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

npj Quantum Information

Efficient bosonic nonlinear phase gates

Ki-min Park B, Radim Filip

Published Feb 23, 2024• 6 citations
Publisher

Abstract

Abstract Continuous-variable (CV) quantum information processing harnesses versatile experimental tools that leverage the power of infinite-dimensional oscillators controlled by a single qubit. Increasingly available elementary Rabi gates have been proposed as a resource for implementing universal CV gates, but the requirement of many weak, non-commuting gates is a bottleneck in scaling up such an approach. In this study, we propose a resource-efficient technique using Fourier expansion to implement arbitrary non-linear phase gates in a single oscillator. This method reduces the number of sequentially required gates exponentially. These gates represented by cubic, quartic, and other arbitrary nonlinear potentials have applications in CV quantum information processing with infinite-dimensional oscillators controlled by a single qubit. Our method outperforms previous approaches and enables the experimental realization of a wide range of applications, including the development of bosonic quantum sensors, simulations, and computation using trapped ions and superconducting circuits.

DOI
10.1038/s41534-024-00816-x

Related papers

Near-optimal synthesis of non-Gaussian phase gates via qubit-oscillator Rabi control

Zhen Yang, Shan Jin, Zi-Wen Liu +1 more

Non-Gaussian gates remain a key bottleneck for universal continuous-variable (CV) quantum computation because the nonlinearities they require are difficult to engineer. To address this challenge, we develop an efficient qubit-oscillator Rabi synthesis scheme for polynomial phase gates, with a total interaction time that scales polylogarithmically with the inverse target error \(\varepsilon\). Specifically, for a class of readily preparable initial states, we show that a degree-\(R\) phase gate can be approximated by an analytically constructed Rabi sequence with total time \(O(\log^{(R-1)/2+o(1)}(1/\varepsilon))\). This construction requires no numerical optimization and therefore extends naturally to arbitrarily large multimode systems. We further establish a total-time lower bound of \(Ω(\log^{(R-1)/2}(1/\varepsilon))\), showing that the synthesis is near optimal. As applications, we use this scheme to simulate representative CV quantum dynamics and implement a CV quantum algorithm for solving linear partial differential equations. These results establish qubit-oscillator Rabi control as an efficient, analytically compilable, and near-optimal primitive for CV quantum information processing.

quant-pharXiv:2609.09132•Sep 9, 2026•0 citations

Programmable generation of arbitrary continuous-variable anharmonicities and nonlinear couplings

Teerawat Chalermpusitarak, Kai Schwennicke, Ivan Kassal +1 more

Harmonic oscillators are promising continuous-variable (CV) quantum resources because their infinite-dimensional Hilbert spaces allow for resource-efficient quantum computing and simulation. To reach their full potential, CV platforms need to be able to efficiently implement non-Gaussian operations. Bosonic quantum-signal-processing schemes have emerged as attractive methods to construct arbitrary non-Gaussian operations; however, these schemes are restricted to single modes, i.e., the implementation of anharmonic potentials. Here, we introduce trigonometric-gate-implemented Fourier synthesis (TGIFS), a method for implementing arbitrary non-Gaussian operations applicable to both single- and multi-mode systems, allowing the generation of both anharmonicities and nonlinear multi-mode couplings. TGIFS synthesizes a target Hamiltonian by decomposing it into a Fourier series whose terms are implemented via bosonic quantum signal processing, which uses a discrete-variable (DV) system to induce a nonlinearity in the CV system. Our hybrid CV-DV protocol allows for the direct simulation of a broad range of CV phenomena (such as those in lattice gauge theory, chemical dynamics, and quantum chaos) and provides a richer toolbox for CV circuit compilation.

quant-pharXiv:2511.22286•Nov 28, 2025•0 citations

Cubic Phase Gate with a Trapped Ion Oscillator

Nigel Benjamin Lee Junsheng, Eugene Koh Jun Wei, Mu Young Kim +1 more

The motional modes of trapped ions are promising candidates for continuous-variable (CV) quantum computation and simulation. However, to achieve a universal gate set for CV quantum computation, anharmonic nonlinear unitaries are required. Here, we experimentally demonstrate a protocol that allows us to approximate the cubic phase gate. By numerically optimizing the phase angles and amplitudes of a set of state-dependent force pulses, we demonstrate the cubic phase gate for both vacuum and low-$α$ coherent state inputs and verify its performance. Our protocol can also be extended to approximate other nonlinear unitaries.

quant-pharXiv:2609.34774•Sep 29, 2026•0 citations

Deterministic nonlinear phase gates induced by a single qubit

Ki-min Park B, Petr Marek, Radim Filip

We propose deterministic realizations of nonlinear phase gates by repeating a finite sequence of non-commuting Rabi interactions between a harmonic oscillator and only a single two-level ancillary qubit. We show explicitly that the key nonclassical features of the ideal cubic phase gate and the quartic phase gate are generated in the harmonic oscillator faithfully by our method. We numerically analyzed the performance of our scheme under realistic imperfections of the oscillator and the two-level system. The methodology is extended further to higher-order nonlinear phase gates. This theoretical proposal completes the set of operations required for continuous-variable quantum computation.

arXiv:1706.09660•New Journal of Physics•Apr 4, 2018•21 citations

Building Block For Universal Continuous Variables Computation In Superconducting Devices

Bruno A. Veloso, Ciro M. Diniz, Luiz O. R. Solak +3 more

Continuous variable (CV) quantum computation offers an alternative to qubit-based computing by exploiting the infinite-dimensional Hilbert space of bosonic modes. Despite recent progress, superconducting platforms have yet to demonstrate a scalable architecture capable of universal computation. Here, we design and numerically simulate a two-layer superconducting architecture that implements all five interactions of the universal CV gate set (rotation, displacement, squeezing, Kerr, and beam splitter) within experimentally accessible regimes. To this end, we employ a DC-SQUID as the bosonic mode, a fluxonium qubit to mediate nonlinear interactions, and two ancillary qubits that enable Gaussian and multi-mode operations. By tuning fluxes and frequencies, we achieve high fidelities ($\geq 98\%$) across all gates within state-of-the-art parameter ranges. The modular nature of the design allows straightforward scaling, establishing a feasible pathway toward high-fidelity, universal CV quantum computation based on superconducting circuits.

quant-pharXiv:2604.00212•Apr 2, 2026•0 citations

Efficient quantum simulation of nonlinear interactions using SNAP and Rabi gates

Ki-min Park B, Petr Marek, Radim Filip

Abstract Quantum simulations provide means to probe challenging problems within controllable quantum systems. However, implementing or simulating deep-strong nonlinear couplings between bosonic oscillators on physical platforms remains a challenge. We present a deterministic simulation technique that efficiently and accurately models nonlinear bosonic dynamics. This technique alternates between tunable Rabi and SNAP gates, both of which are available on experimental platforms such as trapped ions and superconducting circuits. Our proposed simulation method facilitates high-fidelity modeling of phenomena that emerge from higher-order bosonic interactions, with an exponential reduction in resource usage compared to other techniques. We demonstrate the potential of our technique by accurately reproducing key phenomena and other distinctive characteristics of ideal nonlinear optomechanical systems. Our technique serves as a valuable tool for simulating complex quantum interactions, simultaneously paving the way for new capabilities in quantum computing through the use of hybrid qubit-oscillator systems.

