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arXiv:2105.05266 · Advanced Quantum Technologies

Playing Quantum Nonlocal Games with Six Noisy Qubits on the Cloud

Meron Sheffer, Daniel Azses, Emanuele G. Dalla Torre

Published Jan 22, 2022• 14 citations
arXivHTMLPDF

Abstract

Abstract Nonlocal games are extensions of Bell inequalities, aimed at demonstrating quantum advantage. These games are well suited for noisy quantum computers because they only require the preparation of a shallow circuit, followed by the measurement of non‐commuting observable. Here, the minimal implementation of the nonlocal game proposed in Science 362, 308 (2018) is considered. This game is tested by preparing a 6‐qubit cluster state using quantum computers on the cloud by IBM, IonQ, and Honeywell. The present implementation includes several levels of optimization, such as circuit identities and error mitigation, and allows us to cross the classical threshold and demonstrate quantum advantage in one quantum computer. The quantum nature of the cluster state is further studied by a Bell inequality that allows us to observe quantum advantage in less accurate quantum computers, at the expense of probing a larger number of circuits.

DOI
10.1002/qute.202100081

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Abstract Nonlocal games are extensions of Bell inequalities, aimed at demonstrating quantum advantage. These games are well suited for noisy quantum computers because they only require the preparation of a shallow circuit, followed by the measurement of non‐commuting observable. Here, the minimal implementation of the nonlocal game proposed in Science 362, 308 (2018) is considered. This game is tested by preparing a 6‐qubit cluster state using quantum computers on the cloud by IBM, IonQ, and Honeywell. The present implementation includes several levels of optimization, such as circuit identities and error mitigation, and allows us to cross the classical threshold and demonstrate quantum advantage in one quantum computer. The quantum nature of the cluster state is further studied by a Bell inequality that allows us to observe quantum advantage in less accurate quantum computers, at the expense of probing a larger number of circuits.
We propose a set of Bell-type nonlocal games that can be used to prove an unconditional quantum advantage in an objective and hardware-agnostic manner. In these games, the circuit depth needed to prepare a cyclic cluster state and measure a subset of its Pauli stabilizers on a quantum computer is compared to that of classical Boolean circuits with the same, nearest-neighboring gate connectivity. Using a circuit-based trapped-ion quantum computer, we prepare and measure a six-qubit cyclic cluster state with an overall fidelity of 60.6% and 66.4%, before and after correcting for measurement-readout errors, respectively. Our experimental results indicate that while this fidelity readily passes conventional (or depth-0) Bell bounds for local hidden-variable models, it is on the cusp of demonstrating a higher probability of success than what is possible by depth-1 classical circuits. Our games offer a practical and scalable set of quantitative benchmarks for quantum computers in the pre-fault-tolerant regime as the number of qubits available increases.
We propose two Bell-type nonlocal games that can be used to prove quantum computational advantage in a hardware-agnostic manner. In these games, the circuit depth needed to prepare a cyclic cluster state and measure a subset of its Pauli stabilizers on a quantum computer is compared to that of classical Boolean circuits with the same gate connectivity. Using a circuit-based trapped-ion quantum computer, we prepare and measure a six-qubit cyclic cluster state with an overall fidelity of 60.6% and 66.4%, before and after correcting measurement-readout errors, respectively. Our experimental results indicate that while this fidelity readily passes conventional (or depth-0) Bell bounds for local hidden variable models, it is on the cusp of demonstrating quantum advantage against depth-1 classical circuits. Our games offer a practical and scalable set of quantitative benchmarks for quantum computers in the pre-fault-tolerant regime as the number of qubits available increases.
