Foundations of quantum computational advantage

Deliverables

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Github release of code for computing with Heisenberg and Clifford groups built on arbitrary abelian groups (T3.1)

Stable release of open source Julia code for computing representations, cohomology, group algebras and other algebraic invariants of Heisenberg and Clifford groups over algebraic number fields using OSCAR (Open Source Computer Algebra Research system). This will enable exact computations in small dimensions that will further inform our theoretical investigations into the arithmetic structures of their orbits on states, codes, circuits, polytopes, etc. It will also let us study the role played by non-isomorphic maximal orders in questions of exact circuit synthesis in arithmetic groups.

Report on resource theory of non-classicality for causal structures (T1.1)

Report on developing a compositional resource theory of non-classicality for arbitrary causal structures. This will extend contextuality analysis and quantification to arbitrary scenarios, including generalisations of the noncontextuality and non-locality constraints on classical ontological models. It will enable a principled extension of contextuality analysis and measures of contextuality to computational settings such as the circuit model and multi-agent communication.

Report on representation of quantum algorithms in extended stabilizer formalisms (T2.2)

Report on the representation of quantum algorithms in extensions of the Pauli stabilizer formalism. The report will discuss (i) algebraic generalizations of the stabilizer formalism based on group theoretic methods for describing quantum algorithms; (ii) the cnc-construction; specifically prospects and limitations, and (iii) the Lambda polytopes; specifically how known hidden-variable descriptions found for certain algorithms carry over to the Lambda polytopes.

Report on non-continuous equivalence transformations for topological circuits (T4.3)

Report on discrete equivalence transformation for encoded gate operation. Based on the currently existing graphical form of the transformation rules, their rigorous mathematical description is established, and a corresponding efficient representation as a data structure is identified.

Publications

Communications in Mathematical Physics

Author(s): Imin Chen, Nadish de Silva
Published in: Communications in Mathematical Physics, Issue accepted, in press., 2024, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.48550/arXiv.2309.15184

Simple proof that anomalous weak values require coherence

Author(s): Rafael Wagner, Ernesto F. Galvão
Published in: Physical Review A, Issue 108, L040202, 2023, ISSN 2469-9926
Publisher: American Physical Society
DOI: 10.48550/arxiv.2303.08700

Mermin polytopes in quantum computation and foundations

Author(s): Cihan Okay, Ho Yiu Chung, Selman Ipek
Published in: Quantum Information and Computation, Issue 23(9&10), 733–782, 2023, ISSN 1533-7146
Publisher: Rinton Press
DOI: 10.48550/arXiv.2210.10186

Quantum circuits to measure scalar spin chirality

Author(s): Leander I. Reascos, Bruno Murta, Ernesto F. Galvão, Joaquín Fernández-Rossier
Published in: Physical Review Research, Issue 5, 043087, 2023, ISSN 2643-1564
Publisher: American Physical Society
DOI: 10.48550/arxiv.2306.14804

Lifting noncontextuality inequalities

Author(s): Raman Choudhary, Rui Soares Barbosa, Adán Cabello
Published in: Physical Review A, Issue 109, 052216, 2024, ISSN 1094-1622
Publisher: American Physical Society
DOI: 10.48550/arXiv.2401.12349

Alternative robust ways of witnessing nonclassicality in the simplest scenario

Author(s): Massy Khoshbin, Lorenzo Catani, Matthew Leifer
Published in: Physical Review A, Issue 109, 032212, 2024, ISSN 2469-9926
Publisher: American Physical Society
DOI: 10.48550/arxiv.2311.13474

Measurement-based quantum computation in finite one-dimensional systems: string order implies computational power

Author(s): Robert Raussendorf, Wang Yang, Arnab Adhikary
Published in: Quantum, Issue 7, 1215, 2023, ISSN 2521-327X
Publisher: Quantum
DOI: 10.22331/q-2023-12-28-1215

Bases for optimising stabiliser decompositions of quantum states

Author(s): Nadish de Silva, Ming Yin, Sergii Strelchuk
Published in: Quantum Science and Technology, Issue accepted, in press, 2024, ISSN 2058-9565
Publisher: IOP Publishing
DOI: 10.48550/arXiv.2311.17384

Topological methods for studying contextuality: N-cycle scenarios and beyond

Author(s): Aziz Kharoof, Selman Ipek, Cihan Okay
Published in: Entropy, Issue 25(8), 1127, 2023, ISSN 1099-4300
Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/e25081127

Contextuality with vanishing coherence and maximal robustness to dephasing

Author(s): Vinicius P. Rossi, David Schmid, John H. Selby, Ana Belén Sainz
Published in: Physical Review A, Issue 108, 032213, 2023, ISSN 2469-9926
Publisher: American Physical Society
DOI: 10.48550/arxiv.2212.06856

Simplicial techniques for operator solutions of linear constraint systems

Author(s): Ho Yiu Chung, Cihan Okay, Igor Sikora
Published in: Topology and its Applications, Issue 348,108883, 2024, ISSN 0166-8641
Publisher: Topology and its applications
DOI: 10.48550/arXiv.2305.07974

