Related papers: Proof of a finite threshold for the union-find dec…
The states needed in a quantum computation are extremely affected by decoherence. Several methods have been proposed to control error spreading. They use two main tools: fault-tolerant constructions and concatenated quantum error correcting…
We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings. For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes…
We present a comprehensive and self-contained simplified review of the quantum computing scheme of Phys. Rev. Lett. 98, 190504 (2007), which features a 2-D nearest neighbor coupled lattice of qubits, a threshold error rate approaching 1%,…
A common approach to studying the performance of quantum error correcting codes is to assume independent and identically distributed single-qubit errors. However, the available experimental data shows that realistic errors in modern…
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.…
Many proposals for fault tolerant quantum computation (FTQC) suffer detectable loss processes. Here we show that topological FTQC schemes, which are known to have high error thresholds, are also extremely robust against losses. We…
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 derive a universal performance limit for coherent quantum control in the presence of modeled and unmodeled uncertainties. For any target unitary $W$ that is implementable in the absence of error, we prove that the worst-case (and hence…
Quantum error correction is a critical technique for transitioning from noisy intermediate-scale quantum (NISQ) devices to fully fledged quantum computers. The surface code, which has a high threshold error rate, is the leading quantum…
Attaining fault tolerance while maintaining low overhead is one of the main challenges in a practical implementation of quantum circuits. One major technique that can overcome this problem is the flag technique, in which high-weight errors…
Quantum error-correcting codes, such as subspace, subsystem, and Floquet codes, are typically constructed within the stabilizer formalism, which does not fully capture the idea of fault-tolerance needed for practical quantum computing…
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…
Solving quantum molecular systems presents a significant challenge for classical computation. The advent of early fault-tolerant quantum computing (EFTQC) devices offers a promising avenue to address these challenges, leveraging advanced…
We consider the impact of the unitary averaging framework on single and two-mode linear optical gates. We demonstrate that this allows a trade-off between the probability of success and gate fidelity, with perfect fidelity gates being…
Mapping quantum error correcting codes to classical disordered statistical mechanics models and studying the phase diagram of the latter has proven a powerful tool to study the fundamental error robustness and associated critical error…
The standard approach to universal fault-tolerant quantum computing is to develop a general purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum…
Polar codes are a class of error-correcting codes that provably achieve the capacity of practical channels under the low-complexity successive-cancellation flip (SCF) decoding algorithm. However, the SCF decoding algorithm has a variable…
Benefiting from performance advantages under short code lengths, polar codes are well-suited for certain scenarios, such as the future Internet of Things (IoT) applications that require high reliability and low power. Existing list flip…
Fast SC decoding overcomes the latency caused by the serial nature of the SC decoding by identifying new nodes in the upper levels of the SC decoding tree and implementing their fast parallel decoders. In this work, we first present a novel…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…