Related papers: Nearly Optimal Quantum Algorithm for Estimating Mu…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
It is known that the estimating equations for quantile regression (QR) can be solved using an EM algorithm in which the M-step is computed via weighted least squares, with weights computed at the E-step as the expectation of independent…
In the accompanying paper of arXiv:2505.00697, we have presented a generalized scheme of adaptive quantum gradient estimation (QGE) algorithm, and further proposed two practical variants which not only achieve doubly quantum enhancement in…
We present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in $\sqrt{N \beta/{\cal Z}}$ and polynomial in…
We consider the problem of pricing discretely monitored Asian options over $T$ monitoring points where the underlying asset is modeled by a geometric Brownian motion. We provide two quantum algorithms with complexity poly-logarithmic in $T$…
The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks, which is an optimization algorithm for finding a local minimum of an objective function. The quantum versions of gradient…
We introduce an approximate description of an $N$-qubit state, which contains sufficient information to estimate the expectation value of any observable to a precision that is upper bounded by the ratio of a suitably-defined seminorm of the…
Estimating properties of quantum states, such as fidelities, molecular energies, and correlation functions, is a fundamental task in quantum information science. Due to the limitation of practical quantum devices, including limited circuit…
Many optimization methods for training variational quantum algorithms are based on estimating gradients of the cost function. Due to the statistical nature of quantum measurements, this estimation requires many circuit evaluations, which is…
Evaluating the expectation of a quantum circuit is a classically difficult problem known as the quantum mean value problem (QMV). It is used to optimize the quantum approximate optimization algorithm and other variational quantum…
Within the context of hybrid quantum-classical optimization, gradient descent based optimizers typically require the evaluation of expectation values with respect to the outcome of parameterized quantum circuits. In this work, we explore…
In this paper, we present a new method for calculating expectation values of operators that can be expressed as a linear combination of unitary (LCU) operators. This method allows to perform this calculation in a single quantum circuit…
We explore a non-variational quantum state preparation approach combined with the ADAPT operator selection strategy in the application of preparing the ground state of a desired target Hamiltonian. In this algorithm, energy gradient…
A hybrid quantum-classical algorithm is a computational scheme in which quantum circuits are used to extract information that is then processed by a classical routine to guide subsequent quantum operations. These algorithms are especially…
We consider the task of estimating the expectation value of an $n$-qubit tensor product observable $O_1\otimes O_2\otimes \cdots \otimes O_n$ in the output state of a shallow quantum circuit. This task is a cornerstone of variational…
Relevant metrological scenarios involve the simultaneous estimation of multiple parameters. The fundamental ingredient to achieve quantum-enhanced performances is based on the use of appropriately tailored quantum probes. However, reaching…
We propose an iterative algorithm for incomplete quantum process tomography, with the help of quantum state estimation, based on the combined principles of maximum-likelihood and maximum-entropy. The algorithm yields a unique estimator for…
This paper proposes a quantum circuit for computing the mean value from a given set of numbers or function evaluations. Suppose a Quantum Random Access Memory is given as a black-box function, which allows us to store and read the values of…
Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions of the…
Measuring the distinguishability between quantum states is a basic problem in quantum information theory. In this paper, we develop optimal quantum algorithms that estimate both the trace distance and the (square root) fidelity between pure…