Related papers: Quantum Logspace Algorithm for Powering Matrices w…
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
Efficient methods for the simulation of quantum circuits on classic computers are crucial for their analysis due to the exponential growth of the problem size with the number of qubits. Here we study lumping methods based on bisimulation,…
In this paper, we present a direct quantum adaptation of the classical shifted power method. The method is very similar to the iterative phase estimation algorithm; however, it does not require any initial estimate of an eigenvector and as…
Solving systems of linear equations is a fundamental problem, but it can be computationally intensive for classical algorithms in high dimensions. Existing quantum algorithms can achieve exponential speedups for the quantum linear system…
We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use…
Significant challenges remain with the development of macroscopic quantum computing, hardware problems of noise, decoherence, and scaling, software problems of error correction, and, most important, algorithm construction. Finding truly…
A novel approach to exploiting the log-convex structure present in many design problems is developed by modifying the classical Sequential Quadratic Programming (SQP) algorithm. The modified algorithm, Logspace Sequential Quadratic…
In this work, we propose a machine learning-based approach to address a specific aspect of the Quantum Marginal Problem: reconstructing a global density matrix compatible with a given set of quantum marginals. Our method integrates a…
This paper investigates the power of polynomial-time quantum computation in which only a very limited number of qubits are initially clean in the |0> state, and all the remaining qubits are initially in the totally mixed state. No…
The characterization of a unitary gate is experimentally accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to reconstruct the underlying operator. The process matrix is typically…
The reconstruction of quantum states from experimental measurements, often achieved using quantum state tomography (QST), is crucial for the verification and benchmarking of quantum devices. However, performing QST for a generic…
Scalable quantum technologies will present challenges for characterizing and tuning quantum devices. This is a time-consuming activity, and as the size of quantum systems increases, this task will become intractable without the aid of…
Quantum contextuality is a limitation on deterministic hidden variable models, testable in measurement scenarios where outcomes differ under quantum or classical descriptions due to a common set of constraints. When considering measurements…
Tensor decomposition serves as a powerful primitive in statistics and machine learning, and has numerous applications in problems such as learning latent variable models or mixture of Gaussians. In this paper, we focus on using power…
The bootstrap is a technique recently developed to get energy eigenvalues of bound states and correlation functions. There are three crucial steps - recursive equations, positivity constraints, search space. We calculate recursive equations…
We give two quantum algorithms for computing (twisted) Kloosterman sums attached to a finite field $\mathbf{F}$ of $q$ elements. The first algorithm computes a quantum state containing, as its coefficients with respect to the standard…
We show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a…
We describe and analyze algorithms for classically simulating measurement of an $n$-qubit quantum state $\psi$ in the standard basis, that is, sampling a bit string $x$ from the probability distribution $|\langle x|\psi\rangle|^2$. Our…
Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and…
This paper provides an introduction to quantum machine learning, exploring the potential benefits of using quantum computing principles and algorithms that may improve upon classical machine learning approaches. Quantum computing utilizes…