Problem
Research questions and friction points this paper is trying to address.
quantum error correction
logical operations
non-additive codes
fault-tolerant quantum computing
hardware-adapted
Learning Logical Operations for Arbitrary Quantum Error Correction Codes
🤖 AI Summary
This work proposes a learning-based universal framework for automatically discovering physical implementations of logical operations that satisfy specific structural constraints—such as transversality or shallow circuit depth—for arbitrary quantum error-correcting codes, including non-additive codes lacking stabilizer descriptions. Relying solely on the encoding circuit, the approach integrates variational quantum machine learning, tailored loss functions, and parameterized circuit templates into an end-to-end optimization pipeline. It further evolves into a Variational Early Fault-Tolerant Quantum Computing (VarEFTQC) co-design paradigm, jointly optimizing both the code and the target logical gate set to align with a given noise model. Experiments not only recover known logical gates for stabilizer codes but also generate novel constraint-compliant logical operations for non-additive codes, demonstrating the method’s effectiveness and practicality in hardware-aware logical gate discovery.
📝 Abstract
Logical operations are essential for quantum computation within quantum error-correcting codes. However, discovering their physical realizations is challenging, especially for non-additive codes that lack a stabilizer description. We present a general learning-based framework that, given only an encoding circuit, constructs physical implementations of logical operations while enforcing structural properties such as transversality or shallow depth. Our approach is validated by rediscovering known logical operations of standard stabilizer codes. We then extend it to a co-design procedure, dubbed variational early fault-tolerant quantum computing (VarEFTQC), which tailors non-additive encodings to a given noise model and enforces desired logical gate sets, such as transversal IQP-type families or low-depth universal sets. A software library implements the complete learning pipeline, including loss-function variants, ansatz families, and optimization routines. Together, these results position VarEFTQC as a practical tool for discovering hardware-adapted logical gadgets for early fault-tolerant quantum computing.
Innovation
Methods, ideas, or system contributions that make the work stand out.
quantum error correction
logical operations
non-additive codes
variational learning
fault-tolerant quantum computing
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