Cohomological framework for contextual quantum computations

Raussendorf, Robert

doi:10.26421/qic19.13-14-4

Cited by 17 publications

(32 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A further cohomological framework for contextuality, which is compatible with MBQC, was described in [16] (left leg). A cohomological formulation of MBQC (right leg) was provided in [23]. The contextual fraction [4] is a measure of the amount of contextuality present in physical settings, and it is related to the success probability of MBQCs [14].…”

Section: Introductionmentioning

confidence: 99%

The cohomological and the resource-theoretic perspective on quantum contextuality: common ground through the contextual fraction

Okay¹,

Tyhurst²,

Raussendorf³

2018

Preprint

Self Cite

View full text Add to dashboard Cite

We unify the resource-theoretic and the cohomological perspective on quantum contextuality. At the center of this unification stands the notion of the contextual fraction. For both symmetry and parity based contextuality proofs, we establish cohomological invariants which are witnesses of state-dependent contextuality. We provide two results invoking the contextual fraction, namely (i) refinements of logical contextuality inequalities, and (ii) upper bounds on the classical cost of Boolean function evaluation, given the contextual fraction of the corresponding measurement-based quantum computation.

show abstract

Section: Introductionmentioning

confidence: 99%

The cohomological and the resource-theoretic perspective on quantum contextuality: common ground through the contextual fraction

Okay¹,

Tyhurst²,

Raussendorf³

2018

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Many connections to other resources exist such as entanglement and negativity of the Wigner function [58,20]. For MBQC, a classification of contextuality in terms of group cohomology has been given in [52,47]. Similar connections between contextuality and cohomology have also been obtained in [53] and within the sheaf theoretic formalism in [3,7,12].…”

Section: Discussionmentioning

confidence: 86%

Contextuality and the fundamental theorems of quantum mechanics

Döring¹,

Frembs²

2019

Preprint

View full text Add to dashboard Cite

Contextuality is a key feature of quantum mechanics, as was first brought to light by Bohr [11] and later realised more technically by Kochen and Specker [43]. Isham and Butterfield put contextuality at the heart of their topos-based formalism and gave a reformulation of the Kochen-Specker theorem in the language of presheaves in [37].Here, we broaden this perspective considerably (partly drawing on existing, but scattered results) and show that apart from the Kochen-Specker theorem, also Wigner's theorem, Gleason's theorem and Bell's theorem relate fundamentally to contextuality. We provide reformulations of the theorems using the language of presheaves over contexts and give general versions valid for von Neumann algebras. This shows that a very substantial part of the structure of quantum theory is encoded by contextuality.

show abstract

“…In addition, we point out that precisely the same cohomomological constructs, [β] and [Φ], were also found to bear on measurement-based quantum computation [42], so far at least in the case of flat temporal order. The case of proper temporal order remains to be understood.…”

Section: Discussionmentioning

confidence: 87%

The role of cohomology in quantum computation with magic states

Raussendorf¹,

Okay²,

Zurel³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

The scheme of quantum computation with magic states, and in particular the role of the Wigner function as an indicator of quantumness, motivate the question of when Cliffordcovariant Wigner functions exist, and when Wigner functions exist that represent Pauli measurements positively. This question has been settled affirmatively for all odd dimensions. Here, we discuss the case of even dimension, for Wigner functions obtained from operator bases. We find that such Clifford-covariant Wigner functions do not exist in any even dimension, and furthermore, Pauli measurement cannot be positively represented by them in any even dimension whenever the number of qudits is n ≥ 2.

show abstract

Cohomological framework for contextual quantum computations

Cited by 17 publications

References 37 publications

The cohomological and the resource-theoretic perspective on quantum contextuality: common ground through the contextual fraction

The cohomological and the resource-theoretic perspective on quantum contextuality: common ground through the contextual fraction

Contextuality and the fundamental theorems of quantum mechanics

The role of cohomology in quantum computation with magic states

Contact Info

Product

Resources

About