Related papers: Error counting in a quantum error-correcting code …
Quantum error correction allows to actively correct errors occurring in a quantum computation when the noise is weak enough. To make this error correction competitive information about the specific noise is required. Traditionally, this…
We suggest a technique for constructing lower (existence) bounds for the fault-tolerant threshold to scalable quantum computation applicable to degenerate quantum codes with sublinear distance scaling. We give explicit analytic expressions…
Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an…
The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based…
Quantum coherence is a central ingredient in quantum physics with several theoretical and technological ramifications. In this work we consider a figure of merit encoding the information on how the coherence generated on average by a…
Ongoing research and experiments have enabled quantum memory to realize the storage of qubits. On the other hand, interleaving techniques are used to deal with burst of errors. Effective interleaving techniques for combating burst of errors…
Among various algorithms designed to exploit the specific properties of quantum computers with respect to classical ones, the quantum adiabatic algorithm is a versatile proposition to find the minimal value of an arbitrary cost function…
Understanding algorithmic error accumulation in quantum simulation is crucial due to its fundamental significance and practical applications in simulating quantum many-body system dynamics. Conventional theories typically apply the triangle…
We study the resilience of the surface code to decoherence caused by the presence of a bosonic bath. This approach allows us to go beyond the standard stochastic error model commonly used to quantify decoherence and error threshold…
In the simple quantum hypothesis testing problem, upper bounds on the error probabilities are shown based on a key operator inequality between a density operator and its pinching. Concerning the error exponents, the upper bounds lead to a…
The schemes for fault-tolerant postselected quantum computation given in [Knill, Fault-Tolerant Postselected Quantum Computation: Schemes, http://arxiv.org/abs/quant-ph/0402171] are analyzed to determine their error-tolerance. The analysis…
We investigate the stability of logical information in quantum stabilizer codes subject to coherent unitary errors. Beginning with a logical state, we apply a random unitary error channel and subsequently measure stabilizer checks,…
We introduce a new quantum decoder based on a variant of the pretty good measurement, but defined via an alternative matrix quotient. We use this decoder to show new lower bounds on the error exponent both in the one-shot and asymptotic…
I develop methods for analyzing quantum error-correcting codes, and use these methods to construct an infinite class of codes saturating the quantum Hamming bound. These codes encode $k=n-j-2$ qubits in $n=2^j$ qubits and correct $t=1$…
We show that quantum computation can be performed in a system at thermal equilibrium if a spontaneous symmetry breaking occurs. The computing process is associated to the time evolution of the statistical average of the qubit coherence…
We study the fidelity of the surface code in the presence of correlated errors induced by the coupling of physical qubits to a bosonic environment. By mapping the time evolution of the system after one quantum error correction cycle onto a…
New bounds on classification error rates for the error-correcting output code (ECOC) approach in machine learning are presented. These bounds have exponential decay complexity with respect to codeword length and theoretically validate the…
The highest information rate at which quantum error-correction schemes work reliably on a channel, which is called the quantum capacity, is proven to be lower bounded by the limit of the quantity termed coherent information maximized over…
The optimally designed control of quantum systems is playing an increasingly important role to engineer novel and more efficient quantum technologies. Here, in the scenario represented by controlling an arbitrary quantum system via the…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…