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Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several…
Quantum simulation is a prominent application of quantum computers. While there is extensive previous work on simulating finite-dimensional systems, less is known about quantum algorithms for real-space dynamics. We conduct a systematic…
Recently developed quantum algorithms suggest that in principle, quantum computers can solve problems such as simulation of physical systems more efficiently than classical computers. Much remains to be done to implement these conceptual…
Many methods solve Poisson equations by using grid techniques which discretize the problem in each dimension. Most of these algorithms are subject to the curse of dimensionality, so that they need exponential runtime. In the paper "Quantum…
We experimentally study the two-dimensional Fermi-Hubbard model using a Rydberg-based quantum processing unit in the analog mode. Our approach avoids encoding directly the original fermions into qubits and instead relies on reformulating…
Supersymmetric models are grounded in the intriguing concept of a hypothetical symmetry that relates bosonic and fermionic particles. This symmetry has profound implications, offering valuable extensions to the Standard Model of particle…
As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a…
Using quantum algorithms to simulate complex physical processes and correlations in quantum matter has been a major direction of quantum computing research, towards the promise of a quantum advantage over classical approaches. In this work…
We present a quantum algorithm for simulating the dynamics of Hamiltonians that are not necessarily sparse. Our algorithm is based on the input model where the entries of the Hamiltonian are stored in a data structure in a quantum random…
We present a comprehensive end-to-end framework for simulating the real-time dynamics of chemical systems on a fault-tolerant quantum computer, incorporating both electronic and nuclear quantum degrees of freedom. An all-particle simulation…
Simulating quantum many-body systems is a highly demanding task since the required resources grow exponentially with the dimension of the system. In the case of fermionic systems, this is even harder since nonlocal interactions emerge due…
With a focus on universal quantum computing for quantum simulation, and through the example of lattice gauge theories, we introduce rather general quantum algorithms that can efficiently simulate certain classes of interactions consisting…
We investigate the problem of simulating classical stochastic processes through quantum dynamics, and present three scenarios where memory or time quantum advantages arise. First, by introducing and analysing a quantum version of the…
We introduce a new method for representing the low energy subspace of a bosonic field theory on the qubit space of digital quantum computers. This discretization leads to an exponentially precise description of the subspace of the…
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…
One of the core research questions in the theory of quantum computing is to find out to what precise extent the classical simulation of a noisy quantum circuits is possible and where potential quantum advantages can set in. In this work, we…
Many-body fermionic systems can be simulated in a hardware-efficient manner using a fermionic quantum processor. Neutral atoms trapped in optical potentials can realize such processors, where non-local fermionic statistics are guaranteed at…
Quantum computers potentially have an exponential advantage over classical computers for the quantum simulation of many-fermion quantum systems. Nonetheless, fermions are more expensive to simulate than bosons due to the fermionic encoding…
Many-body open quantum systems, described by Lindbladian master equations, are a rich class of physical models that display complex equilibrium and out-of-equilibrium phenomena which remain to be understood. In this paper, we theoretically…
The computational complexity of simulating the dynamics of physical quantum systems is a central question at the interface of quantum physics and computer science. In this work, we address this question for the simulation of exponentially…