Related papers: Heisenberg-Limited Quantum Eigenvalue Estimation f…
Thermal states play a fundamental role in various areas of physics, and they are becoming increasingly important in quantum information science, with applications related to semi-definite programming, quantum Boltzmann machine learning,…
Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been…
We investigate the relation between the spectrum of a non-normal matrix and the norm of its resolvent. We provide spectral estimates for the resolvent of matrices whose largest singular value is bounded by $1$ (so-called Hilbert space…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
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…
Achieving the ultimate precisions for multiple parameters simultaneously is an outstanding challenge in quantum physics, because the optimal measurements for incompatible parameters cannot be performed jointly due to the Heisenberg…
In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here we propose a theory of quantum…
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…
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…
In quantum mechanics, measuring the expectation value of a general observable has an inherent statistical uncertainty that is quantified by variance or mean squared error of measurement outcome. While the uncertainty can be reduced by…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
We propose a quantum algorithm for simulating dissipative waves in inhomogeneous linear media as a boundary-value problem. Using the so-called quantum singular value transformation (QSVT), we construct a quantum circuit that models the…
We address the question whether the super-Heisenberg scaling for quantum estimation is realizable. We unify the results of two approaches. In the first one, the original system is compared with its copy rotated by the parameter dependent…
The quantum Fisher information constrains the achievable precision in parameter estimation via the quantum Cram\'er-Rao bound, which has attracted much attention in Hermitian systems since the 60s of the last century. However, less…
We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to…
Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, $PT$ symmetry, and resonances. However, the quantum simulation of these models has been limited by the…
In this paper we analyze and solve eigenvalue programs, which consist of the task of minimizing a function subject to constraints on the "eigenvalues" of the decision variable. Here, by making use of the FTvN systems framework introduced by…
The procedure for simulating the nuclear magnetic resonance spectrum linked to the spin system of a molecule for a certain nucleus entails diagonalizing the associated Hamiltonian matrix. As the dimensions of said matrix grow exponentially…
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…
We provide efficient and intuitive tools for deriving bounds on achievable precision in quantum enhanced metrology based on the geometry of quantum channels and semi-definite programming. We show that when decoherence is taken into account,…