Related papers: State-to-Hamiltonian conversion with a few copies
Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger…
In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that…
Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…
Uhlmann's theorem is a central result in quantum information theory, which associates the closeness of two quantum states with that of their purifications. The theorem also well characterizes a fundamental task: how close a pure quantum…
In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that…
We introduce a quantum algorithm to efficiently prepare states with a small energy variance at the target energy. We achieve it by filtering a product state at the given energy with a Lorentzian filter of width $\delta$. Given a local…
We previously proposed a mechanism to effectively obtain, after a long time development, a Hamiltonian being Hermitian with regard to a modified inner product $I_Q$ that makes a given non-normal Hamiltonian normal by using an appropriately…
Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to…
In this paper we propose a method to estimate the density matrix \rho of a d-level quantum system by measurements on the N-fold system. The scheme is based on covariant observables and representation theory of unitary groups and it extends…
Most quantum algorithms designed to generate or probe properties of the ground state of a quantum many-body system require as input an initial state with a large overlap with the desired ground state. One approach for preparing such a…
Quantum computation has been growing rapidly in both theory and experiments. In particular, quantum computing devices with a large number of qubits have been developed by IBM, Google, IonQ, and others. The current quantum computing devices…
It is a fundamental problem to decide how many copies of an unknown mixed quantum state are necessary and sufficient to determine the state. Previously, it was known only that estimating states to error $\epsilon$ in trace distance required…
We revisit the Pseudo-Bayesian approach to the problem of estimating density matrix in quantum state tomography in this paper. Pseudo-Bayesian inference has been shown to offer a powerful paradign for quantum tomography with attractive…
Particle Marginal Metropolis-Hastings (PMMH) is a general approach to Bayesian inference when the likelihood is intractable, but can be estimated unbiasedly. Our article develops an efficient PMMH method that scales up better to higher…
Recently, sophisticated deep learning-based approaches have been developed for generating efficient initial guesses to accelerate the convergence of density functional theory (DFT) calculations. While the actual initial guesses are often…
Non-Hermitian operators naturally arise in the description of open quantum systems, which exhibit features such as resonances and decay processes, where the associated eigenvalues are complex. Standard quantum algorithms, including the…
Quantum state tomography (QST), the process of reconstructing some unknown quantum state $\hat\rho$ from repeated measurements on copies of said state, is a foundationally important task in the context of quantum computation and simulation.…
Motivated by recent quantum gas microscope experiments for fermions in optical lattices, we present proof of principle calculations showing that it is possible to obtain the complete information about the quantum state on a small subsystem…
Dynamic Mode Decomposition (DMD) and its extensions (EDMD) have been at the forefront of data-based approaches to Koopman operators. Most (E)DMD algorithms assume that the entire state is sampled at a uniform sampling rate. In this paper,…
Estimating the difference between quantum data is crucial in quantum computing. However, as typical characterizations of quantum data similarity, the trace distance and quantum fidelity are believed to be exponentially-hard to evaluate in…