Related papers: Linear-Time Encodable and Decodable Quantum Error-…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…
Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure…
Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this…
Usual scenarios of fault-tolerant computation are concerned with the fault-tolerant realization of quantum algorithms that compute classical functions, such as Shor's algorithm for factoring. In particular, this means that input and output…
It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…
Quantum computers require error correction to achieve universal quantum computing. However, current decoding of quantum error-correcting codes relies on classical computation, which is slower than quantum operations in superconducting…
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…
Channel capacities quantify the optimal rates of sending information reliably over noisy channels. Usually, the study of capacities assumes that the circuits which sender and receiver use for encoding and decoding consist of perfectly…
We study a quantum analogue of locally decodable error-correcting codes. A q-query locally decodable quantum code encodes n classical bits in an m-qubit state, in such a way that each of the encoded bits can be recovered with high…
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
Fault-tolerant quantum computing demands decoders that are fast, accurate, and adaptable to circuit structure and realistic noise. While machine learning (ML) decoders have demonstrated impressive performance for quantum memory, their use…
Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and…
We study error correction type protocols in which a quantum channel encodes logical information into an enlarged Hilbert space. Specifically, we consider channels realized by one dimensional random noisy quantum circuits with spatially…
With the development of quantum hardware bringing the error-corrected quantum circuits to the near future, the lack of an efficient polynomial-time decoding algorithms for logical circuits presents a critical bottleneck. While quantum…
In this work, we study the task of encoding logical information via a noisy quantum circuit. It is known that at superlogarithmic depth, the output of any noisy circuit without reset gates or intermediate measurements becomes…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…
Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation…
Efficient and accurate decoding of quantum error-correcting codes is essential for fault-tolerant quantum computation, however, it is challenging due to the degeneracy of errors, the complex code topology, and the large space for logical…
Recent work [M. J. Gullans et al., Physical Review X, 11(3):031066 (2021)] has shown that quantum error correcting codes defined by random Clifford encoding circuits can achieve a non-zero encoding rate in correcting errors even if the…
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale…