Related papers: How behavior of systems with sparse spectrum can b…
Quantum chemistry has been viewed as one of the potential early applications of quantum computing. Two techniques have been proposed for electronic structure calculations: (i) the variational quantum eigensolver and (ii) the…
We present an efficient quantum algorithm for simulating the evolution of a sparse Hamiltonian H for a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a…
We provide a quantum algorithm for simulating the dynamics of sparse Hamiltonians with complexity sublogarithmic in the inverse error, an exponential improvement over previous methods. Specifically, we show that a $d$-sparse Hamiltonian $H$…
We present a quantum algorithm for simulating the dynamics of Hamiltonians that are not necessarily sparse. Our algorithm is based on the input model where the entries of the Hamiltonian are stored in a data structure in a quantum random…
We study the potential utility of classical techniques of spectral sparsification of graphs as a preprocessing step for digital quantum algorithms, in particular, for Hamiltonian simulation. Our results indicate that spectral sparsification…
Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite lifetime. Hybrid algorithms leveraging classical resources have demonstrated promising initial results…
We present shadow spectroscopy as a simulator-agnostic quantum algorithm for estimating energy gaps using very few circuit repetitions (shots) and no extra resources (ancilla qubits) beyond performing time evolution and measurements. The…
Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
We present a quantum algorithm for approximating the real time evolution $e^{-iHt}$ of an arbitrary $d$-sparse Hamiltonian to error $\epsilon$, given black-box access to the positions and $b$-bit values of its non-zero matrix entries. The…
In engineered quantum systems, the Hamiltonian is often not completely known and needs to be determined experimentally with accuracy and efficiency. We show that this may be done at temperatures that are greater than the characteristic…
We present an efficient algorithm for simulating the time evolution due to a sparse Hamiltonian. In terms of the maximum degree d and dimension N of the space on which the Hamiltonian H acts for time t, this algorithm uses (d^2(d+log*…
The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation…
The problem of simulating sparse Hamiltonians on quantum computers is well studied. The evolution of a sparse N x N Hamiltonian H for time t can be simulated using O(||Ht||poly(log N)) operations, which is essentially optimal due to a…
Quantum algorithms speeding up classical counterparts are proposed for the problems: 1. Recognition of eigenvalues with fixed precision. Given a quantum circuit generating unitary mapping $U$ and a complex number the problem is to determine…
Simulating quantum dynamics is one of the most important applications of quantum computers. Traditional approaches for quantum simulation involve preparing the full evolved state of the system and then measuring some physical quantity.…
Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…
Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although…
We present an efficient method for estimating the eigenvalues of a Hamiltonian $H$ from the expectation values of the evolution operator for various times. For a given quantum state $\rho$, our method outputs a list of eigenvalue estimates…
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly…