Programmable quantum simulation of anharmonic dynamics
Cameron McGarry, Teerawat Chalermpusitarak, Kai Schwennicke, Frank Scuccimarra, Maverick J. Millican, Vassili G. Matsos, Christophe H. Valahu, Prachi Nagpal, Hon-Kwan Chan, Henry L. Nourse, Ivan Kassal, Ting Rei Tan
quant-phSubmitted Mar 5, 2026• Announced Mar 6, 2026• 0 citations
Continuous-variable-discrete-variable (CV-DV) quantum simulators offer a natural route to simulating bosonic dynamics relevant to many branches of physics and chemistry. However, programmable simulation of arbitrary dynamics is an outstanding challenge. In particular, simulating anharmonic dynamics, which is ubiquitous across the physical sciences, is challenging due to the highly harmonic nature of oscillators used in CV-DV simulators. Here, we experimentally demonstrate programmable CV-DV quantum simulation of anharmonic dynamics in a range of double-well potentials, implemented in a trapped-ion system. We synthesise the time-evolution operators using a bosonic-quantum-signal-processing subroutine, which allows the potential to be tuned between experiments by controlling classical experimental parameters. We observe coherent dynamics in various double-well potentials, where a wavepacket tunnels through the potential barrier, and we suppress this effect by programmatically introducing asymmetry.
Continuous-variable-discrete-variable (CV-DV) quantum simulators offer a natural route to simulating bosonic dynamics relevant to many branches of physics and chemistry. However, programmable simulation of arbitrary dynamics is an outstanding challenge. In particular, simulating anharmonic dynamics, which is ubiquitous across the physical sciences, is challenging due to the highly harmonic nature of oscillators used in CV-DV simulators. Here, we experimentally demonstrate programmable CV-DV quantum simulation of anharmonic dynamics in a range of double-well potentials, implemented in a trapped-ion system. We synthesise the time-evolution operators using a bosonic-quantum-signal-processing subroutine, which allows the potential to be tuned between experiments by controlling classical experimental parameters. We observe coherent dynamics in various double-well potentials, where a wavepacket tunnels through the potential barrier, and we suppress this effect by programmatically introducing asymmetry.
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.
Continuous-variable quantum systems offer a natural platform for quantum information processing and analogue quantum simulation of real-world processes. Realising these applications, however, requires anharmonic potentials with programmable functional forms, which are challenging to engineer on demand. Here, in a superconducting harmonic oscillator coupled to a transmon qubit, we construct programmable non-Gaussian phase gates e−iV(X^), corresponding to the impulsive action of an anharmonic potential V(X^), and characterise them by reconstructing their corresponding force pointwise. Using bosonic quantum signal processing, we compile target potentials into modular circuits of qubit rotations interleaved with a fixed conditional-displacement primitive. We first demonstrate a cubic phase gate whose cubic nature is jointly validated by the resulting non-Gaussian states and the force reconstructed pointwise from the gate's action on coherent probe states. We then construct a family of double-well potentials and use the reconstructed force to witness the double-well topology and tunable asymmetry. Finally, we engineer an approximate Morse potential and obtain its force profile using position-compressed probes, which extend reliable reconstruction towards the steep repulsive wall. These results establish a programmable route to constructing the potential landscape of quantum harmonic oscillators and a practical method for reconstructing its spatial structure, providing a building block for quantum simulation of anharmonic dynamics.
This tutorial offers a pedagogical guide to hybrid quantum processors that integrate discrete-variable (DV) qubits and continuous-variable (CV) oscillators. Aimed at computer scientists, engineers, and physicists, it provides an overview of the experimental, algorithmic, and architectural aspects of this novel and rapidly developing hardware model. Experimental realizations of this model include superconducting, trapped-ion, and neutral-atom platforms. By combining DV and CV components, hybrid oscillator-qubit processors enable a powerful new paradigm that offers complementary strengths for quantum control, error correction, computation, and simulation. Working toward the goal of a full-stack system connecting applications to CV-DV hardware, we define and formulate abstract machine models and instruction set architectures. These essential abstractions enable codesign of hardware and software, and resource estimation for exploring the potential of current and future hardware for computational and simulation tasks. Using these abstractions, we present both new and existing examples that illustrate the benefits of hybrid CV-DV processors relative to traditional DV-only hardware in computation as well as quantum simulation of physical models. Examples include algorithms for transferring states between DV and CV systems, performing the quantum Fourier transform, and simulation of lattice gauge theories. Relative to qubit-only hardware, the bosonic degrees of freedom natively available in hybrid architectures can substantially reduce the circuit complexity of simulations for physical models containing bosons. A key technique is the extension of quantum signal processing ideas to CV-DV systems. This work is intended to serve as a timely and comprehensive guide to this relatively unexplored yet promising approach to quantum computation and to provide a road map to guide future development.
