Related papers: Channel-Adapted Quantum Error Correction for the A…
We show how to explicitly construct an $O(nd)$ size and constant quantum depth circuit which encodes any given $n$-qubit stabilizer code with $d$ generators. Our construction is derived using the graphic description for stabilizer codes and…
We study entanglement fluctuations and quantum error correction in the weakly monitored volume-law phase of quantum automaton circuits subject to repeated local measurements. We numerically observe that the entanglement entropy exhibits…
The task of finding a correctable encoding that protects against some physical quantum process is in general hard. Two main obstacles are that an exponential number of experiments are needed to gain complete information about the quantum…
In this paper we introduce a general fault-tolerant quantum error correction protocol using flag circuits for measuring stabilizers of arbitrary distance codes. In addition to extending flag error correction beyond distance-three codes for…
Quantum algorithms manipulate the amplitudes of quantum states to find solutions to computational problems. In this work, we present a framework for applying a general class of non-linear functions to the amplitudes of quantum states, with…
Two observations are given on the fidelity of schemes for quantum information processing. In the first one, we show that the fidelity of a symplectic (stabilizer) code, if properly defined, exactly equals the `probability' of the…
We demonstrate that the performance of quantum error correction can be improved with noise-aware decoders that are calibrated to the likelihood of physical error configurations in a device. We show that noise-aware decoding increases the…
Noise poses a fundamental challenge to quantum information processing, with amplitude-damping (AD) noise being particularly detrimental. Preserving high-fidelity quantum systems therefore relies critically on effective error correction and…
Conventional computers have evolved to device components that demonstrate failure rates of 1e-17 or less, while current quantum computing devices typically exhibit error rates of 1e-2 or greater. This raises concerns about the reliability…
A classical coding across a block of logical qubits is presented. We characterize subgroups of the product stabilizer group on a block of logical qubits corresponding to dual codes of classical error correcting codes. We prove conditions on…
Due to the interaction with the environment, a quantum state is subjected to decoherence which becomes one of the biggest problems for practical quantum computation. Amplitude damping is one of the most important decoherence processes.…
We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high…
Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications,…
This paper proposes a novel deep learning-based error correction coding scheme for AWGN channels under the constraint of one-bit quantization in the receivers. Specifically, it is first shown that the optimum error correction code that…
Quantum error correction is a crucial technology for fault tolerant quantum computing. On superconducting platforms, hardware defects in large scale quantum processors can disrupt the regular lattice structure of topological codes and…
A protocol of quantum dense coding protection of two qubits is proposed in amplitude damping (AD) channel using weak measurement and reversal measurement. It is found that the capacity of quantum dense coding under the weak measurement and…
We investigate cat codes that can correct multiple excitation losses and identify two types of logical errors: bit-flip errors due to excessive excitation loss and dephasing errors due to quantum back-action from the environment. We show…
We derive exact analytical expressions for the quantum capacity of a broad subclasses of generalized dephasing channels of the form $\Lambda(\rho)=(1-x)\rho + x D(\rho)$, where $D(\rho)$ represents a structured decoherence process. These…
When incorporated in quantum sensing protocols, quantum error correction can be used to correct for high frequency noise, as the correction procedure does not depend on the actual shape of the noise spectrum. As such, it provides a powerful…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…