Related papers: Efficient Quantum Hermite Transform
Digital quantum simulation has broad applications in approximating unitary evolution of Hamiltonians. In practice, many simulation tasks for quantum systems focus on quantum states in the low-energy subspace instead of the entire Hilbert…
The utility of effective model spaces in quantum simulations of non-relativistic quantum many-body systems is explored in the context of the Lipkin-Meshkov-Glick model of interacting fermions. We introduce an iterative…
We solve a problem, which while not fitting into the usual paradigm, can be viewed as a quantum computation. Suppose we are given a quantum system described by an N dimensional Hilbert space with a Hamiltonian of the form $E |w >< w|$ where…
Efficient simulation of interacting fermionic systems is a key application of near-term quantum computers, but is hindered by the overhead required to encode fermionic operators on qubit hardware. Here, we consider models with $N$ fermionic…
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…
The aim of this paper is to develop novel quantum algorithms for Gaussian process quadrature methods. Gaussian process quadratures are numerical integration methods where Gaussian processes are used as functional priors for the integrands…
Quantum computers can outperform classical computers in certain tasks. However, there are still many challenges to the current quantum computers such as decoherence and fault tolerance, and other drawbacks such as portability and…
In this work, we initiate the study of Hamiltonian learning for positive temperature bosonic Gaussian states, the quantum generalization of the widely studied problem of learning Gaussian graphical models. We obtain efficient protocols,…
We construct a new model of the quantum oscillator, whose energy spectrum is equally-spaced and lower-bounded, whereas the spectra of position and momentum are a denumerable non-degenerate set of points in [-1,1] that depends on the…
The adiabatic quantum algorithm has drawn intense interest as a potential approach to accelerating optimization tasks using quantum computation. The algorithm is most naturally realised in systems which support Hamiltonian evolution, rather…
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…
We present an algorithm for measurement of $k$-local operators in a quantum state, which scales logarithmically both in the system size and the output accuracy. The key ingredients of the algorithm are a digital representation of the…
Parameterized quantum circuits are a promising technology for achieving a quantum advantage. An important application is the variational simulation of time evolution of quantum systems. To make the most of quantum hardware, variational…
The dual tasks of quantum Hamiltonian learning and quantum Gibbs sampling are relevant to many important problems in physics and chemistry. In the low temperature regime, algorithms for these tasks often suffer from intractabilities, for…
We study quantum anomaly detection with density estimation and multivariate Gaussian distribution. Both algorithms are constructed using the standard gate-based model of quantum computing. Compared with the corresponding classical…
We introduce an efficient stable algorithm for transforms associated with expansions in Hermite functions interpolated at Hermite polynomial roots. The Hermite transform matrix can be factorised into a diagonal component and an orthogonal…
We analyze the possibility of modifying the original Farhi-Gutmann Hamiltonian algorithm in order to speed up the procedure for producing a suitably distributed unknown normalized quantum mechanical state. Such a modification is feasible…
We introduce novel algorithms for the quantum simulation of molecular systems which are asymptotically more efficient than those based on the Trotter-Suzuki decomposition. We present the first application of a recently developed technique…
An algorithm to classify a general Hermitian matrix according to its signature (positive semi-definite, negative or indefinite) is presented. It builds on the Quantum Phase Estimation algorithm, which stores the sign of the eigenvalues of a…
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…