Differentiating and Integrating ZX Diagrams with Applications to Quantum Machine Learning

Abstract

ZX-calculus has proved to be a useful tool for quantum technology with a wide range of successful applications. Most of these applications are of an algebraic nature. However, other tasks that involve differentiation and integration remain unreachable with current ZX techniques. Here we elevate ZX to an analytical perspective by realising differentiation and integration entirely within the framework of ZX-calculus. We explicitly illustrate the new analytic framework of ZX-calculus by applying it in context of quantum machine learning for the analysis of barren plateaus.

43 pages

References in corpus (34)

• Quantum Computing in the NISQ era and beyond
• Barren plateaus in quantum neural network training landscapes
• Improved Simulation of Stabilizer Circuits
• Evaluating analytic gradients on quantum hardware
• Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
• t$|$ket$⟩$ : A Retargetable Compiler for NISQ Devices
• Interacting Quantum Observables: Categorical Algebra and Diagrammatics
• Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus
• Instantaneous Quantum Computation
• Variational Quantum Eigensolver with Fewer Qubits
• QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computer
• The ZX calculus is a language for surface code lattice surgery
• Barren plateaus in quantum tensor network optimization
• Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus
• ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity
• Logical blocks for fault-tolerant topological quantum computation
• Simulating quantum circuits with ZX-calculus reduced stabiliser decompositions
• Geometry of abstraction in quantum computation
• Strong Complementarity and Non-locality in Categorical Quantum Mechanics
• Universal MBQC with generalised parity-phase interactions and Pauli measurements
• Techniques to Reduce $\pi /4$-Parity-Phase Circuits, Motivated by the ZX Calculus
• The GHZ/W-calculus contains rational arithmetic
• Qufinite ZX-calculus: a unified framework of qudit ZX-calculi
• Phase-free ZX diagrams are CSS codes (...or how to graphically grok the surface code)
• A complete graphical calculus for Spekkens' toy bit theory
• Diagrammatic Differentiation for Quantum Machine Learning
• Diagrammatic Design and Study of Ansätze for Quantum Machine Learning
• Algebraic complete axiomatisation of ZX-calculus with a normal form via elementary matrix operations
• AND-gates in ZX-calculus: Spider Nest Identities and QBC-completeness
• Completeness of algebraic ZX-calculus over arbitrary commutative rings and semirings
• Quantum Machine Learning using the ZXW-Calculus
• An Algebraic Axiomatisation of ZX-calculus
• Diagrammatic Analysis for Parameterized Quantum Circuits
• Speedy Contraction of ZX Diagrams with Triangles via Stabiliser Decompositions

Cited by in corpus (3)

• Application of ZX-calculus to Quantum Architecture Search
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• Hybrid quantum recurrent neural network for remaining useful life prediction of turbofan engines