Related papers: Assessing the query complexity limits of quantum p…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
In this work, we study the phase estimation problem. We show an alternative, simpler and self-contained proof of query lower bounds. Technically, compared to the previous proofs [NW99, Bes05], our proof is considerably elementary.…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
Quantum algorithms are promising candidates for the enhancement of computational efficiency for a variety of computational tasks, allowing for the numerical study of physical systems intractable to classical computers. In the Noisy…
Phase estimation protocols provide a fundamental benchmark for the field of quantum metrology. The latter represents one of the most relevant applications of quantum theory, potentially enabling the capability of measuring unknown physical…
We report the quantum computing of reacting flows by simulating the Hamiltonian dynamics. The scalar transport equation for reacting flows is transformed into a Hamiltonian system, mapping the dissipative and non-Hermitian problem in…
The performance of computational methods for many-body physics and chemistry is strongly dependent on the choice of basis used to cast the problem; hence, the search for better bases and similarity transformations is important for progress…
The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. Here, we introduce the concept of an "eigenstate witness" and through it…
The simulation of electronic properties is a pivotal issue in modern electronic structure theory, driving significant efforts over the past decades to develop protocols for computing energy derivatives. In this work, we address this problem…
Many hybrid quantum-classical algorithms for the application of ground state energy estimation in quantum chemistry involve estimating the expectation value of a molecular Hamiltonian with respect to a quantum state through measurements on…
This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cram\`er-Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are…
Simultaneous estimation of multiple parameters is required in many practical applications. A lower bound on the variance of simultaneous estimation is given by the quantum Fisher information matrix. This lower bound is, however, not…
Solving eigenproblem of the Laplacian matrix of a fully connected weighted graph has wide applications in data science, machine learning, and image processing, etc. However, this is very challenging because it involves expensive matrix…
We present a framework for upper bounding the number of iterations required by first-order optimization algorithms implementing constrained LQR controllers. We derive new bounds for the condition number and extremal eigenvalues of the…
A quantum thermodynamic system is described by a Hamiltonian and a list of conserved, non-commuting charges, and a fundamental goal is to determine the minimum energy of the system subject to constraints on the charges. Recently, [Liu et…
Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different…
Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring…
Characterizing noisy quantum devices requires methods for learning the underlying quantum Hamiltonian which governs their dynamics. Often, such methods compare measurements to simulations of candidate Hamiltonians, a task which requires…
Quantum mode parameter estimation determines parameters governing the shape of electromagnetic modes occupied by a quantum state of radiation. Canonical examples, time delays and frequency shifts, underpin radar, lidar, and optical clocks.…
We propose a quantum algorithm for projecting a quantum system to eigenstates of any Hermitian operator, provided one can access the associated control-unitary evolution for the ancilla and the system, as well as the measurement of the…