Related papers: ZX-calculus for the working quantum computer scien…
Diagrammatic techniques for reasoning about monoidal categories provide an intuitive understanding of the symmetries and connections of interacting computational processes. In the context of categorical quantum mechanics, Coecke and…
Logical gates studied in quantum computation suggest a natural logical abstraction that gives rise to a new form of unsharp quantum logic. We study the logical connectives corresponding to the following gates: the Toffoli gate, the NOT and…
This paper proposes an optimized formulation of the parts of speech tagging in Natural Language Processing with a quantum computing approach and further demonstrates the quantum gate-level runnable optimization with ZX-calculus, keeping the…
Given any quantum error correcting code permitting universal fault-tolerant quantum computation and transversal measurement of logical X and Z, we describe how to perform time-optimal quantum computation, meaning the execution of an…
We introduce the qudit ZH-calculus and show how to generalise all the phase-free qubit rules to qudits. We prove that for prime dimensions d, the phase-free qudit ZH-calculus is universal for matrices over the ring Z[e^2(pi)i/d]. For…
In this paper we exploit the utility of the triangle symbol which has a complicated expression in terms of spider diagrams in ZX-calculus, and its role within the ZX-representation of AND-gates in particular. First, we derive spider nest…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular…
The field of quantum machine learning (QML) explores how quantum computers can be used to more efficiently solve machine learning problems. As an application of hybrid quantum-classical algorithms, it promises a potential quantum advantages…
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…
Two circuits are considered to be equivalent under noise if the effect of faults on one circuit is no worse than the effect of faults on the other circuit. We call this relationship fault equivalence. Fault equivalence offers a way to…
Quantum advantage in computation refers to the existence of computational tasks that can be performed efficiently on a quantum computer but cannot be efficiently simulated on any classical computer. Identifying the precise boundary of…
Clifford gates are a winsome class of quantum operations combining mathematical elegance with physical significance. The Gottesman-Knill theorem asserts that Clifford computations can be classically efficiently simulated but this is true…
Geometrical aspects of quantum computing are reviewed elementarily for non-experts and/or graduate students who are interested in both Geometry and Quantum Computation. In the first half we show how to treat Grassmann manifolds which are…
Topological quantum computing is a way of allowing precise quantum computations to run on noisy and imperfect hardware. One implementation uses surface codes created by forming defects in a highly-entangled cluster state. Such a method of…
Classical program analysis techniques, such as abstract interpretation and symbolic execution, are essential for ensuring software correctness, optimizing performance, and enabling compiler optimizations. However, these techniques face…
We present a computational framework based on geometric structures. No quantum mechanics is involved, and yet the algorithms perform tasks analogous to quantum computation. Tensor products and entangled states are not needed -- they are…
A major challenge for scaling up superconducting quantum computers is unwanted couplings between qubits, which lead to always-on ZZ couplings that impact gate fidelities by shifting energy levels conditional on qubit states. To tackle this…
The development of quantum codes with good error correction parameters and useful sets of transversal gates is a problem of major interest in quantum error-correction. Abundant prior works have studied transversal gates which are restricted…
We find a sufficient set of equations between quantum circuits from which we can derive any other equation between stabilizer quantum circuits. To establish this result, we rely upon existing work on the completeness of the graphical ZX…