Quantum codes enable fault-tolerant qubit injection with constant overhead
Constant-Overhead Injection into Quantum Codes
Information Theory
Summary
Quantum computers need to protect information from errors, but putting new information into error-correcting codes usually takes a lot of extra space or time. The authors created a method to add and remove quantum information from these codes using only a small, fixed amount of extra resources, no matter how big the code is. Their approach works even when physical qubits suffer random errors, and the correction steps happen quickly. They build these codes by combining special classical error-correcting codes in a clever way and make them resilient against uniform noise by layering simple inner codes.
What this means in practice
- •For quantum hardware engineers: Implement fault-tolerant qubit encoding and decoding with minimal added hardware and time resources to improve quantum processor scalability.
- •For quantum software developers: Design quantum compilers that efficiently manage state injection and extraction using constant-depth, fault-tolerant circuits for error correction.
Authors
Louis Golowich, Venkatesan Guruswami
Abstract
We construct the first known fault-tolerant scheme for injecting states into quantum error-correcting codes with constant space and time overhead. That is, we construct a family of constant-rate quantum error-correcting codes for which a set of bare physical qubits can be injected, i.e. fault-tolerantly encoded, into a code block. Similarly, a code state can be ejected, i.e. fault-tolerantly decoded, back into bare physical qubits. We show that these injection and ejection procedures succeed under circuit-level locally stochastic noise, while incurring just a small constant probability of corrupting each qubit, which is unavoidable for bare physical qubits. We also show how to perform fault-tolerant error correction and code-state preparation under locally stochastic noise. All of our gadgets can be implemented with constant quantum circuit depth (i.e. are single-shot), and with a number of physical qubits growing linearly with the number of logical qubits, assuming the ability to run polynomial-sized noiseless classical circuits on the side. We construct our quantum codes by taking a high-dimensional hypergraph product of classical LDPC codes, which in turn are a simplified version of Spielman's linear-time encodable codes (STOC'95). As our resulting product codes are only resilient to physical errors occurring with non-uniform probabilities across qubits, we then show how to concatenate with inner codes of various sizes to obtain fault-tolerance against uniform noise.