Related papers: Randomized semi-quantum matrix processing

Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…

To assess whether a gate-based quantum algorithm can be executed successfully on a noisy intermediate-scale quantum (NISQ) device, both complexity and actual value of quantum resources should be considered carefully. Based on quantum phase…

Many quantum algorithms for ground-state preparation and energy estimation require the implementation of high-degree polynomials of a Hamiltonian to achieve better convergence rates. Their circuit implementation typically relies on quantum…

The Harrow-Hassidim-Lloyd quantum algorithm was proposed to solve linear systems of equations $A\vec{x} = \vec{b}$ and it is the core of various applications. However, there is not an explicit quantum circuit for the subroutine which maps…

Randomized measurements are increasingly appreciated as powerful tools to estimate properties of quantum systems, e.g., in the characterization of hybrid classical-quantum computation. On many platforms they constitute natively accessible…

Given an arbitrary single-qubit operation, an important task is to efficiently decompose this operation into an (exact or approximate) sequence of fault-tolerant quantum operations. We derive a depth-optimal canonical form for single-qubit…

Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the…

The aim of this paper is to develop novel quantum algorithms for Gaussian process quadrature methods. Gaussian process quadratures are numerical integration methods where Gaussian processes are used as functional priors for the integrands…

We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm…

The increasing scale of near-term quantum hardware motivates the need for efficient noise characterization methods, since qubit and gate level techniques cannot capture crosstalk and correlated noise in many qubit systems. While scalable…

The Fermi-Hubbard model is of fundamental importance in condensed-matter physics, yet is extremely challenging to solve numerically. Finding the ground state of the Hubbard model using variational methods has been predicted to be one of the…

We propose a novel quantum approach to signal processing, including a quantum algorithm for low-pass and high-pass filtering, based on the sequency-ordered Walsh-Hadamard transform. We present quantum circuits for performing the…

In this work we demonstrate the use of adapted classical phase retrieval algorithms to perform control-free quantum phase estimation. We eliminate the costly controlled time evolution and Hadamard test commonly required to access the…

Quantum computers can in principle simulate quantum physics exponentially faster than their classical counterparts, but some technical hurdles remain. Here we consider methods to make proposed chemical simulation algorithms computationally…

Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…

Evaluating the entanglement spectrum is essential for characterizing exotic quantum phases such as quantum criticality and topological order. However, for large quantum many-body systems, this task is hindered by the exponential measurement…

Randomized quantum algorithms have been proposed in the context of quantum simulation and quantum linear algebra with the goal of constructing shallower circuits than methods based on block encodings. While the algorithmic complexities of…

We define the model of quantum circuits with density matrices, where non-unitary gates are allowed. Measurements in the middle of the computation, noise and decoherence are implemented in a natural way in this model, which is shown to be…

Transition amplitudes and transition probabilities are relevant to many areas of physics simulation, including the calculation of response properties and correlation functions. These quantities can also be related to solving linear systems…

We build a general quantum state tomography framework that makes use of machine learning techniques to reconstruct quantum states from a given set of coincidence measurements. For a wide range of pure and mixed input states we demonstrate…