Experimental certification of contextuality, coherence, and dimension in a programmable universal photonic processor

Author(s): Taira Giordani, Rafael Wagner, Chiara Esposito, Anita Camillini, Francesco Hoch, Gonzalo Carvacho, Ciro Pentangelo, Francesco Ceccarelli, Simone Piacentini, Andrea Crespi, Nicolò Spagnolo, Roberto Osellame, Ernesto F. Galvão, Fabio Sciarrino
Published in: Science Advances, Issue 9(44), eadj4249, 2023, ISSN 2375-2548
Publisher: Science Advances
DOI: 10.1126/sciadv.adj4249

Non-stabilizerness and entanglement from cat-state injection

Author(s): Filipa C R Peres, Rafael Wagner, Ernesto F Galvão
Published in: New Journal of Physics, Issue 26, 013051, 2024, ISSN 1367-2630
Publisher: NJP
DOI: 10.48550/arxiv.2305.19988

Certifying sets of quantum observables with any full-rank state

Author(s): Zhen-Peng Xu, Debashis Saha, Kishor Bharti, Adán Cabello
Published in: Physical Review Letters, Issue 132, 140201, 2024, ISSN 1079-7114
Publisher: American Physical Society
DOI: 10.48550/arXiv.2309.05735

Pauli-based model of quantum computation with higher-dimensional systems

Author(s): Filipa C. R. Peres
Published in: Physical Review A, Issue 108, 032606, 2023, ISSN 2469-9926
Publisher: American Physical Society
DOI: 10.48550/arxiv.2302.13702

Using a resource theoretic perspective to witness and engineer quantum generalized contextuality for prepare-and-measure scenarios

Author(s): Rafael Wagner, Roberto D Baldijão, Alisson Tezzin, and Bárbara Amaral
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 56, 505303, 2023, ISSN 1751-8113
Publisher: Journal of Physics A: Mathematical and Theoretical
DOI: 10.48550/arXiv.2102.10469

Quantum circuits for measuring weak values, Kirkwood–Dirac quasiprobability distributions, and state spectra

Author(s): Rafael Wagner, Zohar Schwartzman-Nowik, Ismael L Paiva, Amit Te'eni, Antonio Ruiz-Molero, Rui Soares Barbosa, Eliahu Cohen, Ernesto F Galvão
Published in: Quantum Science and Technology, Issue 9, 015030, 2024, ISSN 2058-9565
Publisher: Quantum Science and Technology
DOI: 10.48550/arxiv.2302.00705

Combining contextuality and causality: a game semantics approach

Author(s): Samson Abramsky, Rui Soares Barbosa, Amy Searle
Published in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Issue 382(2268), 20230002, 2024, ISSN 1364-503X
Publisher: Royal Society of London
DOI: 10.48550/arxiv.2307.04786

A bundle perspective on contextuality: Empirical models and simplicial distributions on bundle scenarios

Author(s): Rui Soares Barbosa, Aziz Kharoof, Cihan Okay
Published in: arXiv, Issue arXiv:2308.06336 [math.CT], 2023
Publisher: N/A
DOI: 10.48550/arxiv.2308.06336

The operadic theory of convexity

Author(s): Redi Haderi, Cihan Okay, Walker H. Stern
Published in: arXiv, Issue arXiv:2403.18102 [math.CT], 2024
Publisher: N/A
DOI: 10.48550/arXiv.2403.18102

Impossibility of bipartite full nonlocality, all-versus-nothing proofs, and pseudo-telepathy in small Bell scenarios

Author(s): Yuan Liu, Ho Yiu Chung, Emmanuel Zambrini Cruzeiro, Junior R. Gonzales-Ureta, Ravishankar Ramanathan, Adán Cabello
Published in: arXiv, Issue arXiv:2310.10600 [quant-ph], 2023
Publisher: N/A
DOI: 10.48550/ARXIV.2310.10600

On the rank of two-dimensional simplicial distributions

Author(s): Okay, Cihan
Published in: arXiv, Issue arXiv:2312.15794 [quant-ph], 2023
Publisher: N/A
DOI: 10.48550/arxiv.2312.15794

Logical possibilities for physics after MIP*=RE

Author(s): Adán Cabello, Marco Túlio Quintino, Matthias Kleinmann
Published in: arXiv, Issue arXiv:2307.02920 [quant-ph], 2023
Publisher: N/A
DOI: 10.48550/ARXIV.2307.02920

Quantum optimization: Potential, challenges, and the path forward

Author(s): Amira Abbas et al.
Published in: arXiv, Issue arXiv:2312.02279 [quant-ph], 2023
Publisher: N/A
DOI: 10.48550/arXiv.2312.02279

SIC-POVMs from Stark units: dimensions n^2+3=4p, p prime

Author(s): Ingemar Bengtsson, Markus Grassl, Gary McConnell
Published in: arXiv, Issue arXiv:2403.02872 [quant-ph], 2024
Publisher: N/A
DOI: 10.48550/arXiv.2403.02872

Twisted simplicial distributions

Author(s): Cihan Okay, Walker H. Stern
Published in: arXiv, Issue arXiv:2403.19808 [quant-ph], 2024
Publisher: N/A
DOI: 10.48550/arXiv.2403.19808

