Related papers: Accelerating BP-based decoders for QLDPC Codes wit…
Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computation with constant overhead. Recent advancements have shown that qLDPC codes can outperform the quantum memory capability of…
A major challenge in fault-tolerant quantum computation (FTQC) is to reduce both space overhead -- the large number of physical qubits per logical qubit -- and time overhead -- the long physical gate sequences per logical gate. We prove…
A Bounded-Degree Low-Rank Parity-Check (BD-LRPC) code is a rank-metric code that admits a parity-check matrix whose support is generated by a set of powers of an element. This specific structure of the parity-check matrix was employed to…
Quantum error correction (QEC) with single-shot decoding enables reduction of errors after every single round of noisy stabilizer measurement, easing the time-overhead requirements for fault tolerance. Notably, several classes of quantum…
Current quantum processors are fragile, noisy and fairly limited in both quantity and quality with tens of qubits and physical error rates of around 10^-3. To realize practical quantum applications, however, error rates need to be below…
Vast numbers of qubits will be needed for large-scale quantum computing due to the overheads associated with error correction. We present a scheme for low-overhead fault-tolerant quantum computation based on quantum low-density parity-check…
Polar codes are the first provable capacity-achieving forward error correction (FEC) codes. In general polar codes can be decoded via either successive cancellation (SC) or belief propagation (BP) decoding algorithm. However, to date…
Realizing the full potential of quantum computation requires quantum error correction (QEC), with most recent breakthrough demonstrations of QEC using the surface code. QEC codes use multiple noisy physical qubits to encode information in…
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 (QEC) is essential for building robust, fault-tolerant quantum computers; however, the decoding process often presents a significant computational bottleneck. Tesseract is a novel Most-Likely-Error (MLE) decoder for…
Quantum error correction (QEC) is essential for achieving low error rates required for fault-tolerant quantum computation. In stabilizer-based codes such as the surface code, errors are inferred from repeated syndrome measurements and…
Recent research has shown that syndrome-based belief propagation using layered scheduling (sLBP) can not only accelerate the convergence rate but also improve the error rate performance by breaking the quantum trapping sets for quantum…
Recent constructions of quantum low-density parity-check (QLDPC) codes provide optimal scaling of the number of logical qubits and the minimum distance in terms of the code length, thereby opening the door to fault-tolerant quantum systems…
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical…
Quantum low-density parity check (qLDPC) codes offer higher encoding rate than topological codes, e.g. surface codes, making them favourable for practical, fault-tolerant quantum computing with low overhead. These codes are particularly…
Utilizing present and futuristic Quantum Computers to solve difficult problems in different domains has become one of the main endeavors at this moment. Of course, in arriving at the requisite solution both quantum and classical computers…
Lookup table decoding is fast and distance-preserving, making it attractive for near-term quantum computer architectures with small-distance quantum error-correcting codes. In this work, we develop several optimization tools that can…
We introduce a new heuristic decoder, Relay-BP, targeting real-time quantum circuit decoding for large-scale quantum computers. Relay-BP achieves high accuracy across circuit-noise decoding problems: significantly outperforming BP+OSD+CS-10…
In this paper we propose the construction of Spatially Coupled Low-Density Parity-Check (SC-LDPC) codes using a periodic time-variant Quasi-Cyclic (QC) algorithm. The QC based approach is optimized to obtain memory efficiency in storing the…
(Abridged.) This thesis investigates scalable fault-tolerant quantum computation through the development of bosonic quantum codes, quantum LDPC codes, and decoding protocols that connect continuous-variable and discrete-variable error…