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Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…

Quantum Physics · Physics 2022-05-18 Alexis Ralli , Michael I. Williams , Peter V. Coveney

Graphical calculi for representing interacting quantum systems serve a number of purposes: compositionally, intuitive graphical reasoning, and a logical underpinning for automation. The power of these calculi stems from the fact that they…

Logic in Computer Science · Computer Science 2011-03-17 Bob Coecke , Aleks Kissinger , Alex Merry , Shibdas Roy

Despite significant progress in transformer interpretability, an understanding of the computational mechanisms of large language models (LLMs) remains a fundamental challenge. Many approaches interpret a network's hidden representations but…

Machine Learning · Computer Science 2025-10-14 James R. Golden

Despite significant advances in quantum algorithms, quantum programs in practice are often expressed at the circuit level, forgoing helpful structural abstractions common to their classical counterparts. Consequently, as many quantum…

Quantum Physics · Physics 2025-06-18 Zane M. Rossi , Jack L. Ceroni , Isaac L. Chuang

With quantum computers promising advantages even in the near-term NISQ era, there is a lively community that develops software and toolkits for the design of corresponding quantum circuits. Although the underlying problems are different,…

Quantum Physics · Physics 2023-01-11 Robert Wille , Stefan Hillmich , Lukas Burgholzer

Suppressing errors is the central challenge for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected ``logical'' qubits, where information is…

We present VOQC, the first fully verified optimizer for quantum circuits, written using the Coq proof assistant. Quantum circuits are expressed as programs in a simple, low-level language called SQIR, a simple quantum intermediate…

Programming Languages · Computer Science 2020-11-16 Kesha Hietala , Robert Rand , Shih-Han Hung , Xiaodi Wu , Michael Hicks

We introduce the first complete and approximatively universal diagrammatic language for quantum mechanics. We make the ZX-Calculus, a diagrammatic language introduced by Coecke and Duncan, complete for the so-called Clifford+T quantum…

Quantum Physics · Physics 2018-02-26 Emmanuel Jeandel , Simon Perdrix , Renaud Vilmart

Block-encoding is a foundational technique in modern quantum algorithms, enabling the implementation of non-unitary operations by embedding them into larger unitary matrices. While theoretically powerful and essential for advanced protocols…

Quantum Physics · Physics 2026-04-21 Matic Petrič , René Zander

ZX-calculus is a strict mathematical formalism for graphical quantum computing which is based on the field of complex numbers. In this paper, we extend its power by generalising ZX-calculus to such an extent that it is universal both in an…

Quantum Physics · Physics 2020-10-13 Quanlong Wang

Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…

Optimization and Control · Mathematics 2022-01-21 Chin-Yao Chang , Eric Jones , Yiyun Yao , Peter Graf , Rishabh Jain

Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that…

Quantum Physics · Physics 2019-09-18 Nikolas P. Breuckmann , Xiaotong Ni

Quantum programs are notoriously difficult to code and verify due to unintuitive quantum knowledge associated with quantum programming. Automated tools relieving the tedium and errors associated with low-level quantum details would hence be…

Quantum Physics · Physics 2023-12-07 Haowei Deng , Runzhou Tao , Yuxiang Peng , Xiaodi Wu

Utility-scale quantum programs contain operations on the order of $>10^{15}$ which must be prepared and piped from a classical co-processor to the control unit of the quantum device. The latency of this process significantly increases with…

Quantum Physics · Physics 2025-07-29 Ioana Moflic , Alan Robertson , Simon J. Devitt , Alexandru Paler

Molecular representation learning has become a central approach in AI-driven drug discovery, yet existing molecular tokenizations such as SMILES remain largely syntactic and do not naturally align with chemically meaningful substructures.…

Machine Learning · Computer Science 2026-05-19 Takayuki Kimura

Quantum based systems are a relatively new research area for that different modelling languages including process calculi are currently under development. Encodings are often used to compare process calculi. Quality criteria are used then…

Logic in Computer Science · Computer Science 2024-08-07 Anna Schmitt , Kirstin Peters , Yuxin Deng

Decoding a quantum error correction code is generally NP-hard, but corrections must be applied at a high frequency to suppress noise successfully. Matchable codes, like the surface code, exhibit a special structure that makes it possible to…

A recently developed theory for eliminating decoherence and design constraints in quantum computers, ``encoded recoupling and decoupling'', is shown to be fully compatible with a promising proposal for an architecture enabling scalable…

Quantum Physics · Physics 2016-09-08 D. A. Lidar , L. -A Wu

We describe an efficient quantum algorithm for solving the linear matrix equation AX+XB=C, where A, B, and C are given complex matrices and X is unknown. This is known as the Sylvester equation, a fundamental equation with applications in…

Quantum Physics · Physics 2025-08-22 Rolando D. Somma , Guang Hao Low , Dominic W. Berry , Ryan Babbush

We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding…

Quantum Physics · Physics 2020-07-29 Dong-Sheng Wang , Guanyu Zhu , Cihan Okay , Raymond Laflamme
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