相关论文: Simple qudit ZX and ZH calculi, via integrals

A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices. The boundary of the lattice consists of…

Although only two quantum states of a physical system are often used to encode quantum information in the form of qubits, many levels can in principle be used to obtain qudits and increase the information capacity of the system. To take…

In this work, we use semigroup integral to evaluate zeta-function regularized determinants. This is especially powerful for non--positive operators such as the Dirac operator. In order to understand fully the quantum effective action one…

This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…

Recently, we gave a complete axiomatisation of the ZX-calculus for the overall pure qubit quantum mechanics. Based on this result, here we also obtain a complete axiomatisation of the ZX-calculus for the Clifford+T quantum mechanics by…

We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…

Robust quantum computation with d-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high fidelity two-qudit gates. We first describe how to implement parallel single qudit operations. It is by now well…

Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…

This work proposes numerical tests which determine whether a two-qubit operator has an atypically simple quantum circuit. Specifically, we describe formulae, written in terms of matrix coefficients, characterizing operators implementable…

We consider the problem of estimating quantum observables on a collection of qubits, given as a linear combination of Pauli operators, with shallow quantum circuits consisting of single-qubit rotations. We introduce estimators based on…

With the rapid development of quantum computing, automatic verification of quantum circuits becomes more and more important. While several decision diagrams (DDs) have been introduced in quantum circuit simulation and verification, none of…

The physics of quantum walks on graphs is formulated in Hamiltonian language, both for simple quantum walks and for composite walks, where extra discrete degrees of freedom live at each node of the graph. It is shown how to map between…

We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high…

Improving the simulation of quantum circuits on classical computers is important for understanding quantum advantage and increasing development speed. In this paper, we explore a new way to express stabilizer states and further improve the…

Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…

In a recent work arXiv:2201.07655v2 we showed that there is a constant $\lambda >0$ such that it is possible to efficiently classically simulate a quantum system in which (i) qudits are placed on the nodes of a graph, (ii) each qudit…

Measurement-based quantum computing (MBQC), an alternate paradigm for formulating quantum algorithms, can lead to potentially more flexible and efficient implementations as well as to theoretical insights on the role of entanglement in a…

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…

We investigate an extension to the phase shift formalism for calculating one-loop determinants. This extension is motivated by requirements of the computation of Z-string quantum energies in D=3+1 dimensions. A subtlety that seems to imply…

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…