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Most non-relativistic interacting quantum many-body systems, such as atomic and molecular ensembles or materials, are naturally described in terms of continuous-space Hamiltonians. The simulation of their ground-state properties on digital…
Non-smooth optimization models play a fundamental role in various disciplines, including engineering, science, management, and finance. However, classical algorithms for solving such models often struggle with convergence speed,…
The numerical solution of the many-body problem of interacting electrons and ions is a key challenge in condensed matter physics, chemistry, and materials science. Traditional methods to solve the multi-component quantum Hamiltonian are…
Quantum computational chemistry holds great promise for simulating molecular systems more efficiently than classical methods by leveraging quantum bits to represent molecular wavefunctions. However, current implementations face significant…
Flow models are a cornerstone of modern machine learning. They are generative models that progressively transform probability distributions according to learned dynamics. Specifically, they learn a continuous-time Markov process that…
The Vlasov-Maxwell equations provide kinetic simulations of collisionless plasmas, but numerically solving them on classical computers is often impractical. This is due to the computational resource constraints imposed by the time evolution…
We apply the method of flow equations to describe quantum systems subject to a time-periodic drive with a time-dependent envelope. The driven Hamiltonian is expressed in terms of its constituent Fourier harmonics with amplitudes that may…
Hybrid classical-quantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources. Here we present experiments…
Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…
For quantum computing (QC) to emerge as a practically indispensable computational tool, there is a need for quantum protocols with an end-to-end practical applications -- in this instance, fluid dynamics. We debut here a high performance…
The utility of effective model spaces in quantum simulations of non-relativistic quantum many-body systems is explored in the context of the Lipkin-Meshkov-Glick model of interacting fermions. We introduce an iterative…
We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such…
The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here we present a process for obtaining the…
Achieving noise resilience is an outstanding challenge in Hamiltonian-based quantum computation. To this end, energy-gap protection provides a promising approach, where the desired quantum dynamics are encoded into the ground space of a…
Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is…
Parity-time ($PT$)-symmetric Hamiltonians exhibit non-unitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here we present a method for simulating the…
We present a dissipative algorithm for solving nonlinear wave-like equations when the initial data is specified on characteristic surfaces. The dissipative properties built in this algorithm make it particularly useful when studying the…
Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using…
Simulating the real-time dynamics of lattice gauge theories, underlying the Standard Model of particle physics, is a notoriously difficult problem where quantum simulators can provide a practical advantage over classical approaches. In this…
We present the first quantum-hardware implementation of a Hamiltonian simulation algorithm that produces signed vector-field solutions to the time-domain Maxwells equations using a Schrodingerisation-based approach. The electromagnetic…