Related papers: Tight Bounds for Quantum Phase Estimation and Rela…
In this paper with study phase transitions of the $q$-state Potts model, through a number of unsupervised machine learning techniques, namely Principal Component Analysis (PCA), $k$-means clustering, Uniform Manifold Approximation and…
Measurement underpins all quantitative science. A key example is the measurement of optical phase, used in length metrology and many other applications. Advances in precision measurement have consistently led to important scientific…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
We calculate the trade-off between the quality of estimating the quantum state of an ensemble of identically prepared qubits and the minimum level of disturbance that has to be introduced by this procedure in quantum mechanics. The…
Finding a good approximation of the top eigenvector of a given $d\times d$ matrix $A$ is a basic and important computational problem, with many applications. We give two different quantum algorithms that, given query access to the entries…
We compare several quantum phase estimation (QPE) protocols intended for early fault-tolerant quantum computers (EFTQCs) in the context of models of their implementations on a surface code architecture. We estimate the logical and physical…
In this article we propose a method to estimate with high accuracy pure quantum states of a single qudit. Our method is based on the minimization of the squared error between the complex probability amplitudes of the unknown state and its…
Fidelity is arguably the most popular figure of merit in quantum sciences. However, many of its properties are still unknown. In this work, we resolve the open problem of maximizing average fidelity over arbitrary finite ensembles of…
Quantum algorithms require accurate representations of electronic states on a quantum device, yet the approximation of electronic wave functions for strongly correlated systems remains a profound theoretical challenge, with existing methods…
Quantum phase estimation (QPE) serves as a building block of many different quantum algorithms and finds important applications in computational chemistry problems. Despite the rapid development of quantum hardware, experimental…
We present a general quantum circuit design for finding eigenvalues of non-unitary matrices on quantum computers using the iterative phase estimation algorithm. In particular, we show how the method can be used for the simulation of…
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…
The problem of estimating an unknown phase $ \varphi $ using two-level probes in the presence of unital phase-covariant noise and using finite resources is investigated. We introduce a simple model in which the phase-imprinting operation on…
We propose a quantum algorithm based on ridge regression model, which get the optimal fitting parameters w and a regularization hyperparameter {\alpha} by analysing the training dataset. The algorithm consists of two subalgorithms. One is…
In this paper we extend both standard fault tolerance theory and Kitaev's model for quantum computation, combining them so as to yield quantitative results that reveal the interplay between the two. Our analysis establishes a methodology…
Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential…
Phase estimation is one of the most important facets of quantum metrology, with applications in sensing, microscopy, and quantum computation. When estimating a phase shift in a lossy medium, there is an upper bound on the attainable…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
Quantum cooling, a deterministic process that drives any state to the lowest eigenstate, has been widely used from studying ground state properties of chemistry and condensed matter quantum physics, to general optimization problems.…