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We introduce the first randomized algorithms for Quantum Singular Value Transformation (QSVT), a unifying framework for many quantum algorithms. Standard implementations of QSVT rely on block encodings of the Hamiltonian, which are costly…

In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical…

Many fundamental properties of a quantum system are captured by its Hamiltonian and ground state. Despite the significance of ground states preparation (GSP), this task is classically intractable for large-scale Hamiltonians. Quantum neural…

Nonorthogonal quantum state discrimination (QSD) plays an important role in quantum information and quantum communication. In addition, compared to Hermitian quantum systems, parity-time-($\mathcal{PT}$-)symmetric non-Hermitian quantum…

Estimating quantum amplitude, or the overlap between two quantum states, is a fundamental task in quantum computing and underpins numerous quantum algorithms. In this work, we introduce a novel algorithmic framework for quantum amplitude…

Quantum amplitude amplification algorithm is an important and basic technique in quantum computing. In this paper, our goal is to study distributed quantum amplitude amplification algorithms, and the main contributions are: (1) A…

The quantum singular value transformation has revolutionised quantum algorithms. By applying a polynomial to an arbitrary matrix, it provides a unifying picture of quantum algorithms. However, polynomials are restricted to definite parity…

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…

Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is…

Quantum Process Tomography (QPT) methods aim at identifying, i.e. estimating, a quantum process. QPT is a major quantum information processing tool, since it especially allows one to experimentally characterize the actual behavior of…

Impressive progress has been made in the past decade in the study of technological applications of varied types of quantum systems. With industry giants like IBM laying down their roadmap for scalable quantum devices with more than…

In this study, a novel quantum-inspired Bayesian probability (QIBP) algorithm, informed by quantum dynamics, is proposed to improve the predictions of nuclear mass from theoretical models. Within the QIBP framework, residuals between the…

Physical implementation of Quantum Information Processing (QIP) by liquid-state Nuclear Magnetic Resonance (NMR), using weakly coupled spin-1/2 nuclei of a molecule, is well established. Nuclei with spin$>$1/2 oriented in liquid crystalline…

The use of nuclear magnetic resonance (NMR) to carry out quantum information processing (QIP) often requires the preparation, transformation, and detection of pseudopure states. In our previous work, it was shown that the use of pairs of…

The polar decomposition of a matrix is a key element in the quantum linear algebra toolbox. We show that the problem of quantum polar decomposition, recently studied in Lloyd et al. [LBP+20], has a simple and concise implementation via the…

The Traveling Salesman Problem (TSP) is a classical NP-hard problem that plays a crucial role in combinatorial optimization. In this paper, we are interested in the quantum search framework for the TSP because it has robust theoretical…

The preparation of $n$-qubit quantum states is a cross-cutting subroutine for many quantum algorithms, and the effort to reduce its circuit complexity is a significant challenge. In the literature, the quantum state preparation algorithm by…

We introduce a family of variational quantum algorithms called quantum iterative power algorithms (QIPA) that outperform existing hybrid near-term quantum algorithms of the same kind. We demonstrate the capabilities of QIPA as applied to…

Quantum two-level systems, i.e. qubits, form the basis for most quantum machine learning approaches that have been proposed throughout the years. However, higher dimensional quantum systems constitute a promising alternative and are…

This paper introduces Quantum Classical Branch-and-Price (QCBP), a hybrid quantum-classical algorithm for the Vertex Coloring problem on neutral-atom Quantum Processing Units (QPUs). QCBP embeds quantum computation within the classical…