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arXiv:1007.3434 · Physical Review A

Temporal-mode continuous-variable cluster states using linear optics

Nicolas C. Menicucci

Published Jun 13, 2011• 143 citations
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Abstract

An extensible experimental design for optical continuous-variable cluster states of arbitrary size using four offline (vacuum) squeezers and six beam splitters is presented. This method has all the advantages of a temporal-mode encoding [Phys. Rev. Lett. 104, 250503 (2010)], including finite requirements for coherence and stability even as the computation length increases indefinitely, with none of the difficulty of inline squeezing. The extensibility stems from a construction based on Gaussian projected entangled pair states. The potential for use of this design within a fully fault-tolerant model is discussed.

DOI
10.1103/physreva.83.062314

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An extensible experimental design for optical continuous-variable cluster states of arbitrary size using four offline (vacuum) squeezers and six beam splitters is presented. This method has all the advantages of a temporal-mode encoding [Phys. Rev. Lett. 104, 250503 (2010)], including finite requirements for coherence and stability even as the computation length increases indefinitely, with none of the difficulty of inline squeezing. The extensibility stems from a construction based on Gaussian projected entangled pair states. The potential for use of this design within a fully fault-tolerant model is discussed.
Continuous-variable Gaussian cluster states are a potential resource for universal quantum computation. They can be efficiently and unconditionally built from sources of squeezed light using beam splitters. Here we report on the generation of three different kinds of continuous-variable four-mode cluster states. In our realization, the resulting cluster-type correlations are such that no corrections other than simple phase-space displacements would be needed when quantum information propagates through these states. At the same time, the inevitable imperfections from the finitely squeezed resource states and from additional thermal noise are minimized, as no antisqueezing components are left in the cluster states.
Continuous-variable (CV) cluster states are a universal quantum computing platform that has experimentally outscaled qubit platforms by orders of magnitude.Room-temperature implementation of CV cluster states has been achieved with quantum optics by using multimode squeezed Gaussian states.It has also been proven that fault tolerance thresholds for CV quantum computing can be reached at realistic squeezing levels.In this paper, we show that standard approaches to design and characterize CV cluster states can miss entanglement present in the system.Such hidden entanglement may be used to increase the power of a quantum computer but it can also, if undetected, hinder the successful implementation of a quantum algorithm.By a detailed analysis of the structure of Gaussian states, we derive an algorithm that reveals hidden entanglement in an arbitrary Gaussian state and optimizes its use for one-way quantum computing.
The linear optical creation of Gaussian cluster states, a potential resource for universal quantum computation, is investigated. First, using Bloch-Messiah reduction, we show how to achieve canonical cluster-state generation, otherwise based on pairwise acting quantum nondemolition gates, by off-line squeezers and beam splitters. Moreover, we find that, in terms of squeezing resources, the canonical states are rather wasteful. Hence we propose a systematic way to create a whole family of cluster-type states, including potentially cheaper states. Any given cluster (or graph) state can be realized this way. As an example, we consider a protocol in which a single-mode quantum state propagates through a multiple-rail cluster. Such a redundant encoding may reduce errors due to finite squeezing.
We propose an experimental scheme that has the potential for large-scale realization of continuous-variable (CV) cluster states for universal quantum computation. We do this by mapping CV cluster-state graphs onto two-mode squeezing graphs, which can be engineered into a single optical parametric oscillator (OPO). The desired CV cluster state is produced directly from a joint squeezing operation on the vacuum, using a multifrequency pump beam. This method has potential for ultracompact experimental implementation. As an illustration, we detail an experimental proposal for creating a four-mode square CV cluster state with a single OPO.
Continuous-variable (CV) cluster states offer a promising platform for large-scale measurement-based quantum computations (MBQC). However, finite squeezing inevitably introduces Gaussian noise during MBQC. While fault-tolerant MBQC schemes exist in principle, they require the scalable incorporation of non-Gaussian resources, such as GKP states, which remain experimentally challenging. Consequently, a central question at this stage is how finite squeezing fundamentally constrains the intrinsic computational power of CV cluster states themselves. In this work, we address this question by analyzing the classical complexity of measurement-based linear optics (MBLO) implemented with such states, motivated by its near-term feasibility and recent experimental progress. We develop an explicit MBLO framework and examine how the squeezing level governs the complexity of the classical simulation of the resulting output states. Specifically, we identify squeezing-level thresholds that delineate classically tractable and intractable regimes, thereby revealing a squeezing-driven complexity phase transition. These findings advance our understanding of the squeezing resources necessary for meaningful quantum computation in current experimental regimes. Furthermore, they underscore the critical need to either scale the squeezing level or integrate error-correction schemes to achieve reliable, large-scale quantum computation with CV cluster states.