ZX-calculus for the working quantum computer scientist

Wetering, John van de

doi:10.48550/arxiv.2012.13966

Cited by 47 publications

(59 citation statements)

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“…Due to the non-unitary nature of some of the operators used in constructing our spin-networks, and the use of post-selected measurements, this is not a straightforward question. However, we have here forged a link between spin-networks and the qubit world, as the ZX-calculus is usually considered to be a tool to discuss the creation, implementation, and optimisation of quantum algorithms [20,29,41]. It may also be possible to find a more computationally efficient version of the symmetriser or that we somehow obviate their use by means of working with already symmetrised spaces, such as spin systems.…”

Section: Discussionmentioning

confidence: 99%

Spin-networks in the ZX-calculus

East¹,

Martin-Dussaud²,

Wetering³

2021

Preprint

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The ZX-calculus, and the variant we consider in this paper (ZXH-calculus), are formal diagrammatic languages for qubit quantum computing. We show that it can also be used to describe SU(2) representation theory. To achieve this, we first recall the definition of Yutsis diagrams, a standard graphical calculus used in quantum chemistry and quantum gravity, which captures the main features of SU(2) representation theory. Second, we show precisely how it embed within Penrose's binor calculus. Third, we subsume both calculus into ZXH-diagrams. In the process we show how the SU(2) invariance of Wigner symbols is trivially provable in the ZXH-calculus. Additionally, we show how we can explicitly diagrammatically calculate 3jm, 4jm and 6j symbols. It has long been thought that quantum gravity should be closely aligned to quantum information theory. In this paper, we present a way in which this connection can be made exact, by writing the spin-networks of loop quantum gravity (LQG) in the ZX-diagrammatic language of quantum computation.

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Section: Discussionmentioning

confidence: 99%

Spin-networks in the ZX-calculus

East¹,

Martin-Dussaud²,

Wetering³

2021

Preprint

Self Cite

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“…It represents quantum processes using ZX-diagrams which can then graphically be rewritten and simplified using a collection of rewrite rules. For a review see [18]. Here we give a brief overview of the notions we will need.…”

Section: Zx-calculusmentioning

confidence: 99%

Classical simulation of quantum circuits with partial and graphical stabiliser decompositions

Kissinger¹,

Wetering²,

Vilmart³

2022

Preprint

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Recent developments in classical simulation of quantum circuits make use of clever decompositions of chunks of magic states into sums of efficiently simulable stabiliser states. We show here how, by considering certain non-stabiliser entangled states which have more favourable decompositions, we can speed up these simulations. This is made possible by using the ZX-calculus, which allows us to easily find instances of these entangled states in the simplified diagram representing the quantum circuit to be simulated. We additionally find a new technique of partial stabiliser decompositions that allow us to trade magic states for stabiliser terms. With this technique we require only 2 αt stabiliser terms, where α ≈ 0.396, to simulate a circuit with T-count t. This matches the α found by Qassim et al. [16], but whereas they only get this scaling in the asymptotic limit, ours applies for a circuit of any size. Our method builds upon a recently proposed scheme for simulation combining stabiliser decompositions and optimisation strategies implemented in the software QuiZX [15]. With our techniques we manage to reliably simulate 50-qubit 1400 T-count hidden shift circuits in a couple of minutes on a consumer laptop.

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“…More recently, in Ref. [71] the authors proposed a compilation strategy for the Trotterised UCC ansatz into one-and two-qubit gates using techniques from ZX-calculus [72]. They use approximate solutions to the graph colouring problem to partition the Pauli strings into commuting sets.…”

Section: E Compilation Strategiesmentioning

confidence: 99%

A Quantum Computing View on Unitary Coupled Cluster Theory

Anand,

Schleich,

Alperin-Lea

et al. 2021

Preprint

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We present a review of the Unitary Coupled Cluster (UCC) ansatz and related ansätze which are used to variationally solve the electronic structure problem on quantum computers. A brief history of coupled cluster (CC) methods is provided, followed by a broad discussion of the formulation of CC theory. This includes touching on the merits and difficulties of the method and several variants, UCC among them, in the classical context, to motivate their applications on quantum computers. In the core of the text, the UCC ansatz and its implementation on a quantum computer are discussed at length, in addition to a discussion on several derived and related ansätze specific to quantum computing. The review concludes with a unified perspective on the discussed ansätze, attempting to bring them under a common framework, as well as with a reflection upon open problems within the field. CONTENTS I. IntroductionA. A brief history of Coupled Cluster theory B. Assumed background and notation conventions C. Coupled Cluster theory 1. Formulation 2. Projective approaches 3. Variational approaches 4. Moving beyond the classical II. Estimating energies on quantum computers A. Quantum Phase Estimation B. Variational Quantum Eigensolver C. Tackling challenges within QPE and VQE by UCC III. The Unitary Coupled Cluster ansatz for quantum computing A. Fermionic excitations: The basic building blocks B. Qubit perspective on fermionic excitations C. Commutativity of subterms in fermionic excitation operators

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ZX-calculus for the working quantum computer scientist

Cited by 47 publications

References 0 publications

Spin-networks in the ZX-calculus

Spin-networks in the ZX-calculus

Classical simulation of quantum circuits with partial and graphical stabiliser decompositions

A Quantum Computing View on Unitary Coupled Cluster Theory

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