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arXiv:2504.01664 · Physical Review Research

Preparation of conditionally squeezed states in qubit-oscillator systems

Marius K. Hope, Jonas Lidal, Francesco Massel

Published Jan 21, 2026• 4 citations
arXivHTMLPDF

Abstract

Inspired by recent advances in the manipulation of superconducting circuits coupled to mechanical modes in the quantum regime, we propose a protocol for generating superpositions of orthogonally squeezed states in a quantum harmonic oscillator. The protocol relies on a quadratic coupling between the oscillator and a qubit, and is conceptually similar to methods used for preparing cat states in qubit-oscillator systems. We numerically evaluate the robustness of the state-preparation scheme in the presence of decoherence, considering environmental coupling for both the harmonic oscillator and the qubit. As a potential application, we consider a quantum error-correcting code based on conditionally squeezed states and analyze its error correction properties.

DOI
10.1103/jrrb-hymw

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Squeezed states of harmonic oscillators are a central resource for continuous-variable quantum sensing, computation, and communication. Here, we propose a method for the generation of very good approximations to highly squeezed vacuum states with low excess antisqueezing using only a few oscillator-qubit coupling gates through a Rabi-type interaction Hamiltonian. This interaction can be implemented with several different methods, which has previously been demonstrated in superconducting circuit and trapped-ion platforms. The protocol is compatible with other protocols manipulating quantum harmonic oscillators, thus facilitating scalable continuous-variable fault-tolerant quantum computation.
Bosonic quantum codes redundantly encode quantum information in the states of a quantum harmonic oscillator, making it possible to detect and correct errors. Schr\"odinger cat codes---based on the superposition of two coherent states with opposite displacements---can correct phase-flip errors induced by dephasing, but they are vulnerable to bit-flip errors induced by particle loss. Here, we develop a bosonic quantum code relying on squeezed cat states, i.e., cat states made of a linear superposition of displaced-squeezed states. Squeezed cat states allow to partially correct errors caused by particle loss, while at the same time improving the protection against dephasing. We present a comprehensive analysis of the squeezed cat code, including protocols for code generation and elementary quantum gates. We characterize the effect of both particle loss and dephasing and develop an optimal recovery protocol that is suitable to be implemented on currently available quantum hardware. We show that with moderate squeezing, and using typical parameters of state-of-the-art quantum hardware platforms, the squeezed cat code has a resilience to particle loss errors that significantly outperforms that of the conventional cat code.
We consider a system composed of a two-level system (i.e., a qubit) and a harmonic oscillator in the ultrastrong-coupling regime, where the coupling strength is comparable to the qubit and oscillator energy scales. Special emphasis is placed on the possibility of preparing nonclassical states in this system. These nonclassical states include squeezed states, Schr\"odinger-cat states, and entangled states. We start by comparing the predictions of a number of analytical methods that can be used to describe the system under different assumptions, thus analyzing the properties of the system in various parameter regimes. We then examine the ground state of the system and analyze its nonclassical properties. We finally discuss some questions related to the possible experimental observation of the nonclassical states and the effect of decoherence.
We propose a scheme to generate macroscopic Schr\"odinger-cat states in a quantum harmonic oscillator (electromagnetic field or mechanical resonator) coupled to a quantum bit (two-level system) via a conditional displacement mechanism. By driving the qubit monochromatically, the oscillation of the qubit state modifies the effective frequency of the driving force acting on the oscillator, and a resonant or near-resonant driving on the oscillator can be achieved. The displacement of the oscillator is then significantly enhanced due to the small detuning of the driving force and can exceed that of the zero-point fluctuation. This effect can be used to prepare quantum superpositions of macroscopically distinct coherent states in the oscillator. We present detailed studies on this state-generation scheme in both the closed- and open-system cases. This approach can be implemented in various experimental platforms, such as cavity- or circuit-QED systems, electromechanical systems, and spin-cantilever systems.
We introduce a family of bosonic quantum error-correcting codes built as a rotation-symmetric superposition of squeezed vacuum states, which promise protection against both loss and dephasing noise channels. The robustness of these "squeezed-vacuum codes" arises from being arranged at evenly spaced angles in phase-space, and simultaneously in evenly spaced photon-number support n≡2k ⁣(mod2m)n \equiv {2k} \! \pmod {2m}n≡2k(mod2m). We present simple preparation circuits: a two-legged code using a Hadamard-conditional-squeezing-Hadamard sequence on an ancilla qubit, and for general "mmm-legged" codewords using sequences of conditional rotations. The performance of these codes is evaluated against loss and dephasing noises using the Knill-Laflamme violation function and benchmarked against cat codes. As the number mmm of squeezed-vacuum states in a code increases, the code exhibits improved loss tolerance at the cost of higher dephasing sensitivity. We outline implementations in circuit QED and trapped-ion platforms, where high-fidelity Gaussian operations and conditional controls are available or under active development. These results help establish squeezed-vacuum codes as practical, hardware-ready, members of the bosonic codes class.
We propose and experimentally demonstrate a new method to generate arbitrary Fock state superpositions in a superconducting quantum circuit, where a qubit is dispersively coupled to a microwave cavity mode. Here, the qubit is used to conditionally modulate the probability amplitudes of the Fock state components of a coherent state to those of the desired superposition state, instead of pumping photons one by one into the cavity as in previous schemes. Our method does not require the adjustment of the qubit frequency during the cavity state preparation and is more robust to noise and accumulation of experimental errors compared to previous ones. Using the method, we experimentally generate phase eigenstates under various Hilbert-space dimensions and squeezed states, which are useful for the quantum walk and high-precision measurement.