[Paper Review] Unconditional measurement-based quantum computation with optomechanical continuous variables

Oussama Houhou, Darren W. Moore+2 more|arXiv (Cornell University)|Sep 25, 2018

Mechanical and Optical Resonators4 citations

TL;DR

This paper proposes a deterministic, unconditional approach to continuous-variable measurement-based quantum computation using optomechanical systems with integrated linear and quadratic optomechanical couplings. By leveraging driven-dissipative dynamics in cavity optomechanical platforms, the authors demonstrate the deterministic preparation of non-Gaussian cluster states—including cubic-phase states—and show that arbitrary Gaussian measurements can be performed via continuous output field monitoring, enabling universal quantum computation with current technological feasibility.

ABSTRACT

Universal quantum computation encoded over continuous variables can be achieved via Gaussian measurements acting on entangled non-Gaussian states. However, due to the weakness of available nonlinearities, generally these states can only be prepared conditionally, potentially with low probability. Here we show how universal quantum computation could be implemented unconditionally using an integrated platform able to sustain both linear and quadratic optomechanical-like interactions. Specifically, considering cavity opto- and electro-mechanical systems, we propose a realisation of a driven-dissipative dynamics that deterministically prepares the required non-Gaussian cluster states -- entangled squeezed states of multiple mechanical oscillators suitably interspersed with cubic-phase states. We next demonstrate how arbitrary Gaussian measurements on the cluster nodes can be performed by continuously monitoring the output cavity field. Finally, the feasibility requirements of this approach are analysed in detail, suggesting that its building blocks are within reach of current technology.

Motivation & Objective

• To overcome the major roadblock of probabilistic non-Gaussian state preparation in continuous-variable quantum computation.
• To enable universal quantum computation with continuous variables using only Gaussian operations and deterministic state preparation.
• To demonstrate that optomechanical systems with quadratic optomechanical coupling can serve as a scalable, integrated platform for universal measurement-based quantum computation.
• To show that both non-Gaussian cluster states and Gaussian measurements can be implemented unconditionally via dissipative engineering and continuous monitoring.
• To establish feasibility by analyzing realistic parameters and showing high fidelity even under thermal noise and finite squeezing.

Proposed method

• Utilizes a driven-dissipative optomechanical system with time-dependent multi-tone classical driving to engineer effective nonlinear dynamics.
• Employs adiabatic elimination of the cavity mode to derive an effective master equation governing the mechanical oscillators' dynamics.
• Designs a dissipative protocol that prepares a non-Gaussian cluster state as a steady state, including entangled squeezed states and cubic-phase states.
• Uses continuous monitoring of the output cavity field to perform arbitrary Gaussian measurements on the cluster nodes.
• Applies a switching protocol to dynamically control the optomechanical couplings and steer the system toward the target non-Gaussian resource state.
• Validates the scheme via numerical simulations using truncated Fock basis, with fidelity analysis under thermal noise and finite squeezing.

Experimental results

Research questions

• RQ1 Can non-Gaussian cluster states required for universal measurement-based quantum computation be prepared deterministically in continuous-variable systems?
• RQ2 Can optomechanical systems with quadratic optomechanical coupling enable unconditional preparation of such states without post-selection?
• RQ3 Is continuous monitoring of the output field sufficient to implement arbitrary Gaussian measurements in this platform?
• RQ4 What are the feasibility limits of this approach under realistic thermal and decoherence effects?
• RQ5 Can the fidelity of the resource state and measurement operations be maintained under finite squeezing and thermal noise?

Key findings

• The proposed driven-dissipative optomechanical system can deterministically prepare a non-Gaussian cluster state, including entangled squeezed states and cubic-phase states, as a steady state.
• Numerical simulations show that the final fidelity of the cluster state remains high even under thermal noise, with fidelity decreasing as temperature increases.
• The scheme achieves high average fidelity in implementing the cubic-phase gate, with fidelity decreasing under higher temperatures and damping rates.
• The use of continuous monitoring enables effective Gaussian measurements, with results robust under finite-resolution discretization of momentum observables.
• The effective master equation derived via adiabatic elimination confirms the stability and feasibility of the protocol under realistic parameters.
• The approach avoids the need for quantum memories and post-selection, making it more experimentally accessible with current optomechanical technology.