Quantum Circuits for Sparse Isometries

Abstract

We consider the task of breaking down a quantum computation given as an isometry into C-NOTs and single-qubit gates, while keeping the number of C-NOT gates small. Although several decompositions are known for general isometries, here we focus on a method based on Householder reflections that adapts well in the case of sparse isometries. We show how to use this method to decompose an arbitrary isometry before illustrating that the method can lead to significant improvements in the case of sparse isometries. We also discuss the classical complexity of this method and illustrate its effectiveness in the case of sparse state preparation by applying it to randomly chosen sparse states.

arXiv comment12+3 pages, 1 figure. v2: minor changes. Methods introduced here have now been implemented in UniversalQCompiler, see https://github.com/Q-Compiler/UniversalQCompiler . Raw data used in the figure is available in the ancillary file

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