Outcome determinism in measurement-based quantum computation with qudits

Booth, Robert I.; Kissinger, Aleks; Markham, Damian; Meignant, Clément; Perdrix, Simon

doi:10.1088/1751-8121/acbace

Cited by 1 publication

(1 citation statement)

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“…In the broader field of circuit-based quantum computing, qudits have been subject to increased research interest in recent years [8], and some generalisations of adaptive measurement-based quantum computing to higher dimensional systems have already been discussed [9,10]. The denser encoding of information, and thus the reduction of computational costs compared to qubits, as well as the possible simplification of experiments makes them a good candidate for next-generation quantum computing [8,[11][12][13].…”

Section: Introductionmentioning

confidence: 99%

The power of qutrits for non-adaptive measurement-based quantum computing

et al. 2023

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Non-locality is not only one of the most prominent quantum features but can also serve as a resource for various information-theoretical tasks. Analysing it from an information-theoretical perspective has linked it to applications such as non-adaptive measurement-based quantum computing (NMQC). In this type of quantum computing the goal is to output a multivariate function. The success of such a computation can be related to the violation of a generalised Bell inequality. So far, the investigation of binary NMQC with qubits has shown that quantum correlations can compute all Boolean functions using at most $2^n-1$ qubits, whereas local hidden variables (LHVs) are restricted to linear functions. Here, we extend these results to NMQC with qutrits and prove that quantum correlations enable the computation of all three-valued logic functions using the generalised qutrit Greenberger-Horne-Zeilinger (GHZ) state as a resource and at most $3^n-1$ qutrits. This yields a corresponding generalised GHZ type paradox for any three-valued logic function that LHVs cannot compute. We give an example for an $n$-variate function that can be computed with only $n+1$ qutrits, which leads to convenient generalised qutrit Bell inequalities whose quantum bound is maximal. Finally, we prove that not all functions can be computed efficiently with qutrit NMQC by presenting a counterexample.

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