CS Seminar by Andrew Tanggara
Title: Strategic Codes: The Universal Spatio-Temporal Framework for Quantum Error-Correction
Date/Time: 17-Jul, 04:00PM
Venue: CQT Level 3 Seminar Room, S15-03-15
The emerging paradigm of dynamical quantum error-correcting codes (QECC) has led to a plethora of error-correction schemes that uses a sequence of operations evolving how quantum information is spatially encoded over time, as opposed to a fixed spatial many-body encoding in conventional static QECCs. Substantial progress in dynamical QECC research has led to more resource-efficient codes with fundamentally interesting features.However, an understanding of the extent of how error-correction can be performed utilizing both space and time domains is limited due to the lack of a unified framework. We address this gap by proposing the ``strategic code\'\' framework, the most general QECC framework encompassing all existing codes and any physically plausible codes to be discovered, as well as capturing its interplay with the most general type of noise environment with spatio-temporal correlations. The framework uses an ``interrogator\'\' device, which allows a code to perform the most general quantum process that adaptively interacts with the noise environment over multiple time-steps, both of which are represented in the quantum combs formalism. Using the framework, we establish necessary and sufficient error-correction conditions for a strategic code under a general non-markovian error model in two forms: algebraic and information-theoretic, which include analogous known static QECC conditions as a special case. We also provide an optimization problem to systematically obtain a strategic code that recovers quantum information up to a desired fidelity under a given noise model with arbitrary correlations.Arxiv preprint: https://arxiv.org/abs/2405.17567