Related papers: Variational Quantum Algorithms for Trace Distance …

The variational quantum eigensolver (VQE) is one of the most appealing quantum algorithms to simulate electronic structure properties of molecules on near-term noisy intermediate-scale quantum devices. In this work, we generalize the VQE…

Over the past three decades significant reductions have been made to the cost of estimating ground-state energies of molecular Hamiltonians with quantum computers. However, comparatively little attention has been paid to estimating the…

A broad class of hybrid quantum-classical algorithms known as "variational algorithms" have been proposed in the context of quantum simulation, machine learning, and combinatorial optimization as a means of potentially achieving a quantum…

The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are…

Quantum Parameter Estimation (QPE) is important from the perspective of both fundamental quantum research and various practical applications of quantum technologies such as for developing optimal quantum control strategies. Standard and…

The problem of finding the ground state energy of a Hamiltonian using a quantum computer is currently solved using either the quantum phase estimation (QPE) or variational quantum eigensolver (VQE) algorithms. For precision $\epsilon$, QPE…

Recent progress in quantum algorithms and hardware indicates the potential importance of quantum computing in the near future. However, finding suitable application areas remains an active area of research. Quantum machine learning is…

Quantum chemistry is among the most promising applications of quantum computing, offering the potential to solve complex electronic structure problems more efficiently than classical approaches. A critical component of any quantum algorithm…

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…

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…

We introduce a novel hybrid quantum-classical algorithm for the near-term computation of expectation values in quantum systems at finite temperatures. This is based on two stages: on the first one, a mixed state approximating a fiducial…

Current quantum simulators suffer from multiple limitations such as short coherence time, noisy operations, faulty readout and restricted qubit connectivity in some platforms. Variational quantum algorithms are the most promising approach…

The measures of distances between points in a Hilbert space are one of the basic theoretical concepts used to characterize properties of a quantum system with respect to some etalon state. These are not only used in studying fidelity of…

As quantum devices become more complex and the requirements on these devices become more demanding, it is crucial to be able to verify the performance of such devices in a scalable and reliable fashion. A cornerstone task in this challenge…

We present a detailed numerical study of an alternative approach, named Quantum Non-Demolition Measurement (QNDM), to efficiently estimate the gradients or the Hessians of a quantum observable. This is a key step and a resource-demanding…

Quantum computing allows for the manipulation of highly correlated states whose properties quickly go beyond the capacity of any classical method to calculate. Thus one natural problem which could lend itself to quantum advantage is the…

Graph-based methods provide a powerful tool set for many non-parametric frameworks in Machine Learning. In general, the memory and computational complexity of these methods is quadratic in the number of examples in the data which makes them…

Variational Quantum Algorithms (VQAs) are a promising application for near-term quantum processors, however the quality of their results is greatly limited by noise. For this reason, various error mitigation techniques have emerged to deal…

Reducing the dimension of nonlinear data is crucial in data processing and visualization. The locally linear embedding algorithm (LLE) is specifically a representative nonlinear dimensionality reduction method with well maintaining the…

Calculating the trace of the product of $m$ $n$-qubit density matrices (multivariate trace) is a crucial subroutine in quantum error mitigation and information measures estimation. We propose an unified multivariate trace estimation (UMT)…