How to decompose arbitrary continuous-variable quantum operations

TL;DR

This paper introduces a systematic method for decomposing any exponential operator of bosonic mode operators into universal gates, facilitating continuous-variable quantum computation and other quantum state transformations.

Contribution

It provides a general, efficient decomposition scheme for multi-mode Hamiltonian evolutions into universal unitary gates, applicable across various quantum information processing tasks.

Findings

Decomposition scheme demonstrated for nonlinear Hamiltonians including Kerr interactions.

Potential experimental implementations with optical cubic states and homodyne detection.

Method applicable to quantum control, discrete-variable computation, and Hamiltonian simulation.

Abstract

We present a general, systematic, and efficient method for decomposing any given exponential operator of bosonic mode operators, describing an arbitrary multi-mode Hamiltonian evolution, into a set of universal unitary gates. Although our approach is mainly oriented towards continuous-variable quantum computation, it may be used more generally whenever quantum states are to be transformed deterministically, e.g. in quantum control, discrete-variable quantum computation, or Hamiltonian simulation. We illustrate our scheme by presenting decompositions for various nonlinear Hamiltonians including quartic Kerr interactions. Finally, we conclude with two potential experiments utilizing offline-prepared optical cubic states and homodyne detections, in which quantum information is processed optically or in an atomic memory using quadratic light-atom interactions.