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Continuous Variables Cluster States in Photonic Time-Crystals

Mark D. Lyubarov, Michael Birk, O. Segal, A. Horlach, Liat Nemirovsky-Levy, Yonatan Plotnik, Mordechai Segev

Published Jan 1, 2024• 0 citations
Publisher

Abstract

We show that Photonic Time-Crystals (PTCs) produce two-mode squeezing for pairs of photonic modes. We propose an algorithm for generating a cluster state in PTC for a measurement-based quantum computing in a simple three-step process.
DOI
10.1364/cleo_fs.2024.ff1h.1

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Photonic quantum computing has been rapidly advancing over the past decade, with measurement-based approaches emerging as particularly promising. A crucial requirement for these approaches is the generation of large-scale cluster states. In this work, we present a method to create cluster states using Photonic Time Crystals (PTCs)—dielectric materials with their refractive index rapidly modulated in time. PTCs effectively function as a set of optical parametric oscillators and beam-splitters, producing simultaneous two-mode squeezing for many pairs of photonic modes with opposite wavevectors. We utilize this capability to propose a method for generating two-dimensional cluster states, offering important advantages over existing protocols.
Photonics quantum networks are pivotal for quantum technologies, facilitating efficient information distribution and manipulation through quantum states of light. Continuous-variable (CV) cluster states, essential resources for Measurement-Based Quantum Computing, can be deterministically generated using squeezed states of light and mode-basis changes [1]. However, Gaussian states like squeezed states or cluster states, can be efficiently simulated with a classical computer [2]. Thus, to achieve quantum advantage, non-Gaussianity should be introduced, which can be accomplished by subtracting a photon from a squeezed state [3].
We develop a scheme for time-frequency encoded continuous-variable cluster-state quantum computing using quantum memories. In particular, we propose a method to produce, manipulate, and measure two-dimensional cluster states in a single spatial mode by exploiting the intrinsic time-frequency selectivity of Raman quantum memories. Time-frequency encoding enables the scheme to be extremely compact, requiring a number of memories that are a linear function of only the number of different frequencies in which the computational state is encoded, independent of its temporal duration. We therefore show that quantum memories can be a powerful component for scalable photonic quantum information processing architectures.
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Entanglement is the key resource for measurement-based quantum computing. It is stored in quantum states known as cluster states, which are prepared offline and enable quantum computing by means of purely local measurements. Universal quantum computing requires cluster states that are both large and possess (at least) a two-dimensional topology. Continuous-variable cluster states-based on bosonic modes rather than qubits-have previously been generated on a scale exceeding one million modes, but only in one dimension. Here, we report generation of a large-scale two-dimensional continuous-variable cluster state. Its structure consists of a 5- by 1240-site square lattice that was tailored to our highly scalable time-multiplexed experimental platform. It is compatible with Bosonic error-correcting codes that, with higher squeezing, enable fault-tolerant quantum computation.