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We construct quantum circuits for solving one-dimensional Schr\"odinger equations. Simulations of three typical examples, i.e., harmonic oscillator, square-well and Coulomb potential, show that reasonable results can be obtained with eight…

Quantum Physics · Physics 2009-07-21 K. Nakao , A. Matsuyama

Quantum computations are expressed in general as quantum circuits, which are specified by ordered lists of quantum gates. The resulting specifications are used during the optimisation and execution of the expressed computations. However,…

Quantum Physics · Physics 2018-08-08 Alexandru Paler , Simon J. Devitt

The dynamical-algebraic structure underlying all the schemes for quantum information stabilization is argued to be fully contained in the reducibility of the operator algebra describing the interaction with the environment of the coding…

Quantum Physics · Physics 2009-10-31 Paolo Zanardi

We introduce a novel method for strong classical simulation of quantum circuits based on optimally k-partitioning ZX-diagrams, reducing each part individually, and then efficiently cross-referencing their results to conclude the overall…

Quantum Physics · Physics 2024-09-04 Matthew Sutcliffe

We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result --…

Quantum Physics · Physics 2009-10-30 Richard Cleve

The ZX-calculus is a graphical calculus for reasoning about pure state qubit quantum mechanics. It is complete for pure qubit stabilizer quantum mechanics, meaning any equality involving only stabilizer operations that can be derived using…

Quantum Physics · Physics 2014-12-31 Miriam Backens

Generic quantum-circuit simulation appears intractable for conventional computers and may be unnecessary because useful quantum circuits exhibit significant structure that can be exploited during simulation. For example, Gottesman and Knill…

Data Structures and Algorithms · Computer Science 2017-12-12 Héctor J. García , Igor L. Markov

Stabilizer simulation can efficiently simulate an important class of quantum circuits consisting exclusively of Clifford gates. However, all existing extensions of this simulation to arbitrary quantum circuits including non-Clifford gates…

Quantum Physics · Physics 2023-11-22 Benjamin Bichsel , Anouk Paradis , Maximilian Baader , Martin Vechev

The real stabilizer fragment of quantum mechanics was shown to have a complete axiomatization in terms of the angle-free fragment of the ZX-calculus. This fragment of the ZX-calculus---although abstractly elegant---is stated in terms of…

Quantum Physics · Physics 2019-10-02 Cole Comfort

The ZX calculus and ZH calculus use diagrams to denote and compute properties of quantum operations, using `rewrite rules' to transform between diagrams which denote the same operator through a functorial semantic map. Different semantic…

Quantum Physics · Physics 2024-08-26 Niel de Beaudrap , Richard D. P. East

Recent advances in classical simulation of Clifford+T circuits make use of the ZX calculus to iteratively decompose and simplify magic states into stabiliser terms. We improve on this method by studying stabiliser decompositions of ZX…

Quantum Physics · Physics 2025-09-23 Mark Koch , Richie Yeung , Quanlong Wang

We introduce the Scalable ZX-calculus (SZX-calculus for short), a formal and compact graphical language for the design and verification of quantum computations. The SZX-calculus is an extension of the ZX-calculus, a powerful framework that…

Quantum Physics · Physics 2020-07-31 Titouan Carette , Dominic Horsman , Simon Perdrix

We consider design of the quantum stabilizer codes via a two-step, low-complexity approach based on the framework of codeword-stabilized (CWS) codes. In this framework, each quantum CWS code can be specified by a graph and a binary code.…

Quantum Physics · Physics 2012-02-23 Alexey A. Kovalev , Ilya Dumer , Leonid P. Pryadko

We introduce the first minimal and complete equational theory for quantum circuits. Hence, we show that any true equation on quantum circuits can be derived from simple rules, all of them being standard except a novel but intuitive one…

Quantum Physics · Physics 2024-05-20 Alexandre Clément , Noé Delorme , Simon Perdrix

We present the solid-state quantum circuits that have been developed in order to implement quantum bits suitable for a quantum processor. These qubits are either based on the quantum state of a single particle (semiconductor qubits), or on…

Superconductivity · Physics 2007-05-23 D. Esteve , D. Vion

Extensively evaluating the capabilities of (large) language models is difficult. Rapid development of state-of-the-art models induce benchmark saturation, while creating more challenging datasets is labor-intensive. Inspired by the recent…

Computation and Language · Computer Science 2025-06-02 Alan Sun

We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with…

Quantum Physics · Physics 2009-02-19 Andrew Cross , Graeme Smith , John A. Smolin , Bei Zeng

Quantum computers promise to efficiently solve important problems classical computers never will. However, in order to capitalize on these prospects, a fully automated quantum software stack needs to be developed. This involves a multitude…

Quantum Physics · Physics 2023-01-12 Robert Wille , Lukas Burgholzer , Stefan Hillmich , Thomas Grurl , Alexander Ploier , Tom Peham

Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…

Quantum Physics · Physics 2025-02-07 Ilya. A. Simakov , Ilya. S. Besedin

Quantum computers allow a near-exponential speed-up for specific applications when compared to classical computers. Despite recent advances in the hardware of quantum computers, their practical usage is still severely limited due to a…

Quantum Physics · Physics 2025-05-09 Tobias Fischbach , Pierre Talbot , Pascal Bouvry