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arXiv:2510.27661 · Physical Review Research

Teleportation-based squeezer for bosonic cluster states

Michal Matulík, Radim Filip, Petr Marek

Published May 27, 2026• 0 citations
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Abstract

The one-way quantum computation utilizing bosonic modes of light offers unmatched scalability of light modes, and it has seen rapid experimental development recently. Scalability requires robust and low-error gates and measurements. Squeezing gate is one of the necessary Gaussian operations. We find the optimal squeezing gate in cluster-state architecture. Our approach newly uses amplitude transmission coefficients of unbalanced beam splitters and homodyne detection with subsequent unity-gain feedforward to squeeze the input state. The approach outperforms the current method based on optimally rotated homodyne detection but fixed balanced beam splitters. The performance of both cluster-state squeezers is evaluated for Gaussian and non-Gaussian input states. We use different metrics to benchmark the quality of squeezed output states. The result opens a road to low-noise squeezing gates in experimentally achievable cluster states.

DOI
10.1103/78tf-57jf

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The one-way quantum computation utilizing bosonic modes of light offers unmatched scalability of light modes, and it has seen rapid experimental development recently. Scalability requires robust and low-error gates and measurements. Squeezing gate is one of the necessary Gaussian operations. We find the optimal squeezing gate in cluster-state architecture. Our approach newly uses amplitude transmission coefficients of unbalanced beam splitters and homodyne detection with subsequent unity-gain feedforward to squeeze the input state. The approach outperforms the current method based on optimally rotated homodyne detection but fixed balanced beam splitters. The performance of both cluster-state squeezers is evaluated for Gaussian and non-Gaussian input states. We use different metrics to benchmark the quality of squeezed output states. The result opens a road to low-noise squeezing gates in experimentally achievable cluster states.
We show explicitly how to realize an arbitrary linear unitary Bogoliubov (LUBO) transformation on a multimode quantum state through homodyne-based one-way quantum computation. Any LUBO transformation can be approximated by means of a fixed, finite-sized, sufficiently squeezed Gaussian cluster state that allows for the implementation of beam splitters (in form of three-mode connection gates) and general one-mode LUBO transformations. In particular, we demonstrate that a linear four-mode cluster state is a sufficient resource for an arbitrary one-mode LUBO transformation. Arbitrary-input quantum states including non-Gaussian states could be efficiently attached to the cluster through quantum teleportation.
Measurement-induced quantum computation with continuous-variable cluster states utilizes teleportation to transmit and alter quantum states via measurement-and-feedforward control. One of the key challenges of this approach is the deterioration of quantum states caused by the noise added due to imperfect entanglement of the cluster. We analyze the propagation of a quantum non-Gaussian state with nonlinear squeezing through a small cluster state. We show that a nonlinear feedforward in the deterministic teleportation protocol reduces the added noise and improves the nonlinear squeezing transferred. In a probabilistic regime, the improvement can be manifested even with current experimental resources. Better processing of non-Gaussian states can bring us closer to the necessary interplay between cluster states and non-Gaussianity required by quantum computing.
We present an architecture for the generation of GKP states in which quadrature squeezing operations are used to control the average photon number statistics of probabilistic photon number measurements on Gaussian resource states. Specifically, we present an architecture employing a teleportation-based squeezing protocol and polynomial-gate applications integrated into a time-multiplexed multi-mode cluster state to generate cat states with high amplitudes, which are consequently used to generate GKP states with high quadrature effective squeezing. Compared to our previous work, in addition to using squeezing as a resource, the present architecture reduces damping and noise by minimizing the number of homodyne measurements required in GKP state generation. We demonstrate the effectiveness of these improvements - including dynamic input-state resetting and an improved breeding algorithm - by achieving a fault-tolerance threshold of 11.5 dB cluster squeezing using the RHG surface code for error correction, without requiring active switching or photon-number resource states.
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 demonstrate a quadratic phase gate for one-way quantum computation in the continuous-variable regime. This canonical gate, together with phase-space displacements and Fourier rotations, completes the set of universal gates for realizing any single-mode Gaussian transformation such as arbitrary squeezing. As opposed to previous implementations of measurement-based squeezers, the current gate is fully controlled by the local oscillator phase of the homodyne detector. Verifying this controllability, we give an experimental demonstration of the principles of one-way quantum computation over continuous variables. Moreover, we can observe sub-shot-noise quadrature variances in the output states, confirming that nonclassical states are created through cluster computation.
Continuous-variable cluster states allow for fault-tolerant measurement-based quantum computing when used in tandem with the Gottesman-Kitaev-Preskill (GKP) encoding of a qubit into a bosonic mode. For quad-rail-lattice macronode cluster states, whose construction is defined by a fixed, low-depth beam splitter network, we show that a Clifford gate and GKP error correction can be simultaneously implemented in a single teleportation step. We give explicit recipes to realize the Clifford generating set, and we calculate the logical gate-error rates given finite squeezing in the cluster-state and GKP resources. We find that logical error rates of ${10}^{\ensuremath{-}2}$--${10}^{\ensuremath{-}3}$, compatible with the thresholds of topological codes, can be achieved with squeezing of 11.9--13.7 dB. The protocol presented eliminates noise present in prior schemes and puts the required squeezing for fault tolerance in the range of current state-of-the-art optical experiments. Finally, we show how to produce distillable GKP magic states directly within the cluster state.