Related papers: Efficient algorithm for generating Pauli coordinat…
Analysis of quantum processes, especially in the context of noise, errors, and decoherence is essential for the improvement of quantum devices. An intuitive representation of those processes modeled by quantum channels are Pauli transfer…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…
We introduce a simple algorithm that efficiently computes tensor products of Pauli matrices. This is done by tailoring the calculations to this specific case, which allows to avoid unnecessary calculations. The strength of this strategy is…
We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such…
The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts…
Solving a Poisson equation is generally reduced to solving a linear system with a coefficient matrix $A$ of entries $a_{ij}$, $i,j=1,2,...,n$, from the discretized Poisson equation. Although the variational quantum algorithms are promising…
The construction of quantum circuits to simulate Hamiltonian evolution is central to many quantum algorithms. State-of-the-art circuits are based on oracles whose implementation is often omitted, and the complexity of the algorithm is…
A variety of quantum algorithms employ Pauli operators as a convenient basis for studying the spectrum or evolution of Hamiltonians or measuring multi-body observables. One strategy to reduce circuit depth in such algorithms involves…
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for…
We propose a new quantum computing formalism named Pauli quantum computing. In this formalism, we use the Pauli basis $I$ and $X$ on the non-diagonal blocks of density matrices to encode information and treat them as the computational basis…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to…
We develop a novel approach for efficiently applying variational quantum linear solver (VQLS) in context of structured sparse matrices. Such matrices frequently arise during numerical solution of partial differential equations which are…
Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…
Pauli channels are fundamental in the context of quantum computing as they model the simplest kind of noise in quantum devices. We propose a quantum algorithm for simulating Pauli channels and extend it to encompass Pauli dynamical maps…
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
A quantum algorithm for computing the determinant of a unitary matrix $U\in U(N)$ is given. The algorithm requires no preparation of eigenstates of $U$ and estimates the phase of the determinant to $t$ binary digits accuracy with…