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This paper studies the quantum computational complexity of the discrete logarithm (DL) and related group-theoretic problems in the context of generic algorithms -- that is, algorithms that do not exploit any properties of the group…

Entanglement is essential for quantum information processing, but is limited by noise. We address this by developing high-yield entanglement distillation protocols with several advancements. (1) We extend the 2-to-1 recurrence entanglement…

Complex quantum circuits are constituted by combinations of quantum subroutines. The computation is possible as long as the quantum data encoding is consistent throughout the circuit. Despite its fundamental importance, the formalization of…

As quantum processors grow in scale and reliability, the need for efficient quantum gate decomposition of circuits to a set of specific available gates, becomes ever more critical. The decomposition of a particular algorithm into a sequence…

Recently, Niu, et. al. introduced a new variant of Federated Learning (FL), called Federated Submodel Learning (FSL). Different from traditional FL, each client locally trains the submodel (e.g., retrieved from the servers) based on its…

A Finite-Difference Time-Domain (FDTD) scheme with Perfectly Matched Layers (PMLs) is considered for solving the time-dependent Schr\"{o}dinger equation, and simulate the ionization of an electron initially bound to a one-dimensional…

The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The…

Many real-world problems, like modelling environment dynamics, physical processes, time series etc., involve solving Partial Differential Equations (PDEs) parameterised by problem-specific conditions. Recently, a deep learning architecture…

Quantum computing is a promising technology that accelerates the partial differential equations solver for practical problems. The reconstruction of solutions (i.e., the readout of quantum states) remains a crucial problem, although…

In this work, we propose a framework in the form of a Python package, specifically designed for the analysis of Quantum Machine Learning models. This framework is based on the PennyLane simulator and facilitates the evaluation and training…

In this work we study the encoding of smooth, differentiable multivariate functions in quantum registers, using quantum computers or tensor-network representations. We show that a large family of distributions can be encoded as…

This work presents a quantum algorithm for solving linear systems of equations of the form $\mathbf{A}{\frac{\mathbf{\partial f}}{\mathbf{\partial x}}} = \mathbf{B}\mathbf{f}$, based on the Quantum Singular Value Transformation (QSVT). The…

Matrix product states provide efficient classical descriptions of quantum systems that may be useful as reference states for quantum algorithms such as quantum phase estimation and quantum-selected configuration interaction. Shallow circuit…

With the rising popularity of intelligent mobile devices, it is of great practical significance to develop accurate, realtime and energy-efficient image Super-Resolution (SR) inference methods. A prevailing method for improving the…

Implementing many important sub-circuits on near-term quantum devices remains a challenge due to the high levels of noise and the prohibitive depth on standard nearest-neighbour topologies. Overcoming these barriers will likely require…

The quantum circuit layout (QCL) problem is to map a quantum circuit such that the constraints of the device are satisfied. We introduce a quantum circuit mapping heuristic, QXX, and its machine learning version, QXX-MLP. The latter infers…

We propose a universal quantum circuit design that can estimate any arbitrary one-dimensional periodic functions based on the corresponding Fourier expansion. The quantum circuit contains N-qubits to store the information on the different…

We present a systematic pathway for solving differential equations within the quantum linear systems framework by combining block encoding with Quantum Singular Value Transformation (QSVT). The approach is demonstrated on a complex…

We present a computational method to automatically design the n-qubit realisations of quantum algorithms. Our approach leverages a domain-specific language (DSL) that enables the construction of quantum circuits via modular building blocks,…

Quantum error correction, which utilizes logical qubits that are encoded as redundant multiple physical qubits to find and correct errors in physical qubits, is indispensable for practical quantum computing. Surface code is considered to be…