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Related papers: Towards a Minimal Stabilizer ZX-calculus

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We consider an unstable scalar linear stochastic system, $X_{n+1}=a X_n + Z_n - U_n$, where $a \geq 1$ is the system gain, $Z_n$'s are independent random variables with bounded $\alpha$-th moments, and $U_n$'s are the control actions that…

Systems and Control · Computer Science 2021-11-25 Victoria Kostina , Yuval Peres , Gireeja Ranade , Mark Sellke

Simulation of stabilizer circuits is a well-studied problem in quantum information processing, with a number of highly optimized algorithms available. Yet, we argue that further improvements can arise from the theoretical structure of…

Optimising quantum circuits to minimise resource usage is crucial, especially with near-term hardware limited by quantum volume. This paper introduces an optimisation algorithm aiming to minimise non-Clifford gate count and two-qubit gate…

Quantum Physics · Physics 2024-01-29 Calum Holker

This paper presents the Pi-graphs, a visual paradigm for the modelling and verification of mobile systems. The language is a graphical variant of the Pi-calculus with iterators to express non-terminating behaviors. The operational semantics…

Formal Languages and Automata Theory · Computer Science 2010-11-02 Frédéric Peschanski , Hanna Klaudel , Raymond Devillers

Reducing the number of non-Clifford quantum gates present in a circuit is an important task for efficiently implementing quantum computations, especially in the fault-tolerant regime. We present a new method for reducing the number of…

Quantum Physics · Physics 2020-08-13 Aleks Kissinger , John van de Wetering

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 concept of generalized concatenated quantum codes (GCQC) provides a systematic way for constructing good quantum codes from short component codes. We introduce a stabilizer formalism for GCQCs, which is achieved by defining quantum…

Quantum Physics · Physics 2013-10-14 Yun-Jiang Wang , Bei Zeng , Markus Grassl , Barry C. Sanders

As state-of-the-art quantum computers are capable of running increasingly complex algorithms, the need for automated methods to design and test potential applications rises. Equivalence checking of quantum circuits is an important, yet…

Quantum Physics · Physics 2022-08-30 Tom Peham , Lukas Burgholzer , Robert Wille

The ZH-calculus is a graphical calculus for linear maps between qubits that allows a natural representation of the Toffoli+Hadamard gate set. The original version of the calculus, which allows every generator to be labelled by an arbitrary…

Quantum Physics · Physics 2019-04-17 John van de Wetering , Sal Wolffs

We develop a unified geometric framework for quantum circuit compilation based on quantized orbifold phases and their diagrammatic semantics. Physical qubit platforms impose heterogeneous phase resolutions, anisotropic Bloch-ball…

Quantum Physics · Physics 2025-12-02 Gunhee Cho , Jason Cheng , Evelyn Li

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

Complex safety-critical systems require multiple models for a comprehensive description, resulting in error-prone development and laborious verification. Bidirectional transformation (BX) is an approach to automatically synchronizing these…

Software Engineering · Computer Science 2024-05-02 Jianhong Zhao , Yongwang Zhao , Peisen Yao , Fanlang Zeng , Bohua Zhan , Kui Ren

In this paper, we give a modified version of the qutrit ZX-calculus, by which we represent qutrit graph states as diagrams and prove that the qutrit version of local complementation property is true if and only if the qutrit Hadamard gate…

Quantum Physics · Physics 2017-04-21 Xiaoyan Gong , Quanlong Wang

Mapping fermionic systems to qubits on a quantum computer is often the first step for algorithms in quantum chemistry and condensed matter physics. However, it is difficult to reconcile the many different approaches that have been proposed,…

Quantum Physics · Physics 2025-05-12 Haytham McDowall-Rose , Razin A. Shaikh , Lia Yeh

The stabiliser formalism allows the efficient description of a sizeable class of pure as well as mixed quantum states of N-qubit systems. That same formalism has important applications in the field of quantum error correcting codes, where…

Quantum Physics · Physics 2009-11-11 Koenraad M. R. Audenaert , Martin B. Plenio

We address the task of verifying whether a quantum computer, designed to be protected by a specific stabilizer code, correctly encodes the corresponding logical qubits. To achieve this, we develop a general framework for subspace…

Quantum Physics · Physics 2024-12-10 Congcong Zheng , Xutao Yu , Zaichen Zhang , Ping Xu , Kun Wang

The codeword stabilized ("CWS") quantum codes formalism presents a unifying approach to both additive and nonadditive quantum error-correcting codes (arXiv:0708.1021). This formalism reduces the problem of constructing such quantum codes to…

Quantum Physics · Physics 2015-05-13 Isaac L. Chuang , Andrew W. Cross , Graeme Smith , John A. Smolin , Bei Zeng

This note describes how the the scalable ZXH calculus can be used to represent in a compact way the quantum gates that are diagonal in the computational basis. This includes controlled and multi-controlled Z gates, their generalizations,…

Quantum Physics · Physics 2020-12-18 Titouan Carette

The notion of symmetry is shown to be at the heart of all error correction/avoidance strategies for preserving quantum coherence of an open quantum system S e.g., a quantum computer. The existence of a non-trivial group of symmetries of the…

Quantum Physics · Physics 2007-05-23 P. Zanardi

We introduce \emph{stratified colimit codes}: stabiliser codes obtained by taking the degree-wise colimit $\mathcal C_\bullet(X):=\operatorname*{colim}_{\sigma\in X}F(\sigma)$ of a functor $F\colon X\to\mathbf{Ch}(R)$ from a finite poset…

Quantum Physics · Physics 2025-09-10 William Boone Samuels