CSS Codes Enable Self-Testing Quantum Matter through Many-body Contextuality

Contextuality, a property distinguishing quantum mechanics from classical physics, underpins potential computational advantages and can be directly investigated using multiplayer nonlocal games. Oliver Hart, David T. Stephen, and Evan Wickenden, alongside Rahul Nandkishore, all from the University of Colorado Boulder, demonstrate how these games reveal the contextuality of quantum states, specifically those forming codewords within error-correcting codes. The team shows that winning these games requires a level of deterministic computation unattainable classically, and they have developed a new method, inspired by many-body physics, to efficiently quantify this contextuality through analysis of code symmetries. This research not only establishes a link between contextuality, error correction, and statistical mechanics, but also introduces a powerful technique for ‘self-testing’ quantum matter, explicitly demonstrated for the 2D toric code, and opens avenues for exploring extensive contextuality in complex quantum systems.

Scientists explore whether the violation of Bell inequalities, when extended to systems with many interacting particles, can demonstrate the genuinely quantum nature of a state without needing complete knowledge of its properties. The team developed a framework to analyse how the strength of contextual behaviour relates to the confidence with which a quantum state can be self-tested, revealing a direct link between these two concepts. Specifically, they demonstrate that a stronger violation of a nonlocal game corresponds to a higher confidence in the identified quantum state, allowing for more robust certification of quantumness.

The approach involves formulating a self-testing protocol based on the CHSH game, adapted for multi-particle systems, and analysing the conditions under which observed behaviour uniquely identifies a specific quantum state. The results show that for certain states, a sufficiently strong violation of the CHSH inequality guarantees that the observed correlations originate from a quantum system in the predicted state, with a quantifiable level of confidence. Furthermore, the research investigates the robustness of this self-testing procedure against noise and imperfections, demonstrating its effectiveness even in realistic experimental scenarios. This work extends to explore the implications for certifying quantum advantage in many-body systems, demonstrating that the self-testing framework provides a powerful tool for validating the performance of quantum devices. By establishing a direct connection between contextual behaviour and self-testing, this research provides new insights into the foundations of quantum mechanics and opens up new avenues for developing robust and reliable quantum technologies.

Quantum superposition is a fundamental property distinguishing quantum mechanics from classical physics. It is responsible for quantum computational speedups and can be directly probed in a many-body setting by multiplayer nonlocal quantum games. This work discusses games that can be won with certainty when performing single-site Pauli measurements on a state that is a codeword of a Calderbank-Shor-Steane (CSS) error-correcting quantum code. The research demonstrates that these games require deterministic computation of a code-dependent Boolean function, and that the classical probability of success is upper bounded.

Quantum Information, Computation and Error Correction

This compilation presents a comprehensive overview of research in quantum information, computation, and related areas, covering foundational concepts, quantum contextuality and nonlocality, quantum algorithms and applications, quantum hardware and characterization, and advanced topics. Foundational work covers the core principles of quantum information and the development of error correction techniques, including stabilizer formalism and topological codes. Research on entanglement and Bell inequalities establishes the power and limitations of entanglement, while work on quantum communication explores unique capabilities like quantum pseudo-telepathy. Studies on quantum supremacy and advantage investigate when and how quantum computers can outperform classical computers, often focusing on specific models like shallow circuits and their connection to classical complexity classes.

A major theme throughout the research is quantum contextuality and nonlocality, highlighting its importance as a fundamental feature of quantum mechanics and a potential resource for computation. Significant work focuses on self-testing, a process of verifying that a quantum device is behaving as expected without strong assumptions about its internal workings, and is particularly important for realistic scenarios. Research also explores specific quantum algorithms, such as quantum graph coloring and sampling techniques, which could potentially outperform classical algorithms. Studies on bent functions are relevant because of their connections to quantum error correction and algorithms.

Work on quantum device characterization presents methods for characterizing quantum devices without full tomography, crucial for scaling up quantum computers. Advanced topics include topological quantum computation, a promising approach to building fault-tolerant quantum computers, and many-body contextuality, an emerging area exploring the connections between contextuality and many-body physics. Research on 3D-local quantum circuits explores the potential advantages of using higher-dimensional circuits, while work on self-testing with dishonest parties is crucial for building secure quantum communication networks. The research demonstrates a clear trend towards developing methods for building and characterizing realistic quantum devices, including dealing with noise and imperfections, and highlights the increasing importance of contextuality and nonlocality as fundamental resources for quantum computation and communication.

Quantum Contextuality Powers Game-Theoretic Advantage

This research demonstrates a strong connection between quantum contextuality and classical computation, specifically through the lens of multiplayer games. Scientists have shown that certain games, designed around codewords from Calderbank-Shor-Steane (CSS) codes, can be won with certainty using quantum resources, while classical strategies are fundamentally limited. The team developed a method to quantify this contextuality by calculating the probability of classical success in these games, linking it to the nonlinearity of Boolean functions and the symmetries of auxiliary hypergraph states. Calculations performed for several CSS codes, including the GHZ state, the 1D cluster state, and the 2D toric code, reveal a quantifiable relationship between quantum contextuality and classical statistical mechanics. Furthermore, the researchers introduced “submeasurement games”, which require players to share a specific quantum state to win, enabling a process called “self-testing”, verifying the state’s properties through gameplay, as demonstrated with the 2D toric code.