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Quantum Information Processing

Implementing 2-qubit pseudo-telepathy games on noisy intermediate-scale quantum computers

Colm Kelleher, Mohammad Roomy, Frédéric Holweck

Published May 13, 2024• 6 citations
Publisher

Abstract

Abstract It is known that Mermin-Peres like proofs of quantum contextuality can furnish non-local games with a guaranteed quantum strategy, when classically no such guarantee can exist. This phenomenon, also called quantum pseudo-telepathy, has been studied in the case of the so-called Mermin Magic square game. In this paper we review in detail two different ways of implementing on a quantum computer such a game and propose a new Doily game based on the geometry of 2-qubit Pauli group. We show that the quantumness of these games are almost revealed when we play them on the IBM Quantum Experience, however the inherent noise in the available quantum machines prevents a full demonstration of the non-classical aspects.

DOI
10.1007/s11128-024-04386-x

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Abstract It is known that Mermin-Peres like proofs of quantum contextuality can furnish non-local games with a guaranteed quantum strategy, when classically no such guarantee can exist. This phenomenon, also called quantum pseudo-telepathy, has been studied in the case of the so-called Mermin Magic square game. In this paper we review in detail two different ways of implementing on a quantum computer such a game and propose a new Doily game based on the geometry of 2-qubit Pauli group. We show that the quantumness of these games are almost revealed when we play them on the IBM Quantum Experience, however the inherent noise in the available quantum machines prevents a full demonstration of the non-classical aspects.
It is known that Mermin-Peres like proofs of quantum contextuality can furnish non-local games with a guaranteed quantum strategy, when classically no such guarantee can exist. This phenomenon, also called quantum pseudo-telepathy, has been studied in the case of the so-called Mermin Magic square game. In this paper we review in detail two different ways of implementing on a quantum computer such a game and propose a new Doily game based on the geometry of 2-qubit Pauli group. We show that the quantumness of these games are almost revealed when we play them on the IBM Quantum Experience, however the inherent noise in the available quantum machines prevents a full demonstration of the non-classical aspects.
The Mermin-Peres magic square game is a cooperative two-player nonlocal game in which shared quantum entanglement allows the players to win with certainty, while players limited to classical operations cannot do so, a phenomenon dubbed "quantum pseudo-telepathy". The game has a referee separately ask each player to color a subset of a 3x3 grid. The referee checks that their colorings satisfy certain parity constraints that can't all be simultaneously realized. We define a generalization of these games to be played on an arbitrary arrangement of intersecting sets of elements. We characterize exactly which of these games exhibit quantum pseudo-telepathy, and give quantum winning strategies for those that do. In doing so, we show that it suffices for the players to share three Bell pairs of entanglement even for games on arbitrarily large arrangements. Moreover, it suffices for Alice and Bob to use measurements from the three-qubit Pauli group. The proof technique uses a novel connection of Mermin-style games to graph planarity.
Abstract Quantum pseudo-telepathy games, such as the Mermin–Peres magic square and the doily game (DG), theoretically allow players to win with unit probability when using entangled quantum strategies. We quantitatively characterize the quantum advantage in these games and compare it with violations of two Bell inequalities: the Clauser–Horne–Shimony–Holt and the Collins–Gisin inequalities. The analysis is restricted to two families of two-qubit states: modified Werner states and Bell-diagonal states. For each case, we identify and quantify the regions of quantum state space that exhibit either a quantum advantage or a Bell inequality violation, relative to the set of all entangled states. Within these families, the DG encompasses a larger fraction of entangled states than the Mermin–Peres magic square game, although both cover significantly smaller regions of entangled states compared to those where Bell inequalities are violated. Although both approaches are fundamentally linked to quantum contextuality, our analysis of the examined two-qubit state families suggests that Bell inequalities are more effective at revealing entanglement, even if pseudo-telepathy games offer a more intuitive and conceptually appealing perspective.
We present definitive violations of non-contextual hidden variable bounds in the latest generation of IBM noisy intermediate-scale quantum computers (NISQ). These violations are based on known tests for contextuality such as the Rio Negro inequality and pseudo-telepathic Mermin games. These are the first violations of the classical Mermin game on IBM NISQ computers, and the largest such violations for the Rio Negro inequality. The use of finite geometries proves instrumental in the development of more effective tests, with larger geometries providing sizeable datasets from which multiple distinct experiments can be compared.
A pseudo-telepathy game is a game for two or more players for which there is no classical winning strategy, but there is a winning strategy based on sharing quantum entanglement by the players. Since it is generally very hard to perfectly implement a quantum winning strategy for a pseudo-telepathy game, quantum players are almost certain to make errors even though they use a winning strategy. After introducing a model for pseudo-telepathy games, we investigate the impact of several basic noisy quantum channels on the quantum winning strategy for the Mermin-GHZ game. The question of how strong the noise can be so that quantum players would still be better than classical ones is also dealt with.
Communication complexity is an area of classical computer science which studies how much communication is necessary to solve various distributed computational problems. Quantum information processing can be used to reduce the amount of communication required to carry out some distributed problems. We speak of pseudo-telepathy when it is able to completely eliminate the need for communication. Since it is generally very hard to perfectly implement a quantum winning strategy for a pseudo-telepathy game, quantum players are almost certain to make errors even though they use a winning strategy. After introducing a model for pseudo-telepathy games, we investigate the impact of erroneously performed unitary transformations on the quantum winning strategy for the Mermin-GHZ game. The question of how strong the unitary noise can be so that quantum players would still be better than classical ones is also dealt with.