Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1704.04533

Quadrature readout and generation of squeezed states of a harmonic oscillator using a qubit-based indirect measurement

Mehmet Cantürk, Adrian Lupaşcu

Published Apr 14, 2017• 0 citations
arXivHTMLPDF

Abstract

We present a protocol for measuring the quadrature of a harmonic oscillator (HO). The HO is coupled to a qubit, with an interaction modulated by the qubit control and effectively proportional to the HO quadrature $I$. Repeated measurement of the qubit leads to gradually increasing information on the quadrature $I$, leading to squeezing. We derive an analytical formula for the quadrature variance, $(ΔI)^2 = 1/(1+4ϕ^2 s)$, with $ϕ$ the product of interaction strength and interaction time and $s$ the number of repetitions of the measurement. We discuss the robustness of this scheme against decoherence. We find that this protocol could lead to significant squeezing in a realistic setup formed of a superconducting flux qubit used to measure an electrical or mechanical resonator.

DOI
10.48550/arxiv.1704.04533

Related papers

Quantum nondemolition-like fast measurement scheme for a superconducting qubit

I. Serban, B. L. T. Plourde, Frank K. Wilhelm

We present a measurement protocol for a flux qubit coupled to a dc-superconducting quantum interference device (SQUID), representative of any two-state system with a controllable coupling to a harmonic-oscillator quadrature, which consists of two steps. First, the qubit state is imprinted onto the SQUID via a very short and strong interaction. We show that at the end of this step the qubit dephases completely, although the perturbation of the measured qubit observable during this step is weak. In the second step, information about the qubit is extracted by measuring the SQUID. This step can have arbitrarily long duration, since it no longer induces qubit errors.

arXiv:0803.0958•Physical Review B•Aug 12, 2008•19 citations

Mapping of a many-qubit state onto an oscillator using controlled displacements

Anders J. E. Bjerrum, Ulrik L. Andersen, Peter Rabl

We extend the controlled displacement interaction between a qubit and a harmonic oscillator to the multi-qubit (qudit) case. We define discrete quadratures of the qudit and show how the qudit state can be displaced in these quadratures controlled by an oscillator quadrature. Using this interaction, a periodic repetition of the state encoded in the qudit, can be deterministically mapped onto the oscillator, which is initialized in a squeezed state. Based on this controlled displacement interaction, we present a full circuit that encodes quantum information in a superposition of qudit quadrature states, and successively prepares the oscillator in the corresponding superposition of approximate Gottesman-Kitaev-Preskill (GKP) states. This preparation scheme is found to be similar to phase estimation, with the addition of a disentanglement gate. Our protocol for GKP state preparation is efficient in the sense, that the set of qubits need only interact with the oscillator through two time-independent interactions, and in the sense that the squeeze factor (in dB) of the produced GKP state grows linearly in the number of qubits used.

arXiv:2410.22385•Physical Review A•May 12, 2025•0 citations

Preparation of conditionally squeezed states in qubit-oscillator systems

Marius K. Hope, Jonas Lidal, Francesco Massel

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.

arXiv:2504.01664•Physical Review Research•Jan 21, 2026•4 citations

Sequential Measurements as a Resource in Ancilla-Assisted Quantum Metrology

Koray Mentesoglu, Rahul Trivedi, Sara Mouradian

We present a protocol for simultaneous estimation of both quadratures of a displacement channel on a quantum harmonic oscillator using a single ancilla qubit, without complex state preparation or adaptive control. The qubit is coupled to the quantum harmonic oscillator via controlled displacements of strength $A$ and undergoes $N$ rounds of measurement and reset, while the oscillator coherently accumulates the displacement signal. The non-commuting displacements imprint an order-dependent geometric phase at each round, giving a quantum Fisher information that scales as $\mathcal{O}(A^{2} N^{3})$. Although the measurement record space grows as $2^N$, we show that exact likelihoods for any individual measurement record can be computed in $\mathcal{O}(N^{2})$ time. With this, we show that measurement in the computational basis approximately saturates the quantum bound and maintains the $\mathcal{O}(A^2 N^3)$ scaling. Furthermore, the periodic information extraction makes the protocol robust to decoherence. Our results provide a framework for the design and analysis of sequential measurement in ancilla-assisted protocols.

quant-pharXiv:2605.00287•Physical Review A•May 4, 2026•0 citations

Quantum metrology with a squeezed Kerr oscillator

Jiajie Guo, Qiongyi He, Matteo Fadel

We study the squeezing dynamics in a Kerr-nonlinear oscillator, and quantify the metrological usefulness of the resulting states. Even if the nonlinearity limits the attainable squeezing by making the evolution non-Gaussian, the states obtained still have a high quantum Fisher information for sensing displacements. However, contrary to the Gaussian case, the amplitude of the displacement cannot be estimated by simple quadrature measurements. Therefore, we propose the use of a measurement-after-interaction protocol where a linear quadrature measurement is preceded by an additional nonlinear evolution, and show the significant sensitivity enhancement that can be obtained. Our results are robust when considering realistic imperfections such as energy relaxation, and can be implemented in state-of-the-art experimental setups.

arXiv:2406.11789•Physical Review A•May 6, 2024•13 citations

Controlled Generation of Squeezed States of Microwave Radiation in a Superconducting Resonant Circuit

