Related papers: Simulating quantum computers with probabilistic me…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
Quantum circuit simulators running on classical computers offer a vital platform for designing, testing, and optimizing quantum algorithms, driving innovation despite limited access to real quantum hardware. However, their scalability is…
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure…
In breakthrough work, Bravyi, Gosset, and K\"{o}nig (BGK) [Science, 2018] unconditionally proved that constant depth quantum circuits are more powerful than their classical counterparts. Their result is equivalent to saying that a…
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…
In the effort to develop useful quantum computers simulating quantum machines with conventional computing resources is a key capability. Such simulations will always face limits preventing the emulation of quantum computers of substantial…
With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical…
Hamiltonian simulation is a promising application for quantum computers to achieve a quantum advantage. We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. We show that, compared to…
We identify a broad class of physical processes in an optical quantum circuit that can be efficiently simulated on a classical computer: this class includes unitary transformations, amplification, noise, and measurements. This…
Efficiently simulating quantum circuits on classical computers is a fundamental challenge in quantum computing. This paper presents a novel theoretical approach that achieves substantial speedups over existing simulators for a wide class of…
We study the classical simulatability of commuting quantum circuits with n input qubits and O(log n) output qubits, where a quantum circuit is classically simulatable if its output probability distribution can be sampled up to an…
We discuss a new approach to simulate quantum algorithms using classical probabilistic bits and circuits. Each qubit (a two-level quantum system) is initially mapped to a vector in an eight dimensional probability space (equivalently, to a…
Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have…
Quantum computing has the potential to revolutionize multiple fields by solving complex problems that can not be solved in reasonable time with current classical computers. Nevertheless, the development of quantum computers is still in its…
A key open question in quantum computing is whether quantum algorithms can potentially offer a significant advantage over classical algorithms for tasks of practical interest. Understanding the limits of classical computing in simulating…
We present a comprehensive study of quantum simulation methods and quantum simulators for classical computers. We first study an exhaustive set of 150+ simulators and quantum libraries. Then, we short-list the simulators that are actively…
As simulations of quantum systems cross the limits of classical computability, both quantum and classical approaches become hard to verify. Scaling predictions are therefore based on local structure and asymptotic assumptions, typically…
We study the classical simulation complexity in both the weak and strong senses, of matchgate (MG) computations supplemented with all combinations of settings involving inclusion of intermediate adaptive or nonadaptive computational basis…
Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to…