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We delve into the use of photonic quantum computing to simulate quantum mechanics and extend its application towards quantum field theory. We develop and prove a method that leverages this form of Continuous-Variable Quantum Computing…
A critical question for the field of quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of state-of-the-art classical computers,…
Many important quantities in quantum information science, such as entropy and entanglement, are non-linear functions of the density matrix and cannot be expressed as operator observables. Standard open-system approaches evolve only a single…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
We provide a quantum method for simulating Hamiltonian evolution with complexity polynomial in the logarithm of the inverse error. This is an exponential improvement over existing methods for Hamiltonian simulation. In addition, its scaling…
Compared with time independent Hamiltonians, the dynamics of generic quantum Hamiltonians $H(t)$ are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty…
While rigorous quantum dynamical simulations of many-body systems are extremely difficult (or impossible) due to the exponential scaling with dimensionality, corresponding classical simulations completely ignore quantum effects.…
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…
Simulating the stochastic evolution of real quantities on a digital computer requires a trade-off between the precision to which these quantities are approximated, and the memory required to store them. The statistical accuracy of the…
The entropy of a classical thermally isolated Hamiltonian system is given by the logarithm of the measure of phase space enclosed by the constant energy hyper-surface, also known as volume entropy. It has been shown that on average the…
Stochastic models are highly relevant tools in science, engineering, and society. Recent work suggests emerging quantum computing technologies can substantially decrease the memory requirements for simulating stochastic models. Here we show…
We analyze the complexity of classically simulating continuous-time dynamics of locally interacting quantum spin systems with a constant rate of entanglement breaking noise. We prove that a polynomial time classical algorithm can be used to…
What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? We provide an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling n-qubit…
It is shown that the existence of a time operator in the Liouville space representation of both classical and quantum evolution provides a mechanism for effective entropy change of physical states. In particular, an initially effectively…
Product formulas can be used to simulate Hamiltonian dynamics on a quantum computer by approximating the exponential of a sum of operators by a product of exponentials of the individual summands. This approach is both straightforward and…
We describe a simple method for simulating time-independent Hamiltonian $H$ that could be decomposed as $H = \sum_{i=1}^m H_i$ where each $H_i$ can be efficiently simulated. Approaches relying on product formula generally work by splitting…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
Understanding the computational power of noisy intermediate-scale quantum (NISQ) devices is of both fundamental and practical importance to quantum information science. Here, we address the question of whether error-uncorrected noisy…
We prove classical simulation hardness, under the generalized $\mathsf{P}\neq\mathsf{NP}$ conjecture, for quantum circuit families with applications in near-term chemical ground state estimation. The proof exploits a connection to particle…
We investigate the relationship between two distinct classical approaches to quantum systems: direct simulation from a classical description and sample-based learning from measurement data. While both tasks ultimately aim to reproduce…