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Fault-tolerant quantum computing demands decoders that are fast, accurate, and adaptable to circuit structure and realistic noise. While machine learning (ML) decoders have demonstrated impressive performance for quantum memory, their use…

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…

The solution for non-linear, complex partial differential Equations (PDEs) is achieved through numerical approximations, which yield a linear system of equations. This approach is prevalent in Computational Fluid Dynamics (CFD), but it…

The quantum Fourier transform (QFT) plays an important role in many known quantum algorithms such as Shor's algorithm for prime factorisation. In this paper we show that the QFT algorithm can, on a restricted set of input states, be…

Quantum signal processing (QSP) is a methodology for constructing polynomial transformations of a linear operator encoded in a unitary. Applied to an encoding of a state $\rho$, QSP enables the evaluation of nonlinear functions of the form…

We present an efficient tensor-network-based approach for simulating large-scale quantum circuits, demonstrated using Quantum Support Vector Machines (QSVMs). Our method effectively reduces exponential runtime growth to near-quadratic…

We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed…

Singular Value Decomposition (SVD) is one of the most useful techniques for analyzing data in linear algebra. SVD decomposes a rectangular real or complex matrix into two orthogonal matrices and one diagonal matrix. In this work we…

This article introduces the Generalized Fourier Series (GFS), a novel spectral method that extends the clas- sical Fourier series to non-periodic functions. GFS addresses key challenges such as the Gibbs phenomenon and poor convergence in…

A central ingredient in fault-tolerant quantum algorithms is the initialization of a logical state for a given quantum error-correcting code from a set of noisy qubits. A scheme that has demonstrated promising results for small code…

We present a general method for decomposing non-unitary operators into a linear combination of unitary operators, where the approximation error decays exponentially. The decomposition is based on a smooth periodic extension of the identity…

Implementing algorithms on a fault-tolerant quantum computer will require fast decoding throughput and latency times to prevent an exponential increase in buffer times between the applications of gates. In this work we begin by quantifying…

Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity…

Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set $\{\U(2), \textrm{CNOT}\}$, the discrete Fourier transforms $F_N=(\omega^{ij})_{N\times N},i,j=0,1,..., N-1,…

Decoherence-free subspaces and subsystems (DFS) preserve quantum information by encoding it into symmetry-protected states unaffected by decoherence. An inherent DFS of a given experimental system may not exist; however, through the use of…

Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…

The solving of linear systems provides a rich area to investigate the use of nearer-term, noisy, intermediate-scale quantum computers. In this work, we discuss hybrid quantum-classical algorithms for skewed linear systems for…

Dynamic quantum circuits (DQCs) incorporate mid-circuit measurements and gates conditioned on these measurement outcomes. DQCs can prepare certain long-range entangled states in constant depth, making them a promising route to preparing…

Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…

Quantum computing has the potential to speed up some optimization methods. One can use quantum computers to solve linear systems via Quantum Linear System Algorithms (QLSAs). QLSAs can be used as a subroutine for algorithms that require…