Related papers: Quantum Algorithms based on the Block-Encoding Fra…
We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.
Circulant matrices are an important family of operators, which have a wide range of applications in science and engineering related fields. They are in general non-sparse and non-unitary. In this paper, we present efficient quantum circuits…
We present a universal framework for quantum error-correcting codes, i.e., the one that applies for the most general quantum error-correcting codes. This framework is established on the group algebra, an algebraic notation for the nice…
We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix. Under low-rank assumptions, the remaining entries can be…
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…
Based on the matrix realignment and partial transpose, we develop an approach to entangling power and operator entanglement of quantum unitary operators. We demonstrate efficiency of the approach by studying several unitary operators on…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
Block-encodings of matrices have become an essential element of quantum algorithms derived from the quantum singular value transformation. This includes a variety of algorithms ranging from the quantum linear systems problem to quantum…
Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…
Iteration method is commonly used in solving linear systems of equations. We present quantum algorithms for the relaxed row and column iteration methods by constructing unitary matrices in the iterative processes, which generalize row and…
Contour integral algorithms seek to compute a small number of eigenvalues located within a bounded region of the complex plane. These methods can be applied to both linear and nonlinear matrix eigenvalue problems. In the latter case, the…
This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness…
Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need…
Quantum computing can enable a variety of breakthroughs in research and industry in the future. Although some quantum algorithms already exist that show a theoretical speedup compared to the best known classical algorithms, the…
An efficient technique of computing on encrypted data allows a client with limited capability to perform complex operations on a remote fault-tolerant server without leaking anything about the input or output. Quantum computing provides…
A central task in medical imaging is the reconstruction of an image or function from data collected by medical devices (e.g., CT, MRI, and PET scanners). We provide quantum algorithms for image reconstruction with exponential speedup over…