Frontiers in quantum error-correcting codes: New constructions, models, and connections
Abstract
Quantum computing has the potential to be one of the most disruptive technological and computational advances of recent times. Realizing this potential requires the ability to precisely control and process quantum bits (called qubits), and harness uniquely quantum phenomena such as entanglement in a robust manner. A significant challenge in realizing the promise of scalable quantum computing is the inherent noise that corrupts quantum states, making it impossible to precisely control the evolution of qubits within a larger physical system. Left unchecked, this noise builds up and quickly degrades the accuracy of any quantum computation. Reliable quantum computing therefore crucially needs quantum error-correcting codes to protect the integrity and accuracy of the computation. Such a code encodes logical qubits into a larger number of entangled physical qubits, in a manner that allows recovery of the original state of the logical qubits even if the physical bits are corrupted by errors. Unlike classical error-correcting codes which protect data in storage and communication on top of an already reliable physical computing layer, quantum error-correction is not something to-do with quantum computers once we have them, rather it is absolutely crucial to realize quantum computing in the first place!The design of such quantum error-correcting codes with desirable properties is a difficult challenge, with much recent progress and yet many key challenges remaining. This project will investigate a collection of intertwined and timely challenges concerning quantum error-correcting codes. This will include the goal of fully explicit constructions of asymptotically good quantum low-density parity-check (LDPC) codes, following recent breakthroughs which give such constructions relying on random components. Efficient algorithms to decode weaker but more practically applicable LDPC codes, taking into account considerations that arise in using quantum codes in fault-tolerant computation, will be another thrust. Other thrusts will include a study of the effect of the structure of code s stabilizer checks on its parameters, further study of quantum locally recoverable codes and variants, attempts to construct quantum locally testable codes, and constructing much better quantum codes when allowing for a tiny approximation error in decoding. In addressing these challenges, the project will harness the rich experience and track record of the PI in research at the frontiers of classical error-correcting codes. Technically, quantum codes rely heavily on tools, techniques, intuitions, and results from classical coding theory. The PI is thus ideally poised to make progress on the challenges of the project, and indeed has already made successful forays into quantum error-correction. The PI has also recruited an exceptionally strong group of PhD students who are highly qualified and interested to participate in the proposed project. The specific topics have been carefully chosen to have high impact on advancing the frontiers of the subject, while at the same time having a good likelihood of success given the background of the PI and his recent research trajectory. The project will advance our understanding of fundamental issues in quantum coding theory and inform the next generation of fault-tolerant quantum computing architectures. Error-correction is a natural requirement for reliable naval communications under varied and challenging circumstances, and being at the cutting edge of technological needs, naval applications are a likely testbed for early-stage quantum devices. As the driver of reliable quantum computing and processing of quantum states, quantum error-correction will be central to any future deployment of quantum devices in naval applications. Addressing fundamental questions at the frontiers of quantum error-correction as proposed here therefore naturally fits the mission of Naval research.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Nov 08, 2024
- Source ID
- N000142412491
Entities
People
- Venkatesan Guruswami
Organizations
- Office of Naval Research
- United States Navy
- University of California Regents