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We demonstrate a scaling method for non-Markovian Monte Carlo wave-function simulations used to study open quantum systems weakly coupled to their environments. We derive a scaling equation, from which the result for the expectation values…
This work presents a new approach for simulating the HHL linear systems of equations solver algorithm with tensor networks. First, a novel HHL in the qudits formalism, the generalization of qubits, is developed, and then its operations are…
Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its…
Spectral analysis of the {\em adjoint} propagator in a suitable Hilbert space (and Lie algebra) of quantum observables in Heisenberg picture is discussed as an alternative approach to characterize infinite temperature dynamics of non-linear…
Time evolution of the expectation values of various dynamical operators of the harmonic oscillator with dissipation is analitically obtained within the framework of the Lindblad theory for open quantum systems. We deduce the density matrix…
We study the computational complexity of simulating the time-dependent expectation value of a local operator in a one-dimensional quantum system by using temporal matrix product states. We argue that such cost is intimately related to that…
We offer new results and new directions in the study of operator-valued kernels and their factorizations. Our approach provides both more explicit realizations and new results, as well as new applications. These include: (i) an explicit…
We represent low dimensional quantum mechanical Hamiltonians by moderately sized finite matrices that reproduce the lowest O(10) boundstate energies and wave functions to machine precision. The method extends also to Hamiltonians that are…
Quantum signal processing (QSP), originally developed for composite pulse sequences in nuclear magnetic resonance systems, has recently attracted attention as a unified framework for quantum algorithms. A pioneering study applied QSP to…
The time-dependence of multi-point observable correlation functions are essential quantities in analysis and simulation of quantum dynamics. Open quantum systems approaches utilize two-point correlations to describe the influence of an…
A system of two coupled quantum harmonic oscillators with the Hamiltonian ${\hat H}=\frac{1}{2}\left(\frac{1}{m_1}{\hat p}^{2}_1 + \frac{1}{m_2}{\hat p}^{2}_2+A x^2_1+B x^2_2+ C x_1 x_2\right)$ can be found in many applications of quantum…
Dynamics of a quantum system can be described by coupled Heisenberg equations. In a generic many-body system these equations form an exponentially large hierarchy that is intractable without approximations. In contrast, in an integrable…
Implementing general functions of operators is a powerful tool in quantum computation. It can be used as the basis for a variety of quantum algorithms including matrix inversion, real and imaginary-time evolution, and matrix powers. Quantum…
Exact Heisenberg operator solutions for independent `sinusoidal coordinates' as many as the degree of freedom are derived for typical exactly solvable multi-particle quantum mechanical systems, the Calogero systems based on any root system.…
In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
This text is addressed to mathematicians who are interested in generalized functions and unbounded operators on a Hilbert space. We expose in detail (in a "formal way" - as done by Heisenberg and Pauli - i.e. without mathematical…
A systematic mathematical framework for the study of numerical algorithms would allow comparisons, facilitate conjugacy arguments, as well as enable the discovery of improved, accelerated, data-driven algorithms. Over the course of the last…
In this paper, we provide a theoretical analysis of strongly interacting quantum systems confined by a time-dependent external potential in one spatial dimension. We show that such systems can be used to simulate spin chains described by…
Quantum effects like entanglement and coherent amplification can be used to drastically enhance the accuracy of quantum parameter estimation beyond classical limits. However, challenges such as decoherence and time-dependent errors hinder…