Abstract In a nonlocal game, two noncommunicating players cooperate to convince a referee that they possess a strategy that does not violate the rules of the game. Quantum strategies allow players to optimally win some games by performing joint measurements on a shared entangled state, but computing these strategies can be challenging. We present a variational quantum algorithm to compute quantum strategies for nonlocal games by encoding the rules of a nonlocal game into a Hamiltonian. We show how this algorithm can generate a short-depth optimal quantum strategy for a graph coloring game with a quantum advantage. This quantum strategy is then evaluated on fourteen different quantum hardware platforms to demonstrate its utility as a benchmark. Finally, we discuss potential sources of errors that can explain the observed decreased performance of the executed task and derive an expression for the number of samples required to accurately estimate the win rate in the presence of noise.
Abstract This laboratory work presents a practical implementation of the CHSH game using the Qiskit framework and IBM quantum hardware. The material is based on educational resources developed by the International Quantum Center at CERN (Switzerland) and aims to provide an experimental demonstration of quantum nonlocality and Bell inequality violation. In Laboratory Work No. 4, participants implement a simplified version of the Clauser–Horne–Shimony–Holt (CHSH) game to test whether IBM quantum processors exhibit genuinely quantum behavior. The CHSH game is a fundamental protocol in quantum information theory that distinguishes classical correlations from quantum correlations through statistical violation of Bell inequalities. Using Qiskit, a two-qubit entangled state is prepared and measurement settings corresponding to different basis choices are applied. By executing the circuit multiple times on a simulator and real quantum hardware, participants collect measurement statistics and compute the CHSH correlation parameter. If the experimentally obtained value exceeds the classical bound, the results provide empirical evidence of quantum entanglement and nonlocal correlations. This laboratory exercise demonstrates how foundational concepts of quantum mechanics—entanglement, superposition, and measurement basis dependence—can be directly tested using cloud-accessible quantum processors. The experiment not only reinforces theoretical understanding of Bell inequalities but also introduces practical skills in circuit construction, parameterized measurements, statistical analysis, and noise considerations in real quantum devices.
Experimental tests of shallow-circuit quantum advantage require explicit classical bounds at finite circuit sizes. We refine the finite-size classical soundness bound of Aasnaess's graph-distributed construction to depend linearly on the number of players. Combined with standard disjoint-player repetition, this gives a two-round test on a single processor for any finite nonlocal game with a finite-dimensional perfect quantum strategy and classical winning probability γ<1γ<1γ<1, with arbitrarily small classical success. The method is based on playing mmm copies with disjoint players and teleporting each player's register to a uniformly random one of NNN sites before the questions are revealed. Each answer bit of a depth-DDD, fan-in-KKK classical response with fixed wiring depends on at most KDK^DKD question wires, making cross-player dependencies unlikely when NNN is large. The quantum implementation has constant depth per round and wins with certainty. A classical device wins with probability at most γm+O(mKD/N)γ^m+O(mK^D/N)γm+O(mKD/N), which vanishes as O(log⁡N/N)O(\log N/N)O(logN/N) for m=⌈log⁡1/γN⌉m=\lceil\log_{1/γ}N\rceilm=⌈log1/γ​N⌉ at fixed DDD and KKK. We present an explicit proposal for an experimentally testable quantum advantage with 99 qubits.
We show that quantum computers can be used for producing large nnn-partite nonlocality, thereby providing a method to benchmark them. The main challenges to overcome are as follows: (i) The interaction topology might not allow arbitrary two-qubit gates. (ii) Noise limits the Bell violation. (iii) The number of combinations of local measurements grows exponentially with nnn. To overcome (i), we point out that graph states that are compatible with the two-qubit connectivity of the computer can be efficiently prepared. To mitigate (ii), we note that for specific graph states, there are nnn-partite Bell inequalities whose resistance to white noise increases exponentially with nnn. To address (iii) for any nnn and any connectivity, we introduce an estimator that relies on random sampling. As a result, we propose a method for producing nnn-partite Bell nonlocality with unprecedented large nnn. This allows one, in return, to benchmark nonclassical correlations regardless of the number of qubits or the connectivity. We test our approach by using a simulation for a noisy IBM quantum computer, which predicts nnn-partite Bell nonlocality for at least n=24n=24n=24 qubits.