Self-verifying variational quantum simulation of lattice models

By C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M. Joshi, P. Jurcevic, Christine A. Muschik, P. Silvi, Rainer Blatt, C. F. Roos and 1 more. Nature, 2018

605 citations recorded by the source corpus.

Hybrid classical–quantum algorithms aim to variationally solve optimization problems using a feedback loop between a classical computer and a quantum co-processor, while benefiting from quantum resources. Here we present experiments that demonstrate self-verifying, hybrid, variational quantum simulation of lattice models in condensed matter and high-energy physics. In contrast to analogue quantum simulation, this approach forgoes the requirement of realizing the targeted Hamiltonian directly in the laboratory, thus enabling the study of a wide variety of previously intractable target models. We focus on the lattice Schwinger model, a gauge theory of one-dimensional quantum electrodynamics. Our quantum co-processor is a programmable, trapped-ion analogue quantum simulator with up to 20 qubits, capable of generating families of entangled trial states respecting the symmetries of the target Hamiltonian. We determine ground states, energy gaps and additionally, by measuring variances of the Schwinger Hamiltonian, we provide algorithmic errors for the energies, thus taking a step towards verifying quantum simulation. Quantum-classical variational techniques are combined with a programmable analogue quantum simulator based on a one-dimensional array of up to 20 trapped calcium ions to simulate the ground state of the lattice Schwinger model.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/b0593876bc823e36c590b1d83032117da0f50272

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Citations in the corpus

Quantum simulation and computing with Rydberg-interacting qubits (2020, background): “However recent ideas, such as self-verifying quantum simulations 11 and randomized benchmarking protocols 72,100 would be interesting to implement Rydberg quantum systems (particularly as we approach regimes that cannot be simulated on classical computers).”
Quantum computing with neutral atoms (2020, methodology): “In that respect, one pioneering experiment studied the Lattice Schwinger model with trapped ions [52] using a variational approach.”
Theory of variational quantum simulation (2018, methodology): “For solving static problems, the Rayleigh-Ritz variational method can be naturally generalised to the quantum regime, such as the variational quantum eigensolver (VQE) [29–40] and the quantum approximate optimisation algorithm (QAOA) [28].”
Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe (2022, background): “, the case in the variational quantum eigensolver (VQE) [462] for theoretical chemistry [354], high energy physics [343] or computationally hard problems in graph theory [211].”
Variational quantum algorithms (2020, methodology): “useful to study Hamiltonians that are similar to the device’s interactions [14].”
Materials challenges and opportunities for quantum computing hardware (2021, positive): “Variational quantum algorithms such as variational quantum eigensolvers (12) and quantum circuit learning (13) have been used to calculate energies of simple molecules (14–16), simulate lattice models (17), and improve efficiency of machine learning (18).”
QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits (2021, methodology): “The variational method has shown huge potentials in applications such as quantum machine learning [4], [7], [56], [63], numerical analysis [37], [39], quantum simulation [30], [31], [52], and optimizations [18], [47].”
Variational Quantum Linear Solver (2019, neutral): “[25] C.”