Contextuality as a resource for models of quantum computation on qubits

Abstract

A central question in quantum computation is to identify the resources that are responsible for quantum speed-up. Quantum contextuality has been recently shown to be a resource for quantum computation with magic states for odd-prime dimensional qudits and two-dimensional systems with real wavefunctions. The phenomenon of state-independent contextuality poses a priori an obstruction to characterizing the case of regular qubits, the fundamental building block of quantum computation. Here, we establish contextuality of magic states as a necessary resource for a large class of quantum computation schemes on qubits. We illustrate our result with a concrete scheme related to measurement-based quantum computation.

Published version. We have revised the title, introduction and discussion, as well as slightly simplified the setting in this version

References in corpus (5)

• Wigner function negativity and contextuality in quantum computation on rebits
• Contextuality and Wigner function negativity in qubit quantum computation
• Equivalence between contextuality and negativity of the Wigner function for qudits
• The computational power of normalizer circuits over black-box groups
• Abelian Hypergroups and Quantum Computation

Cited by in corpus (90)

• Kochen-Specker Contextuality
• Quantifying magic for multi-qubit operations
• Quantum fluctuation theorems, contextuality and work quasi-probabilities
• Enhancing Generative Models via Quantum Correlations
• Phase space simulation method for quantum computation with magic states on qubits
• Simulation of Qubit Quantum Circuits via Pauli Propagation
• Measurement incompatibility and steering are necessary and sufficient for operational contextuality
• Sustained state-independent quantum contextual correlations from a single ion
• Machine Learning meets Quantum Foundations: A Brief Survey
• Uniqueness of noncontextual models for stabilizer subtheories
• Quantum Advantage from Sequential-Transformation Contextuality
• Contextuality as a resource for measurement-based quantum computation beyond qubits
• Critical behaviors of non-stabilizerness in quantum spin chains
• New Phase Space Formulations and Quantum Dynamics Approaches
• Noncontextual wirings
• Resource theory of contextuality for arbitrary prepare-and-measure experiments
• Witnessing Wigner Negativity
• 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
• Measures of Contextuality and Noncontextuality
• Stabilizer extent is not multiplicative
• The physical meaning of the holographic principle
• One-Shot Manipulation of Dynamical Quantum Resources
• Measurement-Based Quantum Computation
• Contextuality and Noncontextuality Measures and Generalized Bell Inequalities for Cyclic Systems
• Deriving robust noncontextuality inequalities from algebraic proofs of the Kochen-Specker theorem: the Peres-Mermin square
• Quantum correlations from simple assumptions
• Experimental test of contextuality in quantum and classical systems
• Memory cost of temporal correlations
• Quantum computational advantage with string order parameters of 1D symmetry-protected topological order
• Quantum Advantage in Information Retrieval
• Constraints on magic state protocols from the statistical mechanics of Wigner negativity
• Quantifying dynamical magic with completely stabilizer preserving operations as free
• Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements
• Classical simulation of non-Gaussian fermionic circuits
• Contextuality bounds the efficiency of classical simulation of quantum processes
• Contextuality and The Single-Qubit Stabilizer Formalism
• A comonadic view of simulation and quantum resources
• Incompatibility of observables, channels and instruments in information theories
• Solvable Criterion for the Contextuality of any Prepare-and-Measure Scenario
• State-injection schemes of quantum computation in Spekkens' toy theory
• Neither Contextuality nor Nonlocality Admits Catalysts
• Magic informationally complete POVMs with permutations
• Fluctuating work in coherent quantum systems: proposals and limitations
• A mathematical framework for operational fine tunings
• Bell non-locality and Kochen-Specker contextuality: How are they connected?
• Analogue Quantum Simulation: A New Instrument for Scientific Understanding
• Bridging magic and non-Gaussian resources via Gottesman-Kitaev-Preskill encoding
• Separability, Contextuality, and the Quantum Frame Problem
• Majorana representation, qutrit Hilbert space and NMR implementation of qutrit gates
• Testing quantum theory by generalizing noncontextuality
• Contextuality in multipartite pseudo-telepathy graph games
• Hierarchies of resources for measurement-based quantum computation
• Contextuality in composite systems: the role of entanglement in the Kochen-Specker theorem
• Contextual bound states for qudit magic state distillation
• Optimal and tight Bell inequalities for state-independent contextuality sets
• No-broadcasting characterizes operational contextuality
• Corrected Bell and Noncontextuality Inequalities for Realistic Experiments
• The rank of contextuality
• A classical formulation of quantum theory?
• Self-testing of multiple unsharpness parameters through sequential violations of non-contextual inequality
• Closing Bell: Boxing black box simulations in the resource theory of contextuality
• Continuous-variable nonlocality and contextuality
• Scalable noncontextuality inequalities and certification of multiqubit quantum systems
• Irreducible magic sets for $n$-qubit systems
• Connecting XOR and XOR* games
• Hidden variable model for quantum computation with magic states on qudits of any dimension
• Bosonic Indistinguishability-Dependent Contextuality
• Classifying space for quantum contextuality
• Quantum advantage in temporally flat measurement-based quantum computation
• Quantum computational advantage implies contextuality
• An Entanglement Monotone from the Contextual Fraction
• A new heuristic approach for contextuality degree estimates and its four- to six-qubit portrayals
• How contextuality and antidistinguishability are related
• Translating Bell Non-Locality to Prepare-and-Measure Scenarios under Dimensional Constraints
• Entanglement and magic on the light-front
• Demonstration of universal contextuality through communication games free of both operational inequivalence and compatibility loopholes
• Three-Qubit-Embedded Split Cayley Hexagon is Contextuality Sensitive
• The Interplay between Quantum Contextuality and Wigner Negativity
• Frame dependence of Spekkens' contextuality for relativistic spin systems
• Convexity of noncontextual wirings and how they order the set of correlations
• Efficient Classical Simulation of the DQC1 Circuit with Zero Discord
• Contextuality and Expressivity of Non-locality
• All fundamental non-contextuality inequalities are unique
• Contextuality, superlocality and nonclassicality of supernoncontextuality
• Noncontextual Pauli Hamiltonians
• Anomalous non-classicality via correlative and entropic Bell inequalities
• Quantum contextuality from measurement invasiveness
• k-Contextuality as a Heuristic for Memory Separations in Learning