Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian circuits
Journal article, 2022

We study the classical simulatability of Gottesman-Kitaev-Preskill (GKP) states in combination with arbitrary displacements, a large set of symplectic operations and homodyne measurements. For these types of circuits, neither continuous-variable theorems based on the non-negativity of quasi-probability distributions nor discrete-variable theorems such as the Gottesman-Knill theorem can be employed to assess the simulatability. We first develop a method to evaluate the probability density function corresponding to measuring a single GKP state in the position basis following arbitrary squeezing and a large set of rotations. This method involves evaluating a transformed Jacobi theta function using techniques from analytic number theory. We then use this result to identify two large classes of multimode circuits which are classically efficiently simulatable and are not contained by the GKP encoded Clifford group. Our results extend the set of circuits previously known to be classically efficiently simulatable.

quantum computing

Author

Cameron Calcluth

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

Alessandro Ferraro

University of Milan

Queen's University Belfast

Giulia Ferrini

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

Quantum

2521327X (eISSN)

Vol. 6 867-

Subject Categories

Atom and Molecular Physics and Optics

DOI

10.22331/Q-2022-12-01-867

More information

Latest update

4/21/2023