相关论文: Towards a Minimal Stabilizer ZX-calculus

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…

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…

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…

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…

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 --…

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…

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…

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…

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 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…

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…

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…

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,…

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…

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…

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…

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,…

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…

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…