Alexandre M. Zagoskin, Evgeni V. Il’ichev, Murray W. McCutcheon +2 more

Superconducting oscillators have been successfully used for quantum control and readout devices in conjunction with superconducting qubits. Also, squeezed states can improve the accuracy of measurements to subquantum, or at least subthermal, levels. Here, we show theoretically how to produce squeezed states of microwave radiation in a superconducting oscillator with tunable parameters. Its resonance frequency can be changed by controlling an rf SQUID inductively coupled to the oscillator. By repeatedly shifting the resonance frequency between any two values, it is possible to produce squeezed and subthermal states of the electromagnetic field in the (0.1-10) GHz range, even when the relative frequency change is small. We propose experimental protocols for the verification of squeezed state generation, and for their use to improve the readout fidelity when such oscillators serve as quantum transducers.

arXiv:0804.4186•Physical Review Letters•Dec 19, 2008•80 citations
We present a protocol for measuring the quadrature of a harmonic oscillator (HO). The HO is coupled to a qubit, with an interaction modulated by the qubit control and effectively proportional to the HO quadrature III. Repeated measurement of the qubit leads to gradually increasing information on the quadrature III, leading to squeezing. We derive an analytical formula for the quadrature variance, (ΔI)2=1/(1+4ϕ2s)(ΔI)^2 = 1/(1+4ϕ^2 s)(ΔI)2=1/(1+4ϕ2s), with ϕϕϕ the product of interaction strength and interaction time and sss the number of repetitions of the measurement. We discuss the robustness of this scheme against decoherence. We find that this protocol could lead to significant squeezing in a realistic setup formed of a superconducting flux qubit used to measure an electrical or mechanical resonator.
We present a measurement protocol for a flux qubit coupled to a dc-superconducting quantum interference device (SQUID), representative of any two-state system with a controllable coupling to a harmonic-oscillator quadrature, which consists of two steps. First, the qubit state is imprinted onto the SQUID via a very short and strong interaction. We show that at the end of this step the qubit dephases completely, although the perturbation of the measured qubit observable during this step is weak. In the second step, information about the qubit is extracted by measuring the SQUID. This step can have arbitrarily long duration, since it no longer induces qubit errors.
We extend the controlled displacement interaction between a qubit and a harmonic oscillator to the multi-qubit (qudit) case. We define discrete quadratures of the qudit and show how the qudit state can be displaced in these quadratures controlled by an oscillator quadrature. Using this interaction, a periodic repetition of the state encoded in the qudit, can be deterministically mapped onto the oscillator, which is initialized in a squeezed state. Based on this controlled displacement interaction, we present a full circuit that encodes quantum information in a superposition of qudit quadrature states, and successively prepares the oscillator in the corresponding superposition of approximate Gottesman-Kitaev-Preskill (GKP) states. This preparation scheme is found to be similar to phase estimation, with the addition of a disentanglement gate. Our protocol for GKP state preparation is efficient in the sense, that the set of qubits need only interact with the oscillator through two time-independent interactions, and in the sense that the squeeze factor (in dB) of the produced GKP state grows linearly in the number of qubits used.
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.
We present a protocol for simultaneous estimation of both quadratures of a displacement channel on a quantum harmonic oscillator using a single ancilla qubit, without complex state preparation or adaptive control. The qubit is coupled to the quantum harmonic oscillator via controlled displacements of strength AAA and undergoes NNN rounds of measurement and reset, while the oscillator coherently accumulates the displacement signal. The non-commuting displacements imprint an order-dependent geometric phase at each round, giving a quantum Fisher information that scales as O(A2N3)\mathcal{O}(A^{2} N^{3})O(A2N3). Although the measurement record space grows as 2N2^N2N, we show that exact likelihoods for any individual measurement record can be computed in O(N2)\mathcal{O}(N^{2})O(N2) time. With this, we show that measurement in the computational basis approximately saturates the quantum bound and maintains the O(A2N3)\mathcal{O}(A^2 N^3)O(A2N3) scaling. Furthermore, the periodic information extraction makes the protocol robust to decoherence. Our results provide a framework for the design and analysis of sequential measurement in ancilla-assisted protocols.
We study the squeezing dynamics in a Kerr-nonlinear oscillator, and quantify the metrological usefulness of the resulting states. Even if the nonlinearity limits the attainable squeezing by making the evolution non-Gaussian, the states obtained still have a high quantum Fisher information for sensing displacements. However, contrary to the Gaussian case, the amplitude of the displacement cannot be estimated by simple quadrature measurements. Therefore, we propose the use of a measurement-after-interaction protocol where a linear quadrature measurement is preceded by an additional nonlinear evolution, and show the significant sensitivity enhancement that can be obtained. Our results are robust when considering realistic imperfections such as energy relaxation, and can be implemented in state-of-the-art experimental setups.
Superconducting oscillators have been successfully used for quantum control and readout devices in conjunction with superconducting qubits. Also, squeezed states can improve the accuracy of measurements to subquantum, or at least subthermal, levels. Here, we show theoretically how to produce squeezed states of microwave radiation in a superconducting oscillator with tunable parameters. Its resonance frequency can be changed by controlling an rf SQUID inductively coupled to the oscillator. By repeatedly shifting the resonance frequency between any two values, it is possible to produce squeezed and subthermal states of the electromagnetic field in the (0.1-10) GHz range, even when the relative frequency change is small. We propose experimental protocols for the verification of squeezed state generation, and for their use to improve the readout fidelity when such oscillators serve as quantum transducers.