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Quantum codes with low-weight stabilizers known as LDPC codes have been actively studied recently due to their simple syndrome readout circuits and potential applications in fault-tolerant quantum computing. However, all families of quantum…
Topological error correction--a novel method to actively correct errors based on cluster states with topological properties--has the highest order of tolerable error rates known to date (10^{-2}). Moreover, the scheme requires only…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
A proof of quantumness is an efficiently verifiable interactive test that an efficient quantum computer can pass, but all efficient classical computers cannot (under some cryptographic assumption). Such protocols play a crucial role in the…
Noise rates in quantum computing experiments have dropped dramatically, but reliable qubits remain precious. Fault-tolerance schemes with minimal qubit overhead are therefore essential. We introduce fault-tolerant error-correction…
The performance of a given quantum error correction (QEC) code depends upon the noise model that is assumed. Independent Pauli noise, applied after each quantum operation, is a simplistic noise model that is easy to simulate and understand…
We discuss stabilizer quantum-error correction codes implemented in a single multi-level qudit to avoid resource escalation typical of multi-qubit codes. These codes can be customized to the specific physical errors on the qudit,…
Quantum low-density parity-check (LDPC) codes are an important class of quantum error correcting codes. In such codes, each qubit only affects a constant number of syndrome bits, and each syndrome bit only relies on some constant number of…
Quantum computers are poised to radically outperform their classical counterparts by manipulating coherent quantum systems. A realistic quantum computer will experience errors due to the environment and imperfect control. When these errors…
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the…
The storage and processing of quantum information are susceptible to external noise, resulting in computational errors that are inherently continuous A powerful method to suppress these effects is to use quantum error correction. Typically,…
The typical model for measurement noise in quantum error correction is to randomly flip the binary measurement outcome. In experiments, measurements yield much richer information - e.g., continuous current values, discrete photon counts -…
Errors in quantum computers are of two kinds: sudden perturbations to isolated qubits, and slow random drifts of all the qubits. The latter may be reduced, but not eliminated, by means of symmetrization, namely by using many replicas of the…
Quantum systems can be used to measure various quantities in their environment with high precision. Often, however, their sensitivity is limited by the decohering effects of this same environment. Dynamical decoupling schemes are widely…
In near-term quantum computations that do not employ error correction, noise can proliferate rapidly, corrupting the quantum state and making results unreliable. These errors originate from both decoherence and control imprecision. The…
Noise is an important factor that influences the reliability of information acquisition, transmission, processing, and storage. In order to suppress the inevitable noise effects, a fault-tolerant information processing approach via quantum…
Photonics provides a viable path to a scalable fault-tolerant quantum computer. The natural framework for this platform is measurement-based quantum computation, where fault-tolerant graph states supersede traditional quantum…
We present relaxed criteria for quantum error correction which are useful when the specific dominant noise process is known. These criteria have no classical analogue. As an example, we provide a four-bit code which corrects for a single…
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms.…
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…