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Estimating the expectation value of an operator corresponding to an observable is a fundamental task in quantum computation. It is often impossible to obtain such estimates directly, as the computer is restricted to measuring in a fixed…
Quantum computing can efficiently simulate Hamiltonian dynamics of many-body quantum physics, a task that is generally intractable with classical computers. The hardness lies at the ubiquitous anti-commutative relations of quantum…
Simulating the dynamics of complex quantum systems is a central application of quantum devices. Here, we propose leveraging the power of measurements to simulate short-time quantum dynamics of physically prepared quantum states in classical…
Quantum simulation has primarily focused on unitary dynamics, while many physical and engineering systems can be modeled by linear ordinary differential equations whose generators include non-Hermitian terms. Recent studies have shown that…
Randomization has been applied to Hamiltonian simulation in a number of ways to improve the accuracy or efficiency of product formulas. Deterministic product formulas are often constructed in a symmetric way to provide accuracy of even…
While quantum simulation is one of the most promising applications of modern quantum devices, accessible simulation times are fundamentally limited by finite coherence times due to omnipresent noise. Based on the ideas of relational…
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…
Classical simulation of quantum computers is an irreplaceable step in the design of quantum algorithms. Exponential simulation costs demand the use of high-performance computing techniques, and in particular distribution, whereby the…
One limitation of the variational quantum eigensolver algorithm is the large number of measurement steps required to estimate different terms in the Hamiltonian of interest. Unitary partitioning reduces this overhead by transforming the…
Simulating dynamics of physical systems is a key application of quantum computing, with potential impact in fields such as condensed matter physics and quantum chemistry. However, current quantum algorithms for Hamiltonian simulation yield…
Extracting the Hamiltonian of interacting quantum-information processing systems is a keystone problem in the realization of complex phenomena and large-scale quantum computers. The remarkable growth of the field increasingly requires…
Measuring the expectation value of Pauli operators on prepared quantum states is a fundamental task in a multitude of quantum algorithms. Simultaneously measuring sets of operators allows for fewer measurements and an overall speedup of the…
Mapping functions on bits to Hamiltonians acting on qubits has many applications in quantum computing. In particular, Hamiltonians representing Boolean functions are required for applications of quantum annealing or the quantum approximate…
The simulation of quantum dynamics on a digital quantum computer with parameterized circuits has widespread applications in fundamental and applied physics and chemistry. In this context, using the hybrid quantum-classical algorithm,…
Quantum simulation is a promising near term application for mesoscale quantum information processors, with the potential to solve computationally intractable problems at the scale of just a few dozen interacting quantum systems. Recent…
Here we describe an approach for simulating electronic structure on quantum computers with significantly lower asymptotic complexity than prior work. The approach uses a real-space first-quantised representation of the molecular Hamiltonian…
We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems that are intractable to solve on a classical computer. Current generation noisy…
We address the problem of simulating pair-interaction Hamiltonians in n node quantum networks where the subsystems have arbitrary, possibly different, dimensions. We show that any pair-interaction can be used to simulate any other by…