DisCoPy for the quantum computer scientist

Toumi, Alexis; Felice, Giovanni de; Yeung, Richie

doi:10.48550/arxiv.2205.05190

Cited by 3 publications

(7 citation statements)

References 26 publications

(34 reference statements)

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“…DisCoPy (Distributional Compositional Python) [7,9], the backend of lambeq, is a Python toolbox for computing with string diagrams and functors. The string diagrams are used to encode various kinds of quantum processes, with functors for compilation and evaluation on quantum hardware.…”

Section: Discopy For Encoding String Diagram As Parameterized Quantum...mentioning

confidence: 99%

“…The string diagrams are used to encode various kinds of quantum processes, with functors for compilation and evaluation on quantum hardware. Their implementation is given by Diagram, a class with the following interface [9] (see also A.1 DisCoPy Implementation of Category Theory):…”

Section: Discopy For Encoding String Diagram As Parameterized Quantum...mentioning

confidence: 99%

“…In this paper we discuss in some detail VQSCs, including category theory [4], DisCoCat for modeling sentence as string diagram, and DisCoPy [7,9] for encoding string diagram as PQC. DisCoCat is a linguistic application of category theory, which is the mathematical study of (abstract) algebras of functions, consisting of objects A,B,C, .…”

Section: Introductionmentioning

confidence: 99%

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lilianggriani0101@gmail.com

Anggriani¹

2021

Preprint

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Section: Discopy For Encoding String Diagram As Parameterized Quantum...mentioning

confidence: 99%

Section: Discopy For Encoding String Diagram As Parameterized Quantum...mentioning

confidence: 99%

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lilianggriani0101@gmail.com

Anggriani¹

2021

Preprint

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“…One contemporary approach to graphical reasoning is the so called, Coecke-Duncan ZX-calculus [14,15], which formalizes graphical reasoning of typical quantum circuits, measurements and states appearing in quantum information processing [14,15,16,17,18,19,20,21]. The ZX-calculus has been used as a tool to study a range of tasks related to quantum computing e.g.…”

mentioning

confidence: 99%

“…quantum circuit optimization [22,23,24], quantum circuit equivalence checking [25,26] and in the design of quantum error correcting codes [27,28]. Diagrammatic manipulations using the ZX-calculus have also been automated by Kissinger and others [18,19].…”

mentioning

confidence: 99%

The ZX-Calculus is Canonical in the Heisenberg Picture for Stabilizer Quantum Mechanics

Biamonte¹,

Nasrallah²

2023

Preprint

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In 2008 Coecke and Duncan proposed the graphical ZX-calculus rewrite system which came to formalize reasoning with quantum circuits, measurements and quantum states. The ZX-calculus is sound for qubit quantum mechanics. Hence, equality of diagrams under ZX-equivalent transformations lifts to an equality of corresponding equations over matrices. Conversely, in 2014 Backens proved completeness, establishing that any derivation done in stabilizer quantum mechanics with matrices can be derived graphically using the ZXcalculus. A graphical rewrite system that is both confluent and also terminates uniquely is called canonical. Applying alternate sequences of rewrites to the same initial diagram, a rewrite system is confluent whenever all resulting diagrams can be manipulated to establish graphical equivalence. Here we show that a reduced ZX-rewrite system is already confluent in the Heisenberg picture for stabilizer quantum mechanics. Moreover, any application of a subset of ZX-rewrites terminates uniquely and irrespective of the order of term rewrites in the Heisenberg picture for stabilizer quantum mechanics. The ZX-system is hence Heisenbergcanonical for stabiliser quantum mechanics. For a stabilizer circuit on n-qubits with l singlequbit gates and g two-qubit gates, the circuit output can be derived graphically in the Heisenberg picture using no more than ( 1 2 • g + l)• n graphical rewrites, thereby providing a graphical proof of the Gottesman-Knill theorem. Finally, we consider the application of this tool as a graphical means to derive parent Hamiltonians which can be used as penalty functions in variational quantum computation. Hence, we establish that each stabilizer state described by a Clifford circuit gives rise to a non-negative parent Hamiltonian with n + 1 terms and a one-dimensional kernel spanned by the corresponding stabilizer state. Such parent Hamiltonians can be derived with O(t • n) graphical rewrites for a low energy state prepared by a t-gate Clifford circuit.

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qujax: Simulating quantum circuits with JAX

Duffield,

Matos,

Johannsen

2023

JOSS

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qujax is a pure JAX (Bradbury et al., 2018), purely functional Python package for the classical simulation of quantum circuits. A JAX implementation of quantum circuits inherits benefits such as seamless automatic differentiation, support for GPUs/TPUs as well as integration with a host of other tools within the JAX ecosystem.qujax is hosted on PyPI for easy installation and comes with detailed documentation and a suite of example notebooks.qujax represents a quantum circuit as a collection of three equal length Python iterables:

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DisCoPy for the quantum computer scientist

Cited by 3 publications

References 26 publications

lilianggriani0101@gmail.com

lilianggriani0101@gmail.com

The ZX-Calculus is Canonical in the Heisenberg Picture for Stabilizer Quantum Mechanics

qujax: Simulating quantum circuits with JAX

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