Hybrid continuous-variable (CV)-discrete-variable (DV) quantum systems present a promising direction for quantum computing by combining the high dimensional encoding capabilities of qumodes with the control offered by DV qubits on the coupled qumodes. There have been exciting recent progresses on hybrid CV-DV quantum computing, including variational algorithms, error correction, compiler-level optimizations for Hamiltonian simulation, etc. However, there is a lack of a standardized CV-DV benchmark suite for assessing various emerging hardware platforms and evaluating software optimizations on hybrid CV-DV circuits. In this work, we introduce a simulation and benchmarking framework for hybrid CV-DV circuits, implemented using Bosonic Qiskit-a tool specifically designed to model CV-DV systems, along with QuTip for functional correctness verification. We construct and characterize representative CV-DV benchmarks, including cat state generation, GKP state generation, CV-DV state transfers, hybrid quantum Fourier transform, variational quantum algorithms, Hamiltonian simulation, and Shor's algorithm. To assess circuit complexity and scalability, we define a feature map organized into two categories: general features (e.g., qubit/qumode count, gate counts) and CV-DV-specific features (e.g., Wigner negativity, energy, truncation cost). These metrics enable evaluation of both classical simulability and hardware resource requirements. Our results, including one benchmark on real hardware, demonstrate that hybrid CV-DV architectures are not only viable but well-suited for a range of computational tasks, from optimization to Hamiltonian simulation. This framework lays the groundwork for systematic evaluation and future development of hybrid quantum systems.
Gaussian wavepacket (GWP) methods are prevalent means of solving the nuclear time-dependent Schrodinger equation (TDSE) on classical computers. They consist of representing the nuclear wave function as a superposition of Gaussians. Here, we present a variational hybrid continuous-variable discrete-variable (CV-DV) algorithm for simulating adiabatic nuclear dynamics on qubit-oscillator quantum hardware. It encodes a superposition of frozen Gaussians (FGs) onto the qubit-oscillator register and evolves it according to the time-dependent variational principle (VP). We test two variants of the approach, one that evolves a single FG and another that evolves a superposition of FGs, on a set of prototypical 1D harmonic and anharmonic systems. We simulate the photoexcited state dynamics of SO2 using the single FG variant of the algorithm and compute its autocorrelation function on physical quantum hardware. For harmonic and Morse potentials, the variant evolving the superposition of FGs converges to the numerically exact solution as the number of Gaussians increases. In the case of the double-well potential, the algorithm simulates wavepacket bifurcation and recurrence correctly, and the ensuing irregular dynamics moderately well. Overall, this work establishes a pathway for simulating molecular dynamics on noisy intermediate-scale quantum devices.
Anharmonic potential quantum system play crucial role in physics as they provide a more realistic description of oscillatory phenomena, which often deviate from the idealized harmonic model. However, simulating such system on classical computers is highly challenging due to nonlinear interactions, large state spaces, and the exponential scaling of memory and computational resources. In this work, quantum simulation is employed to model a quantum anharmonic oscillator (QAHO) using a 3-qubit system implemented on IBM's Quantum Experiences platform. A quantum circuit with a filter-based design and Toffoli gates is constructed to track quantum state evolution, capturing key phenomena like quantum revival. The framework is further extended to n-qubit system to enhance resolution and scalability. For energy estimation, the Variational Quantum Eigensolver (VQE) with a TwoLocal ansatz and variational Quantum Deflation (VQD), are used to compute ground and excited state energies. The proposed approach achieves high accuracy with an error of only 1.11% compared to exact methods. Notably, VQE outperforms classical approximations such as perturbation theory (error 6.71%) and the Wentzel-Kramers-Brillouin (WKB) approximation(error 5.36%), yielding more precise energy values. These results highlight the potential of quantum simulation and VQD as effective tools for investigating complex quantum system, paving the way for future application in quantum chemistry and materials science as quantum hardware continues to advance.