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:2503.15941

Multimode Qubit-Conditional Operations via Generalized Cross-Resonance

Mohammad Ayyash

Published Mar 20, 2025• 0 citations
arXivHTMLPDF

Abstract

We present a general framework for generating single- and multimode qubit-conditional operations by extending cross-resonant driving to a generalized multimode scheme. This includes single-mode conditional displacements and squeezing induced by one- and two-photon cross-resonant drives in the presence of one- and two-photon qubit-oscillator interactions, respectively. In the multimode setting, we derive multimode qubit-conditional joint displacement, beamsplitter and two-mode squeezing operations. This framework enables the realization of arbitrary multimode qubit-conditional operations, which are of great importance to bosonic quantum error correction, phase estimation and quantum simulations.

DOI
10.48550/arxiv.2503.15941

Related papers

Driven multiphoton qubit-resonator interactions

Mohammad Ayyash, Xicheng Xu, Sahel Ashhab +1 more

We develop a general theory for multiphoton qubit-resonator interactions enhanced by a qubit drive. The interactions generate qubit-conditional operations in the resonator when the driving is near $n$-photon cross resonance, i.e., when the qubit drive is $n$ times the resonator frequency. We pay special attention to the strong driving regime, where the resulting effective interactions are conditioned on the qubit dressed states. Next, we investigate the use of a two-tone drive to engineer an effective $n$-photon Rabi Hamiltonian with widely tunable effective system parameters, which could enable the realization of new regimes that have so far been inaccessible. Then, we discuss applications for the specific case where $n=2$, which results in qubit-conditional squeezing (QCS). We show that the QCS protocol can be used to generate a superposition of orthogonally squeezed states following a properly chosen qubit measurement. We outline quantum information processing applications for these states, including encoding a qubit in a resonator via the superposition of orthogonally squeezed states. We show how the QCS operation can be used to realize a controlled-squeeze gate and its use in bosonic phase estimation. The QCS protocol can also be utilized to achieve faster unitary operator synthesis on the joint qubit-resonator Hilbert space. Finally, we propose a multiphoton circuit QED implementation based on a transmon qubit coupled to a resonator via an asymmetric SQUID. We provide realistic parameter estimates for the two-photon operation regime that can host the aforementioned two-photon protocols. We use numerical simulations to show that, even in the presence of spurious terms and decoherence, our analytical predictions are robust.

arXiv:2405.01518•Physical Review A•Nov 19, 2024•18 citations

Efficient Qubit Simulation of Hybrid Oscillator-Qubit Quantum Computation

Xi Lu, Bojko N. Bakalov, Yuan Liu

We introduce a framework for simulating hybrid oscillator-qubit quantum processors on qubit-only systems through position encoding. By encoding continuous-variable position and momentum wave functions into qubit amplitudes, our method efficiently simulates all Gaussian and conditional Gaussian operations -- encompassing the phase-space instruction set (beam splitter, single-qubit rotation, conditional displacement) and extending to squeezing, conditional squeezing, conditional rotation, and conditional beam splitter -- using $O\!\left(\log^2\!\left(Γ+ \log(1/ε)\right)\right)$ qubit gates per hybrid gate, where $Γ$ is the Fock-level bound and $ε$ is the target precision. This polylogarithmic per-gate complexity represents an exponential improvement over Fock basis encoding approaches, which require exponential quantum or classical resources in the number of qubits per mode. We provide rigorous numerical characterization of quantum Fourier transform errors for Fock-bounded states, enabling precise resource estimation for practical implementations. This work establishes that hybrid oscillator-qubit algorithms can be implemented on qubit processors with polynomial overhead, providing new insights into the computational power trade-offs between discrete-variable and hybrid continuous-discrete-variable quantum computing.

