costs (circuit size and computational time) and compare them to existing techniques from the literature. For a final quantum circuit twice as large as the one obtained by the best existing method, we accelerate the computation by orders of magnitude.
31 pages, preprint
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- Quantum Circuits for Sparse Isometries
- T-count and T-depth of any multi-qubit unitary
- Numerical analysis of quantum circuits for state preparation and unitary operator synthesis
- A (quasi-)polynomial time heuristic algorithm for synthesizing T-depth optimal circuits
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