Related papers: In-situ Adaptive Encoding for Asymmetric Quantum E…
Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation…
We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the…
One of the main problems in quantum information systems is the presence of errors due to noise, and for this reason quantum error-correcting codes (QECCs) play a key role. While most of the known codes are designed for correcting generic…
We introduce heterogeneous quantum error-correcting codes composed of qubit types with distinct error channels and study their performance in the code-capacity regime using maximum-likelihood tensor network decoding. In the regime where…
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…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
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…
Information obtained from noise characterization of a quantum device can be used in classical decoding algorithms to improve the performance of quantum error-correcting codes. Focusing on the surface code under local (i.e. single-qubit)…
We study a class of gauge fixings of the Bacon-Shor code at the circuit level, which includes a subfamily of generalized surface codes. We show that for these codes, fault tolerance can be achieved by direct measurements of the stabilizers.…
In this work, we develop a space-time block code for noncoherent communication using techniques from the field of quantum error correction. We decompose the multiple-input multiple-output (MIMO) channel into operators from quantum…
In this paper we estimate the fidelity of stabilizer and CSS codes. First, we derive a lower bound on the fidelity of a stabilizer code via its quantum enumerator. Next, we find the average quantum enumerators of the ensembles of finite…
In this paper, we consider a simplified error-correcting problem: for a fixed encoding process, to find a cascade connected quantum channel such that the worst fidelity between the input and the output becomes maximum. With the use of the…
We present a class of numerical algorithms which adapt a quantum error correction scheme to a channel model. Given an encoding and a channel model, it was previously shown that the quantum operation that maximizes the average entanglement…
A significant hurdle for quantum information and processing using bosonic systems is stochastic phase errors which occur as the photons propagate through a channel. These errors will reduce the purity of states passing through the channel…
Quantum error correction (QEC) is essential for reliable quantum information processing. Targeting a particular error channel, both the encoding and the recovery channel can be optimized through a biconvex optimization to give a…
Quantum metrology and sensing seek advantage in estimating an unknown parameter of some quantum state or channel, using entanglement such as spin squeezing produced by one-axis twists or other quantum resources. In particular, qubit phase…
In a recent paper ([1]=quant-ph/0606035) it is shown how the optimal recovery operation in an error correction scheme can be considered as a semidefinite program. As a possible future improvement it is noted that still better error…
We demonstrate that continuous-variable quantum error correction based on Gaussian ancilla states and Gaussian operations (for encoding, syndrome extraction, and recovery) can be very useful to suppress the effect of non-Gaussian error…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…