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arXiv:2406.15557 · Nature Communications

Observation of a non-Hermitian supersonic mode on a trapped-ion quantum computer

Yuxuan Zhang, Juan Carrasquilla, Yong Baek Kim

Published Apr 6, 2025• 15 citations
arXivHTMLPDF

Abstract

Quantum computers have long been anticipated to excel in simulating quantum many-body physics. In this work, we demonstrate the power of variational quantum circuits for resource-efficient simulations of dynamical and equilibrium physics in non-Hermitian systems. Using a variational quantum compilation scheme for fermionic systems, we reduce gate count, save qubits, and eliminate the need for postselection, a major challenge in simulating non-Hermitian dynamics via standard Trotterization. On the Quantinuum H1 trapped-ion processor, we experimentally observed a supersonic mode on an n = 18 fermionic chain after a non-Hermitian, nearest-neighbor interacting quench, which would otherwise be forbidden in a Hermitian system. Additionally, we investigate sequential quantum circuits generated by tensor networks for ground-state preparation using a variance minimization scheme, accurately capturing correlation functions and energies across an exceptional point on a dissipative spin chain up to length n = 20 using only 3 qubits. On the other hand, we provide an analytical example demonstrating that simulating single-qubit non-Hermitian dynamics for $$\Theta (\log (n))$$ time from certain initial states is exponentially hard on a quantum computer. Our work raises many intriguing questions about the intrinsic properties of non-Hermitian systems that permit efficient quantum simulation. Quantum simulation of non-Hermitian systems is non-trivial, as the use of Trotterization would incur into a huge sampling overhead. Here, the authors use a variational approach to simulate a quench in a 18-site fermionic chain on a trapped-ion quantum processor, seeing the signature of a supersonic mode in the connected density-density correlation function and providing insights on when quantum computers fail to simulate non-Hermitian dynamics.

