Chris Fields, James F. Glazebrook, Antonino Marcianò, Emanuele Zappala • Published: 2025-09-24
We study the relationship between computation and scattering both operationally (hence phenomenologically) and formally. We show how topological quantum neural networks (TQNNs) enable universal quantum computation, using the Reshetikhin-Turaev and Turaev-Viro models to show how TQNNs implement quantum error-correcting codes. We then exhibit a formal correspondences between TQNNs and amplituhedra t...
Thibaud Louvet, Thomas Ayral, Xavier Waintal • Published: 2023-06-05
Quantum chemistry is envisioned as an early and disruptive application for quantum computers. Yet, closer scrutiny of the proposed algorithms shows that there are considerable difficulties along the way. Here, we propose two criteria for evaluating two leading quantum approaches for finding the ground state of molecules. The first criterion applies to the variational quantum eigensolver (VQE) algo...
Peter Brearley, Philipp Pfeffer • Published: 2025-11-24
Dissipation and irreversibility are central to most physical processes, yet they lead to non-unitary dynamics that are challenging to realise on quantum processors. High-order operator splitting is an attractive approach for simulating unitary dynamics, yet conventional product formulas introduce negative time steps at high orders that are numerically unstable for dissipative dynamics. We show how...
Lamine Rihani • Published: 2026-02-15
Artificial intelligence/machine learning (AI/ML) systems and emerging quantum computing software present unprecedented testing challenges characterized by high-dimensional/continuous input spaces, probabilistic/non-deterministic output distributions, behavioral correctness defined exclusively over observable prediction behaviors and measurement outcomes, and critical quality dimensions, trustworth...
Shi-Xin Zhang, Yu-Qin Chen, Weitang Li, Jiace Sun, Wei-Guo Ma, Pei-Lin Zheng, Yu-Xiang Huang, Qi-Xiang Wang, Hui Yu, Zhuo Li, Xuyang Huang, Zong-Liang Li, Zhou-Quan Wan, Shuo Liu, Jiezhong Qiu, Jiaqi Miao, Zixuan Song, Yuxuan Yan, Kazuki Tsuoka, Pan Zhang, Lei Wang, Heng Fan, Chang-Yu Hsieh, Hong Yao, Tao Xiang • Published: 2026-02-15
We present TensorCircuit-NG, a next-generation quantum software platform designed to bridge the gap between quantum physics, artificial intelligence, and high-performance computing. Moving beyond the scope of traditional circuit simulators, TensorCircuit-NG establishes a unified, tensor-native programming paradigm where quantum circuits, tensor networks, and neural networks fuse into a single, end...
Tim Palmer • Published: 2025-09-19
Motivated in part by John Wheeler's assertion that the continuum nature of Hilbert Space conceals the `it-from-bit' information-theoretic character of the quantum wavefunction, a theory of quantum physics (Rational Quantum Mechanics - RaQM) is proposed based on a specific discretisation of complex Hilbert Space. The Schrödinger equation is not modified in RaQM, even during measurement. However, th...
Mark Wildon • Published: 2026-02-14
These notes introduce quantum computation and quantum error correction, emphasising the importance of stabilisers and the mathematical foundations in basic Lie theory. We begin by using the double cover map $\mathrm{SU}_2 \rightarrow \mathrm{SO}_3(\mathbb{R})$ to illustrate the distinction between states and measurements for a single qubit. We then discuss entanglement and CNOT gates, the Deutsch-...
Kaiwen Weng, Zhaoyuan Meng, Guohui Hu • Published: 2026-01-27
The nonlinear Schrödinger equation (NLSE) is a fundamental model that describes diverse complex phenomena in nature. However, simulating the NLSE on a quantum computer is inherently challenging due to the presence of the nonlinear term. We propose a hybrid quantum-classical framework for simulating the NLSE based on the split-step Fourier method. During the linear propagation step, we apply the ki...
Timothy Proctor, Kevin Young, Andrew D. Baczewski, Robin Blume-Kohout • Published: 2024-07-11
The rapid pace of development in quantum computing technology has sparked a proliferation of benchmarks for assessing the performance of quantum computing hardware and software. Good benchmarks empower scientists, engineers, programmers, and users to understand a computing system's power, but bad benchmarks can misdirect research and inhibit progress. In this Perspective, we survey the science of ...
Amirreza Akbari, Xavier Coiteux-Roy, Francesco d'Amore, François Le Gall, Henrik Lievonen, Darya Melnyk, Augusto Modanese, Shreyas Pai, Marc-Olivier Renou, Václav Rozhoň, Jukka Suomela • Published: 2024-03-04
We connect three distinct lines of research that have recently explored extensions of the classical LOCAL model of distributed computing: A. distributed quantum computing and non-signaling distributions [e.g. STOC 2024], B. finitely-dependent processes [e.g. Forum Math. Pi 2016], and C. locality in online graph algorithms and dynamic graph algorithms [e.g. ICALP 2023].
We prove new results on th...