Related papers: Wavefunction preparation and resampling using a qu…
We consider the preparation of single-spinon wave functions, relevant for one-dimensional $S=1/2$ spin models, in a quantum computer. We adopt the recently proposed ansatz \cite{kulk} for the single-spinon wave function, where a state with…
The quantum simulation of real molecules and materials is one of the most highly anticipated applications of quantum computing. Algorithms for simulating electronic structure using a first-quantized plane wave representation are especially…
A visualization scheme for quantum many-body wavefunctions is described, which we have termed qubism. Its main property is its recursivity: increasing the number of qubits reflects in an increase in the image resolution. Thus, the plots are…
This paper constructs the first quantum algorithm for wavelet packet transforms with a "parabolic scaling" tree structure, sometimes called wave atom transforms. Classically, wave atoms are used to construct sparse representations of…
Characterizing quantum phases-of-matter at finite-temperature is essential for understanding complex materials and large-scale thermodynamic phenomena. Here, we develop algorithmic protocols for simulating quantum thermodynamics on quantum…
The approximate numerical method for a calculation of a quantum wave impedance in a case of a potential energy with a complicated spatial structure is considered. It was proved that the approximation of a real potential by a piesewise…
Chemistry and materials science are widely regarded as potential killer application fields for quantum hardware. While the dream of unlocking unprecedented simulation capabilities remains compelling, quantum algorithm development must adapt…
Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…
Numerically solving partial differential equations is a ubiquitous computational task with broad applications in many fields of science. Quantum computers can potentially provide high-degree polynomial speed-ups for solving PDEs, however…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. Quantum computational algorithms have the potential to be an exciting new way of studying quantum cosmology. In quantum…
Due to the advances in the manufacturing of quantum hardware in the recent years, significant research efforts have been directed towards employing quantum methods to solving problems in various areas of interest. Thus a plethora of novel…
Electronic structure and transport in realistically-sized systems often require an open quantum system (OQS) treatment, where the system is defined in the context of an environment. As OQS evolution is non-unitary, implementation on quantum…
We present a preconditioning method for the multi-dimensional Helmholtz equation with smoothly varying coefficient. The method is based on a frame of functions, that approximately separates components associated with different singular…
Quantum computers promise to revolutionise electronic simulations by overcoming the exponential scaling of many-electron problems. While electronic wave functions can be represented using a product of fermionic unitary operators, shallow…
Quantum signal processing allows for quantum eigenvalue transformation with Hermitian matrices, in which each eigenspace component of an input vector gets transformed according to its eigenvalue. In this work, we introduce the multivariate…
Quantum optical metrology aims to identify ultimate sensitivity bounds for the estimation of parameters encoded into quantum states of the electromagnetic field. In many practical applications, including imaging, microscopy, and remote…
This paper presents a comprehensive review of the wave-function approach for derivation of the number-resolved Master equations, used for description of transport and measurement in mesoscopic systems. The review contains important…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
Due to growing interest in quantum measurement, control and feedback, we reproduce a manuscript from 1992, presenting a simple physical and mathematical derivation of stochastic differential equations for wave functions of probed quantum…
We consider an unknown multivariate function representing a system-such as a complex numerical simulator-taking both deterministic and uncertain inputs. Our objective is to estimate the set of deterministic inputs leading to outputs whose…