Fast algorithms for classical specifications of stabiliser states and Clifford gates

Author(s): Nadish de Silva, Wilfred Salmon, Ming Yin
Published in: arXiv, Issue arXiv:2311.10357 [quant-ph], 2023
Publisher: N/A
DOI: 10.48550/arXiv.2311.10357

Verifiable measurement-based quantum random sampling with trapped ions

Author(s): Martin Ringbauer et al.
Published in: arXiv, Issue arXiv:2307.14424 [quant-ph], 2024
Publisher: N/A
DOI: 10.48550/arxiv.2307.14424

The degenerate vertices of the 2-qubit Λ-polytope and their update rules

Author(s): Selman Ipek, Cihan Okay
Published in: arXiv, Issue arXiv:2312.10734 [quant-ph], 2023
Publisher: N/A
DOI: 10.48550/ARXIV.2312.10734

Game semantics for higher-order unitary quantum computation

Author(s): Samson Abramsky, Radha Jagadeesan
Published in: arXiv, Issue arXiv:2404.06646 [cs.PL], 2024
Publisher: N/A
DOI: 10.48550/arXiv.2404.06646

State-independent all-versus-nothing arguments

Author(s): Boseong Kim, Samson Abramsky
Published in: arXiv, Issue arXiv:2311.11218 [quant-ph], 2023
Publisher: N/A
DOI: 10.48550/arXiv.2311.11218

Kirkwood-Dirac representations beyond quantum states (and their relation to noncontextuality)

Author(s): David Schmid, Roberto D. Baldijão, Yìlè Yīng, Rafael Wagner, John H. Selby
Published in: arXiv, Issue arXiv:2405.04573 [quant-ph], 2024
Publisher: N/A
DOI: 10.48550/ARXIV.2405.04573

Relativization is naturally functorial

Author(s): Jan Głowacki
Published in: arXiv, Issue arXiv:2403.03755 [quant-ph], 2024
Publisher: N/A
DOI: 10.48550/ARXIV.2403.03755

Multi-qutrit exact synthesis

Author(s): Amolak Ratan Kalra, Manimugdha Saikia, Dinesh Valluri, Sam Winnick, Jon Yard
Published in: arXiv, Issue arXiv:2405.08147 [quant-ph], 2024
Publisher: N/A
DOI: 10.48550/arXiv.2405.08147

Operational quantum reference frame transformations

Author(s): Titouan Carette, Jan Głowacki, Leon Loveridge
Published in: arXiv, Issue arXiv:2303.14002 [quant-ph], 2023
Publisher: N/A
DOI: 10.48550/ARXIV.2303.14002

Homotopical characterization of strongly contextual simplicial distributions on cone spaces

Author(s): Aziz Kharoof, Cihan Okay
Published in: arXiv, Issue arXiv:2311.14111 [math.AT], 2023
Publisher: N/A
DOI: 10.48550/arxiv.2311.14111

Test of the physical significance of Bell nonlocality

Author(s): Carlos Vieira, Ravishankar Ramanathan, Adán Cabello
Published in: arXiv, Issue arXiv:2402.00801 [quant-ph], 2024
Publisher: N/A
DOI: 10.48550/ARXIV.2402.00801

Minimum full nonlocality, all versus nothing nonlocality, and quantum pseudo telepathy

Author(s): Adán Cabello
Published in: arXiv, Issue arXiv:2311.17735 [quant-ph], 2023
Publisher: N/A
DOI: 10.48550/ARXIV.2311.17735

Simulation of quantum computation with magic states via Jordan-Wigner transformations

Author(s): Michael Zurel, Lawrence Z. Cohen, Robert Raussendorf
Published in: arXiv, Issue arXiv:2307.16034 [quant-ph], 2023
Publisher: N/A
DOI: 10.48550/arXiv.2307.16034

Equivariant simplicial distributions and quantum contextuality

Author(s): Cihan Okay, Igor Sikora
Published in: arXiv, Issue arXiv:2310.18135 [quant-ph], 2023
Publisher: N/A
DOI: 10.48550/arxiv.2310.18135

Unbounded Sharing of Nonlocality Using Projective Measurements

Author(s): Souradeep Sasmal, Som Kanjilal, Alok Kumar Pan
Published in: arXiv, Issue arXiv:2311.07977 [quant-ph], 2023
Publisher: N/A
DOI: 10.48550/arXiv.2311.07977

"Simulating quantum computation: how many ""bits"" for ""it""?"

Author(s): Michael Zurel, Cihan Okay, Robert Raussendorf
Published in: arXiv, Issue arXiv:2305.17287 [quant-ph], 2024
Publisher: N/A
DOI: 10.48550/arXiv.2305.17287

Can multiple observers detect KS-contextuality?

Author(s): Arthur C. R. Dutra, Roberto D. Baldijão, Marcelo Terra Cunha
Published in: arXiv, Issue arXiv:2310.19564 [quant-ph], 2023
Publisher: N/A
DOI: 10.48550/ARXIV.2310.19564

Deliverables

Publications

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