Braiding for the win: Harnessing braiding statistics in topological states to win quantum games

• URL: http://arxiv.org/abs/2412.14288v1
• Date: Wed, 18 Dec 2024 19:30:30 GMT
• Title: Braiding for the win: Harnessing braiding statistics in topological states to win quantum games
• Authors: Oliver Hart, David T. Stephen, Dominic J. Williamson, Rahul Nandkishore,
• Abstract summary: Nonlocal quantum games provide proof of principle that quantum resources can confer advantage at certain tasks. We show that a toric code resource state conferred advantage at a certain nonlocal game, which remained robust to small deformations of the resource state. We show how several other states from paradigmatic topological and fracton ordered phases can function as resources for suitably defined nonlocal games.
• Score: 0.23301643766310368
• License:
• Abstract: Nonlocal quantum games provide proof of principle that quantum resources can confer advantage at certain tasks. They also provide a compelling way to explore the computational utility of phases of matter on quantum hardware. In a recent manuscript [Hart et al., arXiv:2403.04829] we demonstrated that a toric code resource state conferred advantage at a certain nonlocal game, which remained robust to small deformations of the resource state. In this manuscript we demonstrate that this robust advantage is a generic property of resource states drawn from topological or fracton ordered phases of quantum matter. To this end, we illustrate how several other states from paradigmatic topological and fracton ordered phases can function as resources for suitably defined nonlocal games, notably the three-dimensional toric-code phase, the X-cube fracton phase, and the double-semion phase. The key in every case is to design a nonlocal game that harnesses the characteristic braiding processes of a quantum phase as a source of contextuality. We unify the strategies that take advantage of mutual statistics by relating the operators to be measured to order and disorder parameters of an underlying generalized symmetry-breaking phase transition. Finally, we massively generalize the family of games that admit perfect strategies when codewords of homological quantum error-correcting codes are used as resources.

Related papers

• Playing nonlocal games across a topological phase transition on a quantum computer [0.21990652930491852]
  We introduce a family of multiplayer quantum games for which topologically ordered phases of matter are a resource yielding quantum advantage. We demonstrate this robustness experimentally on Quantinuum's H1-1 quantum computer. We also discuss a topological interpretation of the game, which leads to a natural generalization involving an arbitrary number of players.
  arXiv  Detail & Related papers  (2024-03-07T19:00:01Z)
• Photonic implementation of the quantum Morra game [69.65384453064829]
  We study a faithful translation of a two-player quantum Morra game, which builds on previous work by including the classical game as a special case. We propose a natural deformation of the game in the quantum regime in which Alice has a winning advantage, breaking the balance of the classical game. We discuss potential applications of the quantum Morra game to the study of quantum information and communication.
  arXiv  Detail & Related papers  (2023-11-14T19:41:50Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Playing nonlocal games with phases of quantum matter [0.0]
  We show that $N$ players who share the ground state of a generic quantum Ising model, which exhibits non-vanishing quantum fluctuations, still win the parity game using the protocol optimized for the GHZ state. We further prove that the ground state of the exactly $d=1+1$ transverse-field Ising model can provide a quantum advantage for the parity game over an even wider region.
  arXiv  Detail & Related papers  (2022-06-22T17:57:29Z)
• Scalable measures of magic resource for quantum computers [0.0]
  We introduce efficient measures of magic resource for pure quantum states with a sampling cost independent of the number of qubits. We show the transition of classically simulable stabilizer states into intractable quantum states on the IonQ quantum computer.
  arXiv  Detail & Related papers  (2022-04-21T12:50:47Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding [58.720142291102135]
  We define a resource measure for magic, the sought-after property in most fault-tolerant quantum computers. Our formulation is based on bosonic codes, well-studied tools in continuous-variable quantum computation.
  arXiv  Detail & Related papers  (2021-09-27T12:56:01Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Simulating violation of causality using a topological phase transition [0.0]
  We consider a topological Hamiltonian and establish a correspondence between its eigenstates and the resource for a causal order game. We show that quantum correlations generated in the quantum many-body energy eigenstates of the model can mimic the statistics that can be obtained by exploiting different quantum measurements.
  arXiv  Detail & Related papers  (2021-05-20T14:49:41Z)
• Operational Resource Theory of Imaginarity [48.7576911714538]
  We show that quantum states are easier to create and manipulate if they only have real elements. As an application, we show that imaginarity plays a crucial role for state discrimination.
  arXiv  Detail & Related papers  (2020-07-29T14:03:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.