Contextuality and Wigner function negativity in qubit quantum computation

Abstract

We describe a scheme of quantum computation with magic states on qubits for which contextuality is a necessary resource possessed by the magic states. More generally, we establish contextuality as a necessary resource for all schemes of quantum computation with magic states on qubits that satisfy three simple postulates. Furthermore, we identify stringent consistency conditions on such computational schemes, revealing the general structure by which negativity of Wigner functions, hardness of classical simulation of the computation, and contextuality are connected.

published version

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Cited by in corpus (69)

• Kochen-Specker Contextuality
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• Quantifying magic for multi-qubit operations
• Convex geometry of quantum resource quantification
• Equivalence between contextuality and negativity of the Wigner function for qudits
• Phase space simulation method for quantum computation with magic states on qubits
• Simulation of Qubit Quantum Circuits via Pauli Propagation
• Overview of the phase space formulation of quantum mechanics with application to quantum technologies
• Uniqueness of noncontextual models for stabilizer subtheories
• Quantification and manipulation of magic states
• A hidden variable model for universal quantum computation with magic states on qubits
• Symmetric Informationally Complete Measurements Identify the Irreducible Difference between Classical and Quantum Systems
• Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers
• Contextuality as a resource for measurement-based quantum computation beyond qubits
• Witnessing Wigner Negativity
• Nonlocality from local contextuality
• Leggett-Garg macrorealism and the quantum nondisturbance conditions
• Necessary and sufficient condition for contextuality from incompatibility
• Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements
• Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding
• Discrete Wigner Formalism for Qubits and Non-Contextuality of Clifford Gates on Qubit Stabilizer States
• Memory cost of temporal correlations
• Quantifying dynamical magic with completely stabilizer preserving operations as free
• Quantum computational advantage with string order parameters of 1D symmetry-protected topological order
• Classical Simulation of Noncontextual Pauli Hamiltonians
• Contextuality bounds the efficiency of classical simulation of quantum processes
• Classical simulation of non-Gaussian fermionic circuits
• Contextuality and The Single-Qubit Stabilizer Formalism
• Neither Contextuality nor Nonlocality Admits Catalysts
• State-injection schemes of quantum computation in Spekkens' toy theory
• The role of cohomology in quantum computation with magic states
• A mathematical framework for operational fine tunings
• Bridging magic and non-Gaussian resources via Gottesman-Kitaev-Preskill encoding
• Spekkens' toy model in all dimensions and its relationship with stabilizer quantum mechanics
• Sharp complexity phase transitions generated by entanglement
• Homotopical approach to quantum contextuality
• Reliable computation from contextual correlations
• Hierarchies of resources for measurement-based quantum computation
• Contextuality and bundle diagrams
• Semiclassical Formulation of Gottesman-Knill and Universal Quantum Computation
• Universal resources for quantum computing
• Advantages of the Kirkwood-Dirac distribution among general quasi-probabilities for finite-state quantum systems
• Faster Born probability estimation via gate merging and frame optimisation
• Logical structures underlying quantum computing
• Wigner distribution of Sine Gordon and Kink solitons
• Negativity-Mutual Information conversion and coherence in two-coupled harmonic oscillators
• Orbital-Free Quasi-Density Functional Theory
• Kenfack Zyczkowski indicator of nonclassicality for two non-equivalent representations of Wigner function of qutrit
• Quantum Path Computing: Computing Architecture with Propagation Paths in Multiple Plane Diffraction of Classical Sources of Fermion and Boson Particles
• Normalizer Circuits and Quantum Computation
• Hidden variable model for quantum computation with magic states on qudits of any dimension
• The Non-Disjoint Ontic States of the Grassmann Ontological Model, Transformation Contextuality, and the Single Qubit Stabilizer Subtheory
• Connecting XOR and XOR* games
• Signed quantum weight enumerators characterize qubit magic state distillation
• A quantum prediction as a collection of epistemically restricted classical predictions
• Extending Classically Simulatable Bounds of Clifford Circuits with Nonstabilizer States via Framed Wigner Functions
• Classifying space for quantum contextuality
• Harvesting Contextuality from the Vacuum
• Visualization of correlations in hybrid quantum systems
• Characterization of non-adaptive Clifford channels
• How contextuality and antidistinguishability are related
• General entropic constraints on CSS codes within magic distillation protocols
• Symmetries and Wigner representations of operational theories
• Quantum computational advantage implies contextuality
• Contextuality from the vacuum
• Joint quasiprobability distribution on the measurement outcomes of MUB-driven operators
• Preparation and Measurement in Quantum Memory Models
• The Interplay between Quantum Contextuality and Wigner Negativity