arXiv:2312.09936•Quantum Science and Technology•Jan 16, 2024•3 citations
Abstract Continuous-variable (CV) quantum information processing harnesses versatile experimental tools that leverage the power of infinite-dimensional oscillators controlled by a single qubit. Increasingly available elementary Rabi gates have been proposed as a resource for implementing universal CV gates, but the requirement of many weak, non-commuting gates is a bottleneck in scaling up such an approach. In this study, we propose a resource-efficient technique using Fourier expansion to implement arbitrary non-linear phase gates in a single oscillator. This method reduces the number of sequentially required gates exponentially. These gates represented by cubic, quartic, and other arbitrary nonlinear potentials have applications in CV quantum information processing with infinite-dimensional oscillators controlled by a single qubit. Our method outperforms previous approaches and enables the experimental realization of a wide range of applications, including the development of bosonic quantum sensors, simulations, and computation using trapped ions and superconducting circuits.
Non-Gaussian gates remain a key bottleneck for universal continuous-variable (CV) quantum computation because the nonlinearities they require are difficult to engineer. To address this challenge, we develop an efficient qubit-oscillator Rabi synthesis scheme for polynomial phase gates, with a total interaction time that scales polylogarithmically with the inverse target error ε\varepsilonε. Specifically, for a class of readily preparable initial states, we show that a degree-RRR phase gate can be approximated by an analytically constructed Rabi sequence with total time O(log⁡(R−1)/2+o(1)(1/ε))O(\log^{(R-1)/2+o(1)}(1/\varepsilon))O(log(R−1)/2+o(1)(1/ε)). This construction requires no numerical optimization and therefore extends naturally to arbitrarily large multimode systems. We further establish a total-time lower bound of Ω(log⁡(R−1)/2(1/ε))Ω(\log^{(R-1)/2}(1/\varepsilon))Ω(log(R−1)/2(1/ε)), showing that the synthesis is near optimal. As applications, we use this scheme to simulate representative CV quantum dynamics and implement a CV quantum algorithm for solving linear partial differential equations. These results establish qubit-oscillator Rabi control as an efficient, analytically compilable, and near-optimal primitive for CV quantum information processing.
Harmonic oscillators are promising continuous-variable (CV) quantum resources because their infinite-dimensional Hilbert spaces allow for resource-efficient quantum computing and simulation. To reach their full potential, CV platforms need to be able to efficiently implement non-Gaussian operations. Bosonic quantum-signal-processing schemes have emerged as attractive methods to construct arbitrary non-Gaussian operations; however, these schemes are restricted to single modes, i.e., the implementation of anharmonic potentials. Here, we introduce trigonometric-gate-implemented Fourier synthesis (TGIFS), a method for implementing arbitrary non-Gaussian operations applicable to both single- and multi-mode systems, allowing the generation of both anharmonicities and nonlinear multi-mode couplings. TGIFS synthesizes a target Hamiltonian by decomposing it into a Fourier series whose terms are implemented via bosonic quantum signal processing, which uses a discrete-variable (DV) system to induce a nonlinearity in the CV system. Our hybrid CV-DV protocol allows for the direct simulation of a broad range of CV phenomena (such as those in lattice gauge theory, chemical dynamics, and quantum chaos) and provides a richer toolbox for CV circuit compilation.
The motional modes of trapped ions are promising candidates for continuous-variable (CV) quantum computation and simulation. However, to achieve a universal gate set for CV quantum computation, anharmonic nonlinear unitaries are required. Here, we experimentally demonstrate a protocol that allows us to approximate the cubic phase gate. By numerically optimizing the phase angles and amplitudes of a set of state-dependent force pulses, we demonstrate the cubic phase gate for both vacuum and low-ααα coherent state inputs and verify its performance. Our protocol can also be extended to approximate other nonlinear unitaries.
We propose deterministic realizations of nonlinear phase gates by repeating a finite sequence of non-commuting Rabi interactions between a harmonic oscillator and only a single two-level ancillary qubit. We show explicitly that the key nonclassical features of the ideal cubic phase gate and the quartic phase gate are generated in the harmonic oscillator faithfully by our method. We numerically analyzed the performance of our scheme under realistic imperfections of the oscillator and the two-level system. The methodology is extended further to higher-order nonlinear phase gates. This theoretical proposal completes the set of operations required for continuous-variable quantum computation.
Continuous variable (CV) quantum computation offers an alternative to qubit-based computing by exploiting the infinite-dimensional Hilbert space of bosonic modes. Despite recent progress, superconducting platforms have yet to demonstrate a scalable architecture capable of universal computation. Here, we design and numerically simulate a two-layer superconducting architecture that implements all five interactions of the universal CV gate set (rotation, displacement, squeezing, Kerr, and beam splitter) within experimentally accessible regimes. To this end, we employ a DC-SQUID as the bosonic mode, a fluxonium qubit to mediate nonlinear interactions, and two ancillary qubits that enable Gaussian and multi-mode operations. By tuning fluxes and frequencies, we achieve high fidelities (≥98%\geq 98\%≥98%) across all gates within state-of-the-art parameter ranges. The modular nature of the design allows straightforward scaling, establishing a feasible pathway toward high-fidelity, universal CV quantum computation based on superconducting circuits.
Abstract Quantum simulations provide means to probe challenging problems within controllable quantum systems. However, implementing or simulating deep-strong nonlinear couplings between bosonic oscillators on physical platforms remains a challenge. We present a deterministic simulation technique that efficiently and accurately models nonlinear bosonic dynamics. This technique alternates between tunable Rabi and SNAP gates, both of which are available on experimental platforms such as trapped ions and superconducting circuits. Our proposed simulation method facilitates high-fidelity modeling of phenomena that emerge from higher-order bosonic interactions, with an exponential reduction in resource usage compared to other techniques. We demonstrate the potential of our technique by accurately reproducing key phenomena and other distinctive characteristics of ideal nonlinear optomechanical systems. Our technique serves as a valuable tool for simulating complex quantum interactions, simultaneously paving the way for new capabilities in quantum computing through the use of hybrid qubit-oscillator systems.