While quantum simulators promise to explore quantum many-body physics beyond classical computation, their capabilities are limited by the available native interactions in the hardware. On many platforms, accessible Hamiltonians are largely restricted to one- and two-body interactions, limiting access to multi-body Hamiltonians and to systems governed by simultaneous, non-commuting interaction terms that are central to condensed matter, quantum chemistry, and high-energy physics. We introduce and experimentally demonstrate a hybrid digital-analog protocol that overcomes these limitations by embedding analog evolution between shallow entangling-gate layers. This method produces effective Hamiltonians with simultaneous non-commuting three- and four-body interactions that are generated non-perturbatively and without Trotter error -- capabilities not practically attainable on near-term hardware using purely digital or purely analog schemes. We implement our scheme on a trapped-ion quantum processor and use it to realize a topological spin chain exhibiting prethermal strong zero modes persisting at high temperature, as well as models featuring three- and four-body interactions. Our hardware-agnostic and scalable method opens new routes to realizing complex many-body physics across quantum platforms.
While quantum simulators promise to explore quantum many-body physics beyond classical computation, their capabilities are limited by the available native interactions in the hardware. On many platforms, accessible Hamiltonians are largely restricted to one- and two-body interactions, limiting access to multi-body Hamiltonians and to systems governed by simultaneous, non-commuting interaction terms that are central to condensed matter, quantum chemistry, and high-energy physics. We introduce and experimentally demonstrate a hybrid digital-analog protocol that overcomes these limitations by embedding analog evolution between shallow entangling-gate layers. This method produces effective Hamiltonians with simultaneous non-commuting three- and four-body interactions that are generated non-perturbatively and without Trotter error -- capabilities not practically attainable on near-term hardware using purely digital or purely analog schemes. We implement our scheme on a trapped-ion quantum processor and use it to realize a topological spin chain exhibiting prethermal strong zero modes persisting at high temperature, as well as models featuring three- and four-body interactions. Our hardware-agnostic and scalable method opens new routes to realizing complex many-body physics across quantum platforms.
Universal digital quantum computers are able to approximate any Hamiltonian evolution as a digital quantum circuit consisting of discrete time steps. Strongly interacting physics models, for example in high-energy physics or materials science, make this a challenging task for near-term devices as they place a high demand on the quantum resources required [1]. One alternative is analog quantum simulation where the native evolution of a quantum system can be tailored to mimic that of the model of interest. While more efficient at specific problems, there are limits on the types of evolution available and on the observables that can be measured. In this conference paper we present first results towards unifying these two concepts in a trapped-ion experiment. Trapped atomic ions are one of the most advanced experimental platforms for both analog quantum simulation and digital quantum computing. Typically, the internal spin degrees of freedom are used qubits or for the simulation of spin models. The harmonic oscillator modes given by the motion of the ions in the trap are only employed transiently to create quantum gates or spin-spin interactions. However, these motional modes constitute a large Hilbert space themselves and present a bosonic degree of freedom, which is costly to model with qubits. Many systems of interest, for example Lattice gauge theories, require both spin and boson degrees of freedom. It was recently shown that they can be encoded more efficiently using the harmonic oscillator modes directly [2].
Analog quantum simulators emulate complex many-body dynamics through native continuous-time evolution under hardware-defined interactions. Yet once a platform is specified, its interaction structure is largely fixed by the underlying hardware, restricting the Hamiltonians that can be realized and limiting programmability. Here we introduce universal analog quantum simulation (UAQS), a hybrid framework that systematically expands the range of accessible quantum evolutions within a given analog platform. UAQS employs optimized continuous-time control fields to engineer target dynamics directly, avoiding decomposition into discrete gate sequences. By preserving native analog evolution while extending the set of achievable Hamiltonians, UAQS transforms fixed-interaction analog devices into programmable simulators. Numerical studies on representative architectures, including superconducting circuits and Rydberg-atom arrays, show that UAQS accurately reproduces non-trivial many-body dynamics beyond the intrinsic interaction structure of the hardware. These results establish UAQS as a practical route toward programmable analog quantum simulation.
