Displaced rotations of coherent states

TL;DR

This paper introduces a novel optical scheme for constructing rotations of coherent states, including the Hadamard gate, by using displaced number states and photon addition techniques, advancing quantum computation with coherent states.

Contribution

It presents a new method to generate and rotate coherent states and superpositions using photon additions and displacements, enabling quantum gates like the Hadamard for coherent state-based quantum computing.

Findings

High-fidelity approximation of even and odd displaced squeezed superpositions

Optical scheme's sensitivity to seed coherent state parameters

Construction of local rotation operators for coherent states

Abstract

We propose an approach that enables to use it for construction of rotations of coherent states, in particular, it gives a possibility to construct Hadamard gate for the coherent states. Our approach is based on representation of arbitrary one-mode pure state in free-travelling fields, in particular superposition of coherent states (SCSs), in terms of displaced number states with arbitrary amplitude of displacement. Studied optical scheme is based on alternation of photon additions and displacement operators (in general case, photon additions and displacements are required) with seed coherent state to generate both even and odd displaced squeezed SCSs (DSSCSs) regardless of number of used photon additions. It is shown the studied optical scheme is sensitive to seed coherent state provided that other parameters are invariable. Output states approximate with high fidelity either even squeezed SCS or odd SCS shifted relative each other by some value. It enables to construct local rotation operator for coherent states, in particular, Hadamard gate being mainframe element for quantum computation with coherent states. The effects deteriorating quality of output states are considered.