quant-pharXiv:2603.09233•Mar 11, 2026•0 citations

Conditional-not Displacement: Fast Multioscillator Control with a Single Qubit

Asaf A. Diringer, Eliya Blumenthal, Avishay Grinberg +2 more

Bosonic encoding is an approach for quantum information processing, promising lower hardware overhead by encoding in the many levels of a harmonic-oscillator mode. Scaling to multiple modes requires weak interaction for independent control, yet strong interaction for fast control. Applying fast and efficient universal control on multiple modes remains an open problem. Surprisingly, we find that displacements conditioned on the state of a single-qubit ancilla coupled to multiple harmonic oscillators are sufficient for universal control. We present the conditional- operation concept, which can be used to reduce the duration of entangling gates. Within this guiding concept, we develop the conditional- displacement control method which enables fast generation and control of bosonic states in multimode systems weakly coupled to a single-ancilla qubit. Our method is fast despite the weak ancilla coupling. The weak coupling in turn allows for excellent separability and thus independent control. We demonstrate our control on a superconducting transmon qubit weakly coupled to a multimode superconducting cavity. We create both entangled and separable cat states in different modes of the multimode cavity, showing entangling operations at low crosstalk while maintaining independent control of the different modes. We show that the operation time is not limited by the inverse of the coupling rate, which is the typical timescale, and we exceed it by almost 2 orders of magnitude. We verify our results with an efficient method for measurement of the multimode characteristic function which employs our conditional- displacement. Our results inspire a new approach toward general entangling operations and allow for fast and efficient multimode bosonic encoding and measurement. Published by the American Physical Society 2024

arXiv:2301.09831•Physical Review X•Mar 26, 2024•27 citations

Conditional-squeezing gate in superconducting circuits

Roman Schiaffino, Fernando C. Lombardo, Juan Pablo Paz

We present an implementation of a conditional-squeezing gate that squeezes a SQUID-terminated resonator mode along a direction determined by the state of a dispersively coupled qubit. This gate generalizes the controlled-squeezing gate [Phys. Rev. A \textbf{111}, 042606 (2025)], and relies on a refocusing technique to suppress unwanted effects arising from slowly varying time-dependent terms in the Hamiltonian during the state-dependent parametric resonance required for the operation. As an application, we use the gate to encode an arbitrary qubit state into superpositions of single- and two-mode squeezed states of the resonator. These non-Gaussian states enable error-detectable encoding through parity measurements. We show that refocusing substantially improves the encoding fidelity, which is ultimately limited by Kerr nonlinearities and dissipation in realistic implementations. For experimentally optimistic values of the nonlinearities and decay rates, we obtain encoding fidelities above 0.99 for arbitrary input qubit states. Our results provide a route toward extending this scheme to the generation of higher-order superpositions of squeezed states (a class of rotation-symmetric bosonic codes) using a control qudit.

quant-pharXiv:2609.10655•Sep 10, 2026•0 citations

Crosstalk-robust quantum control in multimode bosonic systems

Xinyuan You, Yunwei Lu, T. W. Kim +10 more

High-coherence superconducting cavities offer a hardware-efficient platform for quantum information processing. To achieve universal operations of these bosonic modes, the requisite nonlinearity is realized by coupling them to a transmon ancilla. However, this configuration is susceptible to crosstalk errors in the dispersive regime, where the ancilla frequency is Stark shifted by the state of each coupled bosonic mode. This leads to a frequency mismatch of the ancilla drive, lowering the gate fidelities. To mitigate such coherent errors, we employ quantum optimal control to engineer ancilla pulses that are robust to the frequency shifts. These optimized pulses are subsequently integrated into a recently developed echoed conditional displacement protocol for executing single- and two-mode operations. Through numerical simulations, we examine two representative scenarios: the preparation of single-mode Fock states in the presence of spectator modes and the generation of two-mode entangled Bell-cat states. Our approach markedly suppresses crosstalk errors, outperforming conventional ancilla control methods by orders of magnitude. These results provide guidance for experimentally achieving high-fidelity multimode operations and pave the way for developing high-performance bosonic quantum information processors.