Quantum field theories are the cornerstones of modern physics, providing relativistic and quantum mechanical descriptions of physical systems at the most fundamental level. Simulating real-time dynamics within these theories remains elusive in classical computing. This provides a unique opportunity for quantum simulators, which hold the promise of revolutionizing our simulation capabilities. Trapped-ion systems are successful quantum-simulator platforms for quantum many-body physics and can operate in digital, or gate-based, and analog modes. Inspired by the progress in proposing and realizing quantum simulations of a number of relativistic quantum field theories using trapped-ion systems, and by the hybrid analog-digital proposals for simulating interacting boson-fermion models, we propose hybrid analog-digital quantum simulations of selected quantum field theories, taking recent developments to the next level. On one hand, the semi-digital nature of this proposal offers more flexibility in engineering generic model interactions compared with a fully-analog approach. On the other hand, encoding the bosonic fields onto the phonon degrees of freedom of the trapped-ion system allows a more efficient usage of simulator resources, and a more natural implementation of intrinsic quantum operations in such platforms. This opens up ways for simulating complex dynamics of, e.g., Abelian and non-Abelian gauge theories, by combining the benefits of digital and analog schemes.
We introduce a digital-analog quantum computing framework that enables counterdiabatic protocols to be implemented at constant circuit depth, allowing fast and resource-efficient quantum state preparation on current quantum hardware. Counterdiabatic protocols suppress diabatic excitations in finite-time adiabatic evolution, but their practical application is limited by the non-local structure of the required Hamiltonians and the resource overhead of fully digital implementations. Counterdiabatic terms can be expressed as truncated expansions of nested commutators of the adiabatic Hamiltonian and its parametric derivative. Here, we show how this algebraic structure can be efficiently realized in a digital-analog setting using commutator product formulas. Using native multi-qubit analog interactions augmented by local single-qubit rotations, this approach enables higher-order counterdiabatic protocols whose implementation requires a constant number of analog blocks for any fixed truncation order, independent of system size. We demonstrate the method for two-dimensional spin models and analyze the associated approximation errors. These results show that digital-analog quantum computing enables a qualitatively new resource scaling for counterdiabatic protocols and related quantum control primitives, with direct implications for quantum simulation, optimization, and algorithmic state preparation on current quantum devices.
To investigate gauge theories with near-term quantum computers warrants exploration of nontraditional quantum simulators to find resource-efficient simulation protocols and ultimately access exotic features of different field theories, including unexplored regimes of the QCD phase diagram. In this work, using superconducting transmon qutrit processors, we formulate and implement a pulse-based, three-level, hybrid analog-digital simulation protocol of the (1+1) dimensional Abelian Higgs model (AHM) on two sites. Alongside this approach, we experimentally realize a gate-based implementation of the same model. Using the natural mapping of the three-level truncation of the transmon Hilbert space to the spin-1 truncated AHM, we observe real time dynamics of AHM field observables, which are analogous to electric field operators, with both protocols. For the analog-digital protocol, we engineer a Floquet simulation with a combination of local analog drives, driven modification of the natural interaction Hamiltonian of the two transmons, and dynamical decoupling pulses. For the digital protocol, we use a state-of-the-art qutrit processor to implement a Trotterized simulation of the model incorporating advanced error mitigation techniques. We further discuss the scalability of the two approaches, and their potential to be extended to the simulation of other model Hamiltonians. Our experiments demonstrate a viable platform for future studies of spin-1 and SU(3) based gauge theory models on current and near-term transmon qutrit processors.
Digital-analog quantum computation aims to reduce the currently infeasible resource requirements needed for near-term quantum information processing by replacing sequences of one-and two-qubit gates with a unitary transformation generated by the systems' underlying Hamiltonian.Inspired by this paradigm, we consider superconducting architectures and extend the cross-resonance effect, up to first order in perturbation theory, from a two-qubit interaction to an analog Hamiltonian acting on onedimensional (1D) chains and two-dimensional (2D) square lattices, which, in an appropriate reference frame, results in a purely two-local Hamiltonian.By augmenting the analog Hamiltonian dynamics with single-qubit gates we show how one may generate a larger variety of distinct analog Hamiltonians.We then synthesize unitary sequences, in which we toggle between the various analog Hamiltonians as needed, simulating the dynamics of Ising, XY, and Heisenberg spin models.Our dynamics simulations are Trotter error-free for the Ising and XY models in 1D.We also show that the Trotter errors for 2D XY and 1D Heisenberg chains are reduced, with respect to a digital decomposition, by a constant factor.In order to realize these important near-term speedups, we discuss the practical considerations needed to accurately characterize and calibrate our analog Hamiltonians for use in quantum simulations.We conclude with a discussion of how the Hamiltonian toggling techniques could be extended to derive new analog Hamiltonians, which may be of use in more complex digital-analog quantum simulations for various models of interacting spins.