Related papers: Classical simulation of quantum algorithms using t…
The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our…
We establish a classical heuristic algorithm for exactly computing quantum probability amplitudes. Our algorithm is based on mapping output probability amplitudes of quantum circuits to evaluations of the Tutte polynomial of graphic…
Atomic-scale logic and the minimization of heating (dissipation) are both very high on the agenda for future computation hardware. An approach to achieve these would be to replace networks of transistors directly by classical reversible…
The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and…
Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random…
We develop Monte Carlo methods for sampling random states and corresponding bit strings in qubit systems. To this end, we derive exact probability density functions that yield the Porter-Thomas distribution in the limit of large systems. We…
In optimization, one of the well-known classical algorithms is power iterations. Simply stated, the algorithm recovers the dominant eigenvector of some diagonalizable matrix. Since numerous optimization problems can be formulated as an…
Efficient simulation of quantum circuits has become indispensable with the rapid development of quantum hardware. The primary simulation methods are based on state vectors and tensor networks. As the number of qubits and quantum gates grows…
We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm…
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…
In this paper, we develop a new classical simulation of quantum bit (qubit) by use of analog components in order to be able to simulate the quantum properties such as the superposition of states. As part of this new approach, we have also…
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…
We describe an array of quantum gates implementing Shor's algorithm for prime factorization in a quantum computer. The array includes a circuit for modular exponentiation with several subcomponents (such as controlled multipliers, adders,…
In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts…
Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and the fact that unitary transformations on that Hilbert space can be broken down to universal gates that act only on one or two…
Most research in quantum computing today is performed against simulations of quantum computers rather than true quantum computers. Simulating a quantum computer entails implementing all of the unitary operators corresponding to the quantum…
We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of…
Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks…
Efficient simulation of quantum computers relies on understanding and exploiting the properties of quantum states. This is the case for methods such as tensor networks, based on entanglement, and the tableau formalism, which represents…
We perform quantum simulation on classical and quantum computers and set up a machine learning framework in which we can map out phase diagrams of known and unknown quantum many-body systems in an unsupervised fashion. The classical…