Related papers: Commuting Quantum Circuits with Few Outputs are Un…

Pauli-based computation (PBC) is driven by a sequence of adaptively chosen, non-destructive measurements of Pauli observables. Any quantum circuit written in terms of the Clifford+$T$ gate set and having $t$ $T$ gates can be compiled into a…

Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…

Quantum computational supremacy arguments, which describe a way for a quantum computer to perform a task that cannot also be done by a classical computer, typically require some sort of computational assumption related to the limitations of…

We show that quantum theory allows for transformations of black boxes that cannot be realized by inserting the input black boxes within a circuit in a pre-defined causal order. The simplest example of such a transformation is the classical…

Quantum theory is consistent with a computational model permitting black-box operations to be applied in an indefinite causal order, going beyond the standard circuit model of computation. The quantum switch -- the simplest such example --…

A one-way quantum computer works by only performing a sequence of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. No non-local operations are required in the process of computation. Any quantum logic…

Quantum computing is greatly advanced in recent years and is expected to transform the computation paradigm in the near future. Quantum circuit simulation plays a key role in the toolchain for the development of quantum hardware and…

While quantum computing can accomplish tasks that are classically intractable, the presence of noise may destroy this advantage in the absence of fault tolerance. In this work, we present a classical algorithm that runs in…

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…

Classical simulation of quantum circuits is a pivotal part of the quantum computing landscape, specially within the NISQ era, where the constraints imposed by available hardware are unavoidable. The Gottesman-Knill theorem further motivates…

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 systems are notoriously difficult to simulate with classical means. Recently, the idea of using another quantum system - which is experimentally more controllable - as a simulator for the original problem has gained significant…

In this paper, we design quantum circuits for the exponential of scaled $n$-qubit Pauli strings using single-qubit rotation gates, Hadamard gate, and CNOT gates. A key result we derive is that any two Pauli-string operators composed of…

We study operator scrambling in quantum circuits built from `super-Clifford' gates. For such circuits it was established in arXiv:2002.12824 that the time evolution of operator entanglement for a large class of many-body operators can be…

The commonly used circuit model of quantum computing leaves out the problems of imprecision in the initial state preparation, particle statistics (indistinguishability of particles belonging to the same quantum state), and error correction…

Traditional algorithms for simulating quantum computers on classical ones require an exponentially large amount of memory, and so typically cannot simulate general quantum circuits with more than about 30 or so qubits on a typical PC-scale…

We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g. the…

Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are PAC (probably approximately correct) learnable on a quantum computer via empirical risk minimization: to…

We show that the Variational Quantum-Classical Simulation algorithm admits a finite circuit depth scaling collapse when targeting the critical point of the transverse field Ising chain. The order parameter only collapses on one side of the…

The development of quantum computing hardware is facing the challenge that current-day quantum processors, comprising 50-100 qubits, already operate outside the range of quantum simulation on classical computers. In this paper we…