Related papers: Error Thresholds for Arbitrary Pauli Noise
Current quantum computers suffer from non-stationary noise channels with high error rates, which undermines their reliability and reproducibility. We propose a Bayesian inference-based adaptive algorithm that can learn and mitigate quantum…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This…
Estimating the information transmission capability of a quantum channel remains one of the fundamental problems in quantum information processing. In contrast to classical channels, the information-carrying capability of quantum channels is…
A striking feature of quantum error correcting codes is that they can sometimes be used to correct more errors than they can uniquely identify. Such degenerate codes have long been known, but have remained poorly understood. We provide a…
In an idealistic setting, quantum metrology protocols allow to sense physical parameters with mean squared error that scales as $1/N^2$ with the number of particles involved---substantially surpassing the $1/N$-scaling characteristic to…
The one-way quantum computing model introduced by Raussendorf and Briegel [Phys. Rev. Lett. 86 (22), 5188-5191 (2001)] shows that it is possible to quantum compute using only a fixed entangled resource known as a cluster state, and adaptive…
In this work, the efficient quantum error-correction protocol against the general independent noise is constructed with the three-qubit codes. The rules of concatenation are summarized according to the error-correcting capability of the…
We compare the performance of quantum error correcting codes when memory errors are unitary with the more familiar case of dephasing noise. For a wide range of codes we analytically compute the effective logical channel that results when…
Rigorously establishing that the error in an experimental quantum operation is beneath the threshold for fault-tolerant quantum computation currently requires considering the worst-case error, which can be orders of magnitude smaller than…
How much noise can a given quantum state tolerate without losing its entanglement? For qudits of arbitrary dimension, I investigate this question for two noise models: Global white noise, where a depolarizing channel is applied to all…
We introduce a novel type of quantum error correcting code, called the spinor code, based on spaces defined by total spin. The code is a nonstabilizer code, and is also a nonlinear quantum error correcting code, meaning that quantum…
The surface code represents a promising candidate for fault-tolerant quantum computation due to its high error threshold and experimental accessibility with nearest-neighbor interactions. However, current exact surface code threshold…
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…
Fault-tolerant quantum computing based on surface codes has emerged as a popular route to large-scale quantum computers capable of accurate computation even in the presence of noise. Its popularity is, in part, because the fault-tolerance…
We present a [[7, 1, 3]] quantum error-correcting code that is able to achieve fault-tolerant syndrome measurement using one ancillary qubit per stabilizer for an error model of independent single-qubit Pauli errors. All single-qubit Pauli…
The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation stating that arbitrarily long quantum computations can be performed with a polylogarithmic overhead provided the noise level is below a…
In this paper, we place bounds on when it is impossible to purify a noisy two-qubit state if all the gates used in the purification protocol are subject to adversarial local, independent, noise. It is found that the gate operations must be…
We present a nonintrusive method for reliably estimating the noise level during quantum computation and quantum communication protected by quantum error-correcting codes. As preprocessing of quantum error correction, our scheme estimates…
A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing…