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arXiv:2511.04888

Ballistic bosonic noise suppression with hybrid qumode-qubit rotation gates

Saurabh U. Shringarpure, Siheon Park, Sungjoo Cho, Yong Siah Teo, Hyukjoon Kwon, Srikrishna Omkar, Hyunseok Jeong

quant-phSubmitted Nov 7, 2025• Announced Nov 10, 2025• 0 citations
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Abstract

Noise suppression is of paramount importance for reliable quantum information processing and computation. We show that for any single-mode bosonic code (qumode) corrupted by thermal~noise at rate~$η$ and mean \mbox{excitation}~$\bar{n}$, a hybrid continuous-discrete-variable~(CV-DV) interferometer using only a single qubit ancilla~(DV) and two controlled~Fourier~(CF) gates sandwiching the noise channel suppresses its effects to $\mathcal{O}(η^2)$ \emph{without} any active error correction or destructive measurements of the encoded state and with high success probabilities~$>0.5$ if~$η(1+\bar{n})<0.5$. This suppression scheme works by conditionally monitoring the photon-number parities after the interferometer. Bosonic codes with two logical states of the same photon-number parity (like-parity codes) are \emph{completely resilient} to DV amplitude- and phase-damping ancilla noise. For such codes, the interferometer simplifies to the use of a qumode rotation gate and a \emph{single} CF~gate. This presents a clear advantage of our CF-gate-based error suppression scheme over previously-proposed ``bypass'' protocols, where qubit information transferred to the DV mode is readily corrupted by damping~noise. Finally, we present a simple extension to direct communication of qumode states between two parties over a noisy channel using a preshared DV entangled state, by implementing a CF gate in the first laboratory and its inverse in the other. Such a communication protocol achieves a similar fidelity performance at the same success rate as the single-party case, but with greater resilience to the ancilla noise than DV~teleportation. Resource-efficient multi-qubit codes that depend on a few essential long-range interactions can benefit from it.

Comments
19 pages, 7 figures

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Noise suppression is of paramount importance for reliable quantum information processing and computation. We show that for any single-mode bosonic code (qumode) corrupted by thermalnoise at rateηηη and mean \mbox{excitation}nˉ\bar{n}nˉ, a hybrid continuous-discrete-variable(CV-DV) interferometer using only a single qubit ancilla~(DV) and two controlledFourier(CF) gates sandwiching the noise channel suppresses its effects to O(η2)\mathcal{O}(η^2)O(η2) \emph{without} any active error correction or destructive measurements of the encoded state and with high success probabilities~>0.5>0.5>0.5 if~η(1+nˉ)<0.5η(1+\bar{n})<0.5η(1+nˉ)<0.5. This suppression scheme works by conditionally monitoring the photon-number parities after the interferometer. Bosonic codes with two logical states of the same photon-number parity (like-parity codes) are \emph{completely resilient} to DV amplitude- and phase-damping ancilla noise. For such codes, the interferometer simplifies to the use of a qumode rotation gate and a \emph{single} CFgate. This presents a clear advantage of our CF-gate-based error suppression scheme over previously-proposed ``bypass'' protocols, where qubit information transferred to the DV mode is readily corrupted by dampingnoise. Finally, we present a simple extension to direct communication of qumode states between two parties over a noisy channel using a preshared DV entangled state, by implementing a CF gate in the first laboratory and its inverse in the other. Such a communication protocol achieves a similar fidelity performance at the same success rate as the single-party case, but with greater resilience to the ancilla noise than DV~teleportation. Resource-efficient multi-qubit codes that depend on a few essential long-range interactions can benefit from it.
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Hybrid continuous-variable--discrete-variable (CV--DV) architectures process quantum information in bosonic modes and qubits, but noise limits their performance. To reduce the noise, existing DV error correction must be complemented by CV noise reduction. Existing CV noise-reduction schemes -- such as GKP-stabilizer codes -- can reduce CV noise, but only for Gaussian gates. Therefore, no current noise-reduction scheme can correct arbitrary CV--DV gates, including non-Gaussian ones. Here, we develop noise reduction for a universal CV--DV gate set, making it applicable to arbitrary CV--DV gates. We do so by introducing an ancilla qubit into a GKP-stabilizer code, allowing us to reduce the standard deviation of Gaussian displacement noise from σσσ to O~(σ2)\tilde O(σ^2)O~(σ2). To demonstrate the scheme, we show that it significantly reduces noise and improves fidelity in the preparation of non-Gaussian cat and Fock states.
Bosonic quantum error correction represents a route towards significant hardware overhead reduction for fault-tolerant quantum computation. However, controlling quantum harmonic oscillators that encode the quantum information comes with its own challenges. In many platforms such as superconducting circuits and trapped ions, the bosonic degree of freedom is controlled by an ancillary qubit whose decay during a qubit-oscillator gate propagates to the oscillator as a continuous error. Such errors generally lie beyond the scope of errors that the bosonic code is capable of correcting. We introduce the continuous-variable flag: an auxiliary oscillator coupled to the ancilla whose phase-space position encodes the continuous error corrupting the storage mode. After the gate, a heterodyne measurement of the flag estimates this continuous-variable error and a subsequent feedback control undoes it up to a bosonic code stabilizer. The scheme requires no new ingredients, as the flag is driven by the same dispersive coupling, displacements and rotations that implement the gates it is supposed to protect. We construct sequences protecting conditional rotations to all orders in ancilla decay with one flag, and conditional displacements to first order with one flag and to all orders with two. Simulations with realistic circuit-QED parameters predict more than three orders of magnitude fewer logical errors for the parity measurement of a four-component cat code, and a finite-energy GKP logical lifetime near its noiseless-ancilla bound. By discretizing continuous-variable errors, the flags introduced in this work are a useful tool for any hybrid oscillator-qubit processor, and open the route towards fault-tolerant simulation and computation with bosonic modes.
Robust continuous-variable (CV) quantum information processing requires correcting realistic errors in bosonic systems, but all existing schemes rely on auxiliary Gottesman-Kitaev-Preskill (GKP) states which the preparation and operation are demanding in many platforms. In this work, we propose a novel CV quantum error correction (QEC) scheme that utilizes a broadly accessible resource: discrete-variable (DV) ancilla. Our scheme extracts information about CV displacement to the DV ancilla, measuring that allows counteracting the unwanted displacement error. We show that a simple single-qubit ancilla can already suppress CV infidelity by more than 20%. By concatenating with DV QEC codes, our scheme is robust against the physical errors in hybrid CV-DV systems, and yields a new class of oscillator-in-oscillator code that does not involve GKP states. Our work facilitates the implementation of CV QEC on realistic platforms.
Abstract Quantum-information processing and computation with bosonic qubits are corruptible by noise channels. Using interferometers and photon-subtraction gadgets (PSGs) accompanied by linear amplification and attenuation, we establish linear-optical methods to mitigate and suppress bosonic noise channels. We first show that by employing amplifying and attenuating PSGs respectively at the input and output of either a thermal or random-displacement channel, probabilistic error cancellation (PEC) can be carried out to mitigate errors in expectation-value estimation. We also derive optimal physical estimators that are properly constrained to improve the sampling accuracy of PEC. Next, we prove that a purely-dephasing channel is coherently suppressible using a multimode Mach–Zehnder interferometer and conditional vacuum measurements (vacuum-based Mach–Zehnder scheme or the VMZ scheme). In the limit of infinitely-many ancillas, with nonvanishing success rates, VMZ using either Hadamard or two-design interferometers turns any dephasing channel into a phase-space-rotated linear-attenuation channel that can subsequently be inverted with (rotated) linear amplification without Kerr nonlinearity. Moreover, for weak central-Gaussian dephasing, the suppression fidelity increases monotonically with the number of ancillas and most optimally with Hadamard interferometers. We demonstrate the performance of these linear-optical mitigation and suppression schemes on common noise channels (and their compositions) and popular bosonic codes. While the theoretical formalism pertains to idling noise channels, we also provide numerical evidence supporting mitigation and suppression capabilities with respect to noise from universal gate operations.
Bosonic quantum error-correcting codes offer a viable direction towards reducing the hardware overhead required for fault-tolerant quantum information processing.A broad class of bosonic codes, namely rotation-symmetric codes, can be characterized by their phase-space rotation symmetry.However, their performance has been examined to date only within an idealistic noise model.Here, we further analyze the error-correction capabilities of rotation-symmetric codes using a teleportation-based error-correction circuit.To this end, we numerically compute the average gate fidelity, including measurement errors into the noise model of the data qubit.Focusing on physical measurement models, we assess the performance of heterodyne and adaptive homodyne detection in comparison to the previously studied canonical phase measurement.This setting allows us to shed light on the role of different currently available measurement schemes when decoding the encoded information.We find that with the currently achievable measurement efficiencies in microwave optics, bosonic rotation codes undergo a substantial decrease in their break-even potential.In addition, we perform a detailed analysis of Gottesman-Kitaev-Preskill (GKP) codes using a similar error-correction circuit that allows us to analyze the effect of realistic measurement models on different codes.In comparison to RSB codes, we find for GKP codes an even greater reduction in performance together with a vulnerability to photon-number dephasing.Our results show that highly efficient measurement protocols constitute a crucial building block towards error-corrected quantum information processing with bosonic continuous-variable systems.