DOI
10.1038/s41467-025-57930-3

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Abstract Quantum simulation on noisy intermediate-scale quantum (NISQ) hardware is limited by short coherence time and gate errors. We present a universal variational compilation optimization method (VCOM) that directly leverages the native gate set of trapped-ion processors, namely single-qubit rotations and global Ising-type XX interactions, to construct shallow circuits for simulating molecular Hamiltonians. Specifically, VCOM employs a hybrid optimization strategy combining genetic algorithms with gradient-based refinement to compile Pauli string evolution operators e −i Pt , thereby substantially reducing circuit depth and multi-qubit gate overhead in Hamiltonian simulation. Applied to hydrogen chains, the compiled circuits achieve fidelities comparable to standard decompositions while reducing the proportion of two-qubit operations to only 1.9%–4.6% of the total native gates, a significant improvement over the standard second-order Trotter–Suzuki product formula. Under experimentally motivated laser-intensity and phase-noise models, the proposed scheme maintains high fidelity and exhibits significantly slower degradation than direct native gate decompositions of conventional circuits. These results establish native-gate-based variational compilation as a scalable and practical approach for digital quantum simulation on trapped-ion platforms, with potential extensions to strongly correlated systems and non-equilibrium dynamics.
Ground-state preparation for a given Hamiltonian is a common quantum-computing task of great importance and has relevant applications in quantum chemistry, computational material modeling, and combinatorial optimization. We consider an approach to simulate dissipative non-Hermitian Hamiltonian quantum dynamics using Hamiltonian simulation techniques to efficiently recover the ground state of a target Hamiltonian. The proposed method facilitates the energy transfer by repeatedly projecting ancilla qubits to the desired state, rendering the effective non-Hermitian Hamiltonian evolution on the system qubits. To make the method more resource friendly in the noisy intermediate-scale quantum (NISQ) and early fault-tolerant era, we combine the non-Hermitian projection algorithm with multiple variational gadgets, including variational module enhancement and variational state recording, to reduce the required circuit depth and avoid the exponentially vanishing success probability for postselections. We compare our method, the non-Hermitian-variational algorithm, with a pure variational method, the quantum approximate optimization algorithm (QAOA), for solving the 3-SAT problem and preparing the ground state for the transverse field Ising model. As demonstrated by numerical evidence, the non-Hermitian-variational algorithm outperforms QAOA in convergence speed with improved quantum resource efficiency.
Simulating the time evolution of quantum systems is a classically challenging and often intractable task due to the exponential scaling of its constituent operators. This scaling makes it a promising application for quantum computation, especially for correlated systems. Constructing an approximate time evolution operator can be done using the Trotter-Suzuki decomposition with an error that scales at most polynomially in the target simulation time and can be decreased at the cost of longer circuit depth. Variational approaches to classically optimize this approximation have shown significant improvement in accuracy for large quantum systems in both gate count and accuracy by several orders of magnitude. However, it is unclear if a similar improvement can be obtained for strongly correlated systems. We extend this variational approach to two example systems with strong correlations: a one-dimensional Fermi-Hubbard chain and an extended Fermi-Hubbard chain. The encoding between qubits and fermionic modes in these systems is generally nonlocal and so we propose an encoding scheme for these Hamiltonians with minimal overall operator distance between nearest neighbor connected qubits. We demonstrate that this variational method grants a similarly strong improvement in both gate count and accuracy and examine the performance of these optimized gate sequences using realistic noise models to estimate their performance on noisy quantum hardware. Finally, we discuss an approach to combine the optimized nonlocal gates of small chains to larger systems without the need for additional computational resources.
Ground-state preparation for a given Hamiltonian is a common quantum-computing task of great importance and has relevant applications in quantum chemistry, computational material modeling, and combinatorial optimization. We consider an approach to simulate dissipative non-Hermitian Hamiltonian quantum dynamics using Hamiltonian simulation techniques to efficiently recover the ground state of a target Hamiltonian. The proposed method facilitates the energy transfer by repeatedly projecting ancilla qubits to the desired state, rendering the effective non-Hermitian Hamiltonian evolution on the system qubits. To make the method more resource friendly in the noisy intermediate-scale quantum (NISQ) and early fault-tolerant era, we combine the non-Hermitian projection algorithm with multiple variational gadgets, including variational module enhancement and variational state recording, to reduce the required circuit depth and avoid the exponentially vanishing success probability for post-selections. We compare our method, the non-Hermitian-variational algorithm, with a pure variational method -- QAOA for solving the 3-SAT problem and preparing the ground state for the transverse-field Ising model. As demonstrated by numerical evidence, the non-Hermitian-variational algorithm outperforms QAOA in convergence speed with improved quantum resource efficiency.
Digital quantum computers offer a promising route for studying complex many-body systems that are otherwise inaccessible by their classical counterparts. Capabilities including mid-circuit measurements and feedback allow for simulating the dynamics of interacting open quantum systems. Using the Quantinuum System Model H1 trapped-ion quantum computer, we experimentally realise quantum trajectories for a two-dimensional system of (interacting) particles-hard-core bosons or fermions-undergoing stochastic driving at a source and drain at opposite corners of a square lattice. We study the non-equilibrium steady state with persistent current resulting from the this in/out flow of particles. The particle statistics, presence of interactions, and introduction of a magnetic field produce measurable effects on the steady state. Our findings highlight the rich physics in this corner driven two-dimensional setup and showcases both the power and current limitations of quantum computers as a platform to study it.
Non-Hermitian Hamiltonians are a fascinating class of many-body models that describe the effective dynamics of quantum systems interacting with the environment through particle, energy, or information exchange. Although their theoretical framework is well established, the controlled engineering of such Hamiltonians in the context of quantum simulations remains challenging, even more so when the non-Hermitian part describes a kkk-body interaction. Qudit quantum simulators offer a compelling framework to implement such models. We theoretically investigate the dynamics of a one-dimensional chain of qudits undergoing hybrid unitary-projective evolution, where suitably designed measurements constrain the dynamics to a Zeno subspace. As we illustrate for the case of qutrits, within the Zeno subspace the dynamics is governed by an effective non-Hermitian Hamiltonian for an ensemble of pseudo-spins 1/21/21/2, which can inherit non-Hermitian two-body interactions with the same connectivity as the full qutrit chain. We derive an analytical relation linking the monitored qutrits' evolution to a desired target non-Hermitian Hamiltonian and validate the effective description through numerical simulations of a representative model. Our scheme provides a constructive route for the realization of a large class of interacting non-Hermitian many-body Hamiltonians in experimentally relevant multilevel quantum platforms, including trapped ions and superconducting circuits.