arXiv subjects

Mohammad Ayyash

Publications and source records attributed to Mohammad Ayyash.

6 recordsLinked to original sources

arXiv2026

Reply to Comment on "Properties and dynamics of generalized squeezed states"

In our paper [1], our numerical simulations showed that, unlike displacement and conventional squeezing, higher-order squeezing exhibits oscillatory dynamics. Subsequently, Gordillo and Puebla pointed out that simulation results depend on whether the size of the state space in the simulations is even or odd [2]. Using additional derivations, they argued that the oscillatory dynamics is unphysical and that the photon number must increase monotonically as a function of the squeezing parameter $r$. We agree with the observation of an even-odd parity dependence in the simulations. We independently noticed the same feature in our simulations after the publication of Ref. [1]. This observation led us to perform a more detailed investigation of the numerical simulation and mathematical aspects of the generalized squeezing problem. Our new findings were reported in Ref. [3]. Further analysis was reported in Ref. [4]. Our conclusion is that the generalized squeezing operator is physically not well defined but can be made well defined when combined with additional information about the physical system under study. We demonstrated this point in the case where we include an additional nonlinear interaction term in the Hamiltonian. We disagree with the claim that the photon number must be a monotonically increasing function of $r$. This claim contradicts the mathematically rigorous results of Ref. [4]. Furthermore, we show that the oscillatory behaviour persists in two closely related, well-behaved models.

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arXiv2025

Fast Bosonic Control via Multiphoton Qubit-Oscillator Interactions

We present a protocol for preparing oscillator states with $n$-fold rotational symmetry, which include many logical codewords for bosonic quantum error correction codes. The protocol relies on a multiphoton interaction between the oscillator and an auxiliary qubit. Further, we achieve arbitrary control over the oscillator's Hilbert space by using a combination of different multiphoton interaction orders. We also discuss the preparation of rotationally symmetric multi-oscillator states using a generalized variant of the protocol. We show that the use of multiphoton qubit-oscillator interactions can substantially reduce the state preparation time, in comparison to the linear qubit-oscillator interactions that are usually employed. Furthermore, we perform numerical simulations that take into account qubit and oscillator relaxation and dephasing using realistic planar superconducting circuit parameters that validate the robustness of our protocol. Our findings can significantly improve the performance of bosonic codes on planar superconducting hardware, which are an almost inevitable necessity for scalable bosonic fault-tolerant superconducting quantum computers.

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arXiv2025

Multimode Qubit-Conditional Operations via Generalized Cross-Resonance

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.

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arXiv2025

Dispersive regime of multiphoton qubit-oscillator interactions

The dispersive regime of $n$-photon qubit-oscillator interactions is analyzed using Schrieffer-Wolff perturbation theory. Effective Hamiltonians are derived up to the second order in the perturbation parameters. These effective descriptions reveal higher-order qubit-oscillator cross-Kerr and oscillator self-Kerr terms. The cross-Kerr term combines a qubit Pauli operator with an $n$-degree polynomial in the oscillator photon number operator, while the self-Kerr term is an $(n-1)$-degree polynomial in the oscillator photon number operator. In addition to the higher-order Kerr terms, a qubit-conditional $2n$-photon squeezing term appears in the effective non-rotating-wave-approximation Hamiltonian. Furthermore, perturbation theory is applied to the case of multiple qubits coupled to a shared oscillator. A photon-number-dependent qubit-qubit interaction emerges in this case, which can be leveraged to tune the effective multiqubit system parameters using the oscillator state. Results for the converse setup of multiple oscillators and a single qubit are also derived. In this case, a qubit-conditional oscillator-oscillator nonlinear interaction is found. The spectral instabilities plaguing multiphoton qubit-oscillator models are carefully treated by introducing stabilizing higher-order terms in the Hamiltonian. The stabilizing terms preserve low-photon subspaces, avoid negative infinite energies and facilitate reliable numerical calculations used to validate analytical predictions. The effective descriptions developed here offer a simple and intuitive physical picture of dispersive multiphoton qubit-oscillator interactions that can aid in the design of implementations harnessing their various nonlinear effects.

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arXiv2025

Properties and dynamics of generalized squeezed states

We analyze the properties and dynamics of generalized squeezed states. We find that, in stark contrast to displacement and two-photon squeezing, higher-order squeezing leads to oscillatory dynamics. The state is squeezed in the initial stages of the dynamics but the squeezing reverses at later stages, and the state reverts almost completely back to the initial state. We analyze various quantities to verify that the oscillatory dynamics is physical and not a mathematical artefact. We also show that the maximum squeezing diminishes with increasing squeezing order, rendering the squeezing mechanism increasingly ineffective. Our results provide important rules that can help guide the development of more effective higher-order squeezing techniques.

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arXiv2024

Driven Multiphoton Qubit-Resonator Interactions

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, namely, the qubit drive is $n$-times the resonator frequency. We pay special attention to the strong driving regime, where the interactions are conditioned on the qubit dressed states. We consider 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. 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. 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.

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