Constant-Overhead Addressable Gates via Single-Shot Code Switching

2025-10-08

AI Summary

A key bottleneck in fault-tolerant quantum computing with constant-rate quantum LDPC (qLDPC) codes is the difficulty of addressing and performing parallel operations on logical qubits, accompanied by high resource overhead. Method: This work introduces a low-overhead fault-tolerant code-switching scheme based on lossless expander-graph constructions, classical tensor-product codes, and high-dimensional product codes, integrated with small-set-flip decoders and single-shot code-switching techniques. Contribution/Results: The scheme enables constant-space-and-time execution of Hadamard and CNOT gates on arbitrary logical qubits—marking the first such result—and eliminates reliance on code symmetry inherent in prior protocols. It achieves a constant error threshold, supports logical state preparation, and extends to parallel non-Clifford gate implementation. By unifying efficient decoding, robust code switching, and scalable architecture design, this work establishes a new paradigm for high-efficiency, scalable fault-tolerant qLDPC-based quantum computation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

It is a major challenge to perform addressable and parallel logical operations on constant-rate quantum LDPC (qLDPC) codes. Indeed, the overhead of targeting specific logical qubits represents a crucial bottleneck in many quantum fault-tolerance schemes. We introduce fault-tolerant protocols for performing various addressable as well as parallel logical operations with constant space-time overhead, on a family of constant-rate and polynomial-distance qLDPC codes. Specifically, we construct gadgets for a large class of permutations of logical qubits. We apply these logical permutations to construct gadgets for applying a targeted Hadamard (or $CNOT$) gate on any chosen logical qubit (pair). We also construct gadgets for preparing logical code states, and for applying Hadamard gates on all logical qubits in a codeblock. All of our gadgets use constant quantum space-time overhead along with polynomially bounded classical computation. Prior protocols for such operations required larger overhead, or else relied on codes with certain symmetries that lack known asymptotic constructions. Our codes are given by tensor products of classical codes constructed from lossless expander graphs. Our core technical contribution is a constant-overhead code-switching procedure between 2- and 3-dimensional product codes, which generalizes Bombin's dimensional jump (arXiv:1412.5079). We prove that all of our gadgets exhibit a constant threshold under locally stochastic noise. Along the way, we develop a small-set flip decoder for high-dimensional product codes from lossless expanders. Our techniques yield additional interesting consequences, such as single-shot state preparation of 2-dimensional product codes with constant space-time overhead. We also propose a method for performing parallel non-Clifford gates by extending our techniques to codes supporting transversal application of such gates.

Problem

• Performing addressable logical operations on quantum LDPC codes efficiently
• Reducing overhead bottlenecks in quantum fault-tolerance schemes
• Enabling targeted gates on specific logical qubits with constant overhead

Innovation

• Constant-overhead code-switching between product codes
• Fault-tolerant gadgets for addressable logical operations
• Small-set flip decoder for high-dimensional codes