Periodic Reporting for period 1 - VerNisQDevS (Verifiying Noisy Quantum Devices at Scale)
Período documentado: 2023-06-01 hasta 2025-11-30
The goal of this project is to address the problem of secure delegation of quantum computations on the "quantum cloud". With recent progress in the development of experimental quantum computing devices, we can imagine a medium-term future where large-scale quantum computers are available for rent through a classically accessible cloud. This situation suggests a fundamental challenge: given that such quantum device’s behavior cannot be classically predicted—how can it be benchmarked, and can its computation be trusted?
Traditional methods, such as state and process tomography, are inapplicable due not only to the scale of the systems that need to be tested but also major sources of experimental noise that affect even the highest quality implementations. Due to their fundamental nature these obstacles will only grow with time. In this project we aim to develop methods by which a secure and trustworthy interaction with a powerful quantum computer can be established, even in situations where the quantum computer is not perfect, ie. it may be affected by noise or even behave maliciously. Ultimately our work will lead to concrete protocols that can be used to remotely, securely benchmark and verify the behavior of a quantum computer. In the shorter term, we expect our research to uncover and leverage fundamental properties of quantum information (for example, understanding how the no-cloning principle can be turned from a limitation into an asset bounding the capabilities of malicious quantum devices) as well as develop new techniques in computer science to efficiently and securely interact between classical and quantum devices.
To achieve our results we we draw on a variety of areas across quantum information and computation and classical computer science. In particular we make use of and further develop the framework of interactive proofs in quantum complexity theory, and similarly make use of techniques from quantum cryptography, such as quantum fully homomorphic encryption, while developing new cryptographic principles (such as the notion of a test of quantumness).
Traditional methods, such as state and process tomography, are inapplicable due not only to the scale of the systems that need to be tested but also major sources of experimental noise that affect even the highest quality implementations. Due to their fundamental nature these obstacles will only grow with time. In this project we aim to develop methods by which a secure and trustworthy interaction with a powerful quantum computer can be established, even in situations where the quantum computer is not perfect, ie. it may be affected by noise or even behave maliciously. Ultimately our work will lead to concrete protocols that can be used to remotely, securely benchmark and verify the behavior of a quantum computer. In the shorter term, we expect our research to uncover and leverage fundamental properties of quantum information (for example, understanding how the no-cloning principle can be turned from a limitation into an asset bounding the capabilities of malicious quantum devices) as well as develop new techniques in computer science to efficiently and securely interact between classical and quantum devices.
To achieve our results we we draw on a variety of areas across quantum information and computation and classical computer science. In particular we make use of and further develop the framework of interactive proofs in quantum complexity theory, and similarly make use of techniques from quantum cryptography, such as quantum fully homomorphic encryption, while developing new cryptographic principles (such as the notion of a test of quantumness).
This project has led to the following main achievements. Firstly, we have developed the theory of so-called "many-qubit tests." These are interactive tests that can be used to enforce a robust computation structure within the space of a pair of quantum devices sharing entanglement. Such tests from the basis of all known delegated computing protocols in this framework. In particular, we have demonstrated a link between such tests and the theory of classical error-correcting codes, based on which we hope that future tests may be developed.
Secondly, we have obtained the first construction of quantum error correcting codes that has the property of being locally testable (up to polylogarithmic factors). This work has already been substantially built open in constructions aiming to achieve efficient fault-tolerance. The codes are based on the theory of "cubical" chain complexes and high-dimensional expanders. We expect our codes to be a key ingredient in future delegated computation protocols, as they enable efficiently testing that information is suitably encoded in a code protecting it from errors.
Finally, we initiated a "computational entanglement theory" that considers quantum information tasks related to the manipulation of entanglement, such that entanglement distillation, while taking into account computational efficiency requirements on the parties performing the task. We show that such requirements fundamentally change the nature of basic associated entanglement measures. Our results in this direction have led to multiple follow-up work further developing the theory.
In summary, our work has advanced the state of the art in terms of fundamental tools available for the design of interactive protocols for delegated computation.
Secondly, we have obtained the first construction of quantum error correcting codes that has the property of being locally testable (up to polylogarithmic factors). This work has already been substantially built open in constructions aiming to achieve efficient fault-tolerance. The codes are based on the theory of "cubical" chain complexes and high-dimensional expanders. We expect our codes to be a key ingredient in future delegated computation protocols, as they enable efficiently testing that information is suitably encoded in a code protecting it from errors.
Finally, we initiated a "computational entanglement theory" that considers quantum information tasks related to the manipulation of entanglement, such that entanglement distillation, while taking into account computational efficiency requirements on the parties performing the task. We show that such requirements fundamentally change the nature of basic associated entanglement measures. Our results in this direction have led to multiple follow-up work further developing the theory.
In summary, our work has advanced the state of the art in terms of fundamental tools available for the design of interactive protocols for delegated computation.
We expect our main results, in the design of locally testable codes and in the furthering of multi-qubit tests and entanglement theory, to be used as essential building blocks in future delegated computation protocols. While such protocols currently use computational assumptions, our work opens the way for protocols that may even be information-theoretically sound.
To capitalize on these successes we need to ensure that further work is done in extending our results, and importantly making them more practical and accessible to the community. Eventually some experimental proof of principle demonstrations may be considered. At the moment the theoretical results remain too abstract (and the practical experiments too limited). In the coming period we can envision that successive steps will be taken to bridge both capabilities, from the purely theoretical to the experimental. The need for this becomes ever so pressing as currently it would be fair to say that experimental devices are growing in size and capability faster than the theory is able to meet them.
To capitalize on these successes we need to ensure that further work is done in extending our results, and importantly making them more practical and accessible to the community. Eventually some experimental proof of principle demonstrations may be considered. At the moment the theoretical results remain too abstract (and the practical experiments too limited). In the coming period we can envision that successive steps will be taken to bridge both capabilities, from the purely theoretical to the experimental. The need for this becomes ever so pressing as currently it would be fair to say that experimental devices are growing in size and capability faster than the theory is able to meet them.