arXiv:2403.00275•Physical Review Applied•Oct 25, 2024•20 citations

Multimode bosonic realization of the su(1,1) Lie algebra

Chi‐Fai Lo, K.L. Liu

We have constructed the multimode bosonic realization of the su(1,1) Lie algebra, on the basis of which the su(1,1) generalized coherent state in the multimode Fock space is derived. It is shown that the multimode coherent state is, in fact, the generalized multimode squeezed vacuum state discussed by Lo and Sollie [Phys. Rev. A 47, 733 (1993)], and that the unitary displacement operator can be identified as the generalized multimode squeezing operator. Hence, similar to the single- and two-mode cases, our multimode bosonic realization of the su(1,1) Lie algebra has immediate relevance to the squeezing properties of boson fields.

Physical Review A•Oct 1, 1993•11 citations
We present a general framework for generating single- and multimode qubit-conditional operations by extending cross-resonant driving to a generalized multimode scheme. This includes single-mode conditional displacements and squeezing induced by one- and two-photon cross-resonant drives in the presence of one- and two-photon qubit-oscillator interactions, respectively. In the multimode setting, we derive multimode qubit-conditional joint displacement, beamsplitter and two-mode squeezing operations. This framework enables the realization of arbitrary multimode qubit-conditional operations, which are of great importance to bosonic quantum error correction, phase estimation and quantum simulations.
We develop a general theory for multiphoton qubit-resonator interactions enhanced by a qubit drive. The interactions generate qubit-conditional operations in the resonator when the driving is near nnn-photon cross resonance, i.e., when the qubit drive is nnn times the resonator frequency. We pay special attention to the strong driving regime, where the resulting effective interactions are conditioned on the qubit dressed states. Next, we investigate the use of a two-tone drive to engineer an effective nnn-photon Rabi Hamiltonian with widely tunable effective system parameters, which could enable the realization of new regimes that have so far been inaccessible. Then, we discuss applications for the specific case where n=2n=2n=2, which results in qubit-conditional squeezing (QCS). We show that the QCS protocol can be used to generate a superposition of orthogonally squeezed states following a properly chosen qubit measurement. We outline quantum information processing applications for these states, including encoding a qubit in a resonator via the superposition of orthogonally squeezed states. We show how the QCS operation can be used to realize a controlled-squeeze gate and its use in bosonic phase estimation. The QCS protocol can also be utilized to achieve faster unitary operator synthesis on the joint qubit-resonator Hilbert space. Finally, we propose a multiphoton circuit QED implementation based on a transmon qubit coupled to a resonator via an asymmetric SQUID. We provide realistic parameter estimates for the two-photon operation regime that can host the aforementioned two-photon protocols. We use numerical simulations to show that, even in the presence of spurious terms and decoherence, our analytical predictions are robust.
We introduce a framework for simulating hybrid oscillator-qubit quantum processors on qubit-only systems through position encoding. By encoding continuous-variable position and momentum wave functions into qubit amplitudes, our method efficiently simulates all Gaussian and conditional Gaussian operations -- encompassing the phase-space instruction set (beam splitter, single-qubit rotation, conditional displacement) and extending to squeezing, conditional squeezing, conditional rotation, and conditional beam splitter -- using O ⁣(log⁡2 ⁣(Γ+log⁡(1/ε)))O\!\left(\log^2\!\left(Γ+ \log(1/ε)\right)\right)O(log2(Γ+log(1/ε))) qubit gates per hybrid gate, where ΓΓΓ is the Fock-level bound and εεε is the target precision. This polylogarithmic per-gate complexity represents an exponential improvement over Fock basis encoding approaches, which require exponential quantum or classical resources in the number of qubits per mode. We provide rigorous numerical characterization of quantum Fourier transform errors for Fock-bounded states, enabling precise resource estimation for practical implementations. This work establishes that hybrid oscillator-qubit algorithms can be implemented on qubit processors with polynomial overhead, providing new insights into the computational power trade-offs between discrete-variable and hybrid continuous-discrete-variable quantum computing.
Bosonic encoding is an approach for quantum information processing, promising lower hardware overhead by encoding in the many levels of a harmonic-oscillator mode. Scaling to multiple modes requires weak interaction for independent control, yet strong interaction for fast control. Applying fast and efficient universal control on multiple modes remains an open problem. Surprisingly, we find that displacements conditioned on the state of a single-qubit ancilla coupled to multiple harmonic oscillators are sufficient for universal control. We present the conditional- operation concept, which can be used to reduce the duration of entangling gates. Within this guiding concept, we develop the conditional- displacement control method which enables fast generation and control of bosonic states in multimode systems weakly coupled to a single-ancilla qubit. Our method is fast despite the weak ancilla coupling. The weak coupling in turn allows for excellent separability and thus independent control. We demonstrate our control on a superconducting transmon qubit weakly coupled to a multimode superconducting cavity. We create both entangled and separable cat states in different modes of the multimode cavity, showing entangling operations at low crosstalk while maintaining independent control of the different modes. We show that the operation time is not limited by the inverse of the coupling rate, which is the typical timescale, and we exceed it by almost 2 orders of magnitude. We verify our results with an efficient method for measurement of the multimode characteristic function which employs our conditional- displacement. Our results inspire a new approach toward general entangling operations and allow for fast and efficient multimode bosonic encoding and measurement. Published by the American Physical Society 2024
We present an implementation of a conditional-squeezing gate that squeezes a SQUID-terminated resonator mode along a direction determined by the state of a dispersively coupled qubit. This gate generalizes the controlled-squeezing gate [Phys. Rev. A \textbf{111}, 042606 (2025)], and relies on a refocusing technique to suppress unwanted effects arising from slowly varying time-dependent terms in the Hamiltonian during the state-dependent parametric resonance required for the operation. As an application, we use the gate to encode an arbitrary qubit state into superpositions of single- and two-mode squeezed states of the resonator. These non-Gaussian states enable error-detectable encoding through parity measurements. We show that refocusing substantially improves the encoding fidelity, which is ultimately limited by Kerr nonlinearities and dissipation in realistic implementations. For experimentally optimistic values of the nonlinearities and decay rates, we obtain encoding fidelities above 0.99 for arbitrary input qubit states. Our results provide a route toward extending this scheme to the generation of higher-order superpositions of squeezed states (a class of rotation-symmetric bosonic codes) using a control qudit.
High-coherence superconducting cavities offer a hardware-efficient platform for quantum information processing. To achieve universal operations of these bosonic modes, the requisite nonlinearity is realized by coupling them to a transmon ancilla. However, this configuration is susceptible to crosstalk errors in the dispersive regime, where the ancilla frequency is Stark shifted by the state of each coupled bosonic mode. This leads to a frequency mismatch of the ancilla drive, lowering the gate fidelities. To mitigate such coherent errors, we employ quantum optimal control to engineer ancilla pulses that are robust to the frequency shifts. These optimized pulses are subsequently integrated into a recently developed echoed conditional displacement protocol for executing single- and two-mode operations. Through numerical simulations, we examine two representative scenarios: the preparation of single-mode Fock states in the presence of spectator modes and the generation of two-mode entangled Bell-cat states. Our approach markedly suppresses crosstalk errors, outperforming conventional ancilla control methods by orders of magnitude. These results provide guidance for experimentally achieving high-fidelity multimode operations and pave the way for developing high-performance bosonic quantum information processors.
We have constructed the multimode bosonic realization of the su(1,1) Lie algebra, on the basis of which the su(1,1) generalized coherent state in the multimode Fock space is derived. It is shown that the multimode coherent state is, in fact, the generalized multimode squeezed vacuum state discussed by Lo and Sollie [Phys. Rev. A 47, 733 (1993)], and that the unitary displacement operator can be identified as the generalized multimode squeezing operator. Hence, similar to the single- and two-mode cases, our multimode bosonic realization of the su(1,1) Lie algebra has immediate relevance to the squeezing properties of boson fields.