Related papers: Classical simulation of free-fermionic dynamics an…
I describe, in the simplified context of finite groups and their representations, a mathematical model for a physical system that contains both its quantum and classical aspects. The physically observable system is associated with the space…
Many-electron problems pose some of the greatest challenges in computational science, with important applications across many fields of modern science. Fermionic quantum Monte Carlo (QMC) methods are among the most powerful approaches to…
In the Quantum Supremacy regime, quantum computers may overcome classical machines on several tasks if we can estimate, mitigate, or correct unavoidable hardware noise. Estimating the error requires classical simulations, which become…
We introduce an efficient method to simulate dynamics of an interacting quantum impurity coupled to non-interacting fermionic reservoirs. Viewing the impurity as an open quantum system, we describe the reservoirs by their Feynman-Vernon…
Fermionic linear optics corresponds to the dynamics of free fermions, and is known to be efficiently simulable classically. We define fermionic anyon models by deforming the fermionic algebra of creation and annihilation operators, and…
The most scalable proposed methods of simulating lattice fermions on noisy quantum computers employ encodings that eliminate nonlocal operators using a constant factor more qubits and a nontrivial stabilizer group. In this work, we…
The Fermi-Hubbard model, a fundamental framework for studying strongly correlated phenomena could significantly benefit from quantum simulations when exploring non-trivial settings. However, simulating this problem requires twice as many…
A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational…
Quantum normalizer circuits were recently introduced as generalizations of Clifford circuits [arXiv:1201.4867]: a normalizer circuit over a finite Abelian group $G$ is composed of the quantum Fourier transform (QFT) over G, together with…
The Gottesman-Knill theorem asserts that a quantum circuit composed of Clifford gates can be efficiently simulated on a classical computer. Here we revisit this theorem and extend it to quantum circuits composed of Clifford and T gates,…
Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics. Although qubit-based quantum computers can potentially tackle this…
Many quantum algorithms can be represented in a form of a classical circuit positioned between quantum Fourier transformations. Motivated by the search for new quantum algorithms, we turn to circuits where the latter transformation is…
A recent quantum simulation of observables of the kicked Ising model on 127 qubits implemented circuits that exceed the capabilities of exact classical simulation. We show that several approximate classical methods, based on sparse Pauli…
We investigate a stochastic approach to non-equilibrium quantum spin systems based on recent insights linking quantum and classical dynamics. Exploiting a sequence of exact transformations, quantum expectation values can be recast as…
Exact calculation and even multiplicative error estimation of matrix permanent are challenging for both classical and quantum computers. Regarding the permanents of random Gaussian matrices, the additive error estimation is closely linked…
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…
Simulating physical systems has been an important application of classical and quantum computers. In this article we present an efficient classical algorithm for simulating time-dependent quantum mechanical Hamiltonians over constant…
This work provides a rigorous and self-contained introduction to numerical methods for Hamiltonian simulation in quantum computing, with a focus on high-order product formulas for efficiently approximating the time evolution of quantum…
The explicit computation of amplitudes for fermionic Gaussian pure states in arbitrary Pauli bases is a long-standing challenge in quantum many-body physics, with significant implications for quantum tomography, experimental studies, and…
A quasiclassical correspondent for the fermion degrees of freedom is obtained by using a time-dependent variational principle with Grassmann coherent states as trial functions. In the real parametrization provided by the canonical…