Contextuality as a resource for measurement-based quantum computation beyond qubits

Abstract

Contextuality - the obstruction to describing quantum mechanics in a classical statistical way - has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality as a computational resource, as follows. If local measurements on a multi-qubit state can be used to evaluate non-linear boolean functions with only linear control processing, then this computation constitutes a proof of strong contextuality - the possible local measurement outcomes cannot all be pre-assigned. However, this connection is restricted to the special case when the local measured systems are qubits, which have unusual properties from the perspective of contextuality. A single qubit cannot allow for a proof of contextuality, unlike higher-dimensional systems, and multiple qubits can allow for state-independent contextuality with only Pauli observables, again unlike higher-dimensional generalisations. Here we identify precisely that strong non-locality is necessary in a qudit measurement-based computation that evaluates high-degree polynomial functions with only linear control. We introduce the concept of local universality, which places a bound on the space of output functions accessible under the constraint of single-qudit measurements. Thus, the partition of a physical system into subsystems plays a crucial role for the increase in computational power. A prominent feature of our setting is that the enabling resources for qubit and qudit measurement-based computations are of the same underlying nature, avoiding the pathologies associated with qubit contextuality.

arXiv comment14 pages, 3 figures, comments welcome; v3 published version

References in corpus (25)

• Measurement-based quantum computation with cluster states
• Hidden Variables and the Two Theorems of John Bell
• Contextuality supplies the magic for quantum computation
• The Resource Theory of Stabilizer Computation
• The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
• Negative Quasi-Probability as a Resource for Quantum Computation
• Hudson's Theorem for finite-dimensional quantum systems
• Contextuality in Measurement-based Quantum Computation
• Estimating outcome probabilities of quantum circuits using quasiprobabilities
• Computational power of correlations
• Quantum computation based on d-level cluster states
• The contextual fraction as a measure of contextuality
• Contextuality as a resource for models of quantum computation on qubits
• Wigner function negativity and contextuality in quantum computation on rebits
• Discrete Wigner functions and quantum computational speedup
• Contextuality and Wigner function negativity in qubit quantum computation
• The Cohomology of Non-Locality and Contextuality
• Quantum Advantage from Sequential-Transformation Contextuality
• A linearized stabilizer formalism for systems of finite dimension
• Generalized Bell Inequality Experiments and Computation
• Contextuality bounds the efficiency of classical simulation of quantum processes
• Contextuality and The Single-Qubit Stabilizer Formalism
• State-injection schemes of quantum computation in Spekkens' toy theory
• A complete characterisation of All-versus-Nothing arguments for stabiliser states
• Towards a complete cohomology invariant for non-locality and contextuality

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• Quantum computational advantage implies contextuality
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