Related papers: Statistical Approach to Quantum Phase Estimation
In this paper, we present an online adaptive PCA algorithm that is able to compute the full dimensional eigenspace per new time-step of sequential data. The algorithm is based on a one-step update rule that considers all second order…
Aussel et al. (J Optim Theory Appl 170 818-837 2016) introduced the concept of projected solutions for the quasi-variational inequalities with a non-self constraint map, that is, the case where the constraint map may take values outside the…
The quantum approximate optimization algorithm (QAOA) is a general-purpose algorithm for combinatorial optimization. In this paper, we analyze the performance of the QAOA on a statistical estimation problem, namely, the spiked tensor model,…
The usual way to reveal properties of an unknown quantum state, given many copies of a system in that state, is to perform measurements of different observables and to analyze the measurement results statistically. Here we show that the…
A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over…
We describe an efficient implementation of Bayesian quantum phase estimation in the presence of noise and multiple eigenstates. The main contribution of this work is the dynamic switching between different representations of the phase…
The accumulation of noise in quantum computers is the dominant issue stymieing the push of quantum algorithms beyond their classical counterparts. We do not expect to be able to afford the overhead required for quantum error correction in…
Quantum phase estimation plays a central role in quantum simulation as it enables the study of spectral properties of many-body quantum systems. Most variants of the phase estimation algorithm require the application of the global unitary…
The recently developed Projective Quantum Eigensolver (PQE) has been demonstrated as an elegant methodology to compute the ground state energy of molecular systems in Noisy Intermdiate Scale Quantum (NISQ) devices. The iterative…
Variational algorithms are promising candidates to be implemented on near-term quantum computers. The variational quantum eigensolver (VQE) is a prominent example, where a parametrized trial state of the quantum mechanical wave function is…
We propose a novel method, Phase-IDENT, for identifying partial differential equations (PDEs) from noisy observations of dynamical systems that exhibit phase transitions. Such phenomena are prevalent in fluid dynamics and materials science,…
Mapping out phase diagrams of quantum systems using classical simulations can be challenging or intractable due to the computational resources required to simulate even small quantum systems far away from the thermodynamic limit. We…
It has been demonstrated that the critical point of the phase transition in scalar quantum field theory with a quartic interaction in one space dimension can be approximated via a Gaussian Effective Potential (GEP). We discuss how this…
Variational quantum algorithms (VQAs) are prominent candidates for near-term quantum advantage but lack rigorous guarantees of convergence and generalization. By contrast, quantum phase estimation (QPE) provides provable performance under…
Under suitable assumptions, the quantum phase estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground state energy. However, QPE requires a large number of ancilla qubits and large circuit…
Quantum phase estimation is one of the most powerful quantum primitives. This work proposes a new approach for the problem of multiple eigenvalue estimation: Quantum Multiple Eigenvalue Gaussian filtered Search (QMEGS). QMEGS leverages the…
We present a simple and efficient Bayesian recursive algorithm for the data-pattern scheme for quantum state reconstruction, which is applicable to situations where measurement settings can be controllably varied efficiently. The algorithm…
Comparative analyses of protein-protein interaction networks play important roles in the understanding of biological processes. However, the growing enormity of available data on the networks becomes a computational challenge for the…
Quantum phase estimation (QPE) is a promising quantum algorithm for obtaining molecular ground-state energies with chemical accuracy. However, its computational cost, dominated by the Hamiltonian 1-norm $\lambda$ and the cost of the block…
Quantum scale estimation, as introduced and explored here, establishes the most precise framework for the estimation of scale parameters that is allowed by the laws of quantum mechanics. This addresses an important gap in quantum metrology,…