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Noise is the greatest obstacle in quantum metrology that limits it achievable precision and sensitivity. There are many techniques to mitigate the effect of noise, but this can never be done completely. One commonly proposed technique is to…
The quantum capacity of a memoryless channel is often used as a single figure of merit to characterize its ability to transmit quantum information coherently. The capacity determines the maximal rate at which we can code reliably over…
We develop a theory for finding quantum error correction (QEC) procedures which are optimized for given noise channels. Our theory accounts for uncertainties in the noise channel, against which our QEC procedures are robust. We demonstrate…
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…
Coherent errors in quantum operations are ubiquitous. Whether arising from spurious environmental couplings or errors in control fields, such errors can accumulate rapidly and degrade the performance of a quantum circuit significantly more…
We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear…
A central challenge for the scaling of quantum computing systems is the need to control all qubits in the system without a large overhead. A solution for this problem in classical computing comes in the form of so called crossbar…
Quantum error correction is an indispensable ingredient for scalable quantum computing. In this Perspective we discuss a particular class of quantum codes called low-density parity-check (LDPC) quantum codes. The codes we discuss are…
Quantum machine learning has the potential to provide powerful algorithms for artificial intelligence. The pursuit of quantum advantage in quantum machine learning is an active area of research. For current noisy, intermediate-scale quantum…
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…
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…
Operator quantum error-correction is a technique for robustly storing quantum information in the presence of noise. It generalizes the standard theory of quantum error-correction, and provides a unified framework for topics such as quantum…
The discovery of the family of balanced product codes was pivotal in the subsequent development of 'good' low density quantum error correcting codes that have optimal scaling of the key parameters of distance and storage density. We review…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
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…
We consider the decoding of rank metric codes assuming the error matrix is symmetric. We prove two results. First, for rates $<1/2$ there exists a broad family of rank metric codes for which any symmetric error pattern, even of maximal rank…
Reed-Muller (RM) codes have undergone significant analytical advancements over the past decade, particularly for binary memoryless symmetric (BMS) channels. We extend the scope of RM codes development and analysis to multiple-access…
We apply a dynamical systems approach to concatenation of quantum error correcting codes, extending and generalizing the results of Rahn et al. [1] to both diagonal and nondiagonal channels. Our point of view is global: instead of focusing…
Analog error correction codes have been proposed for analog in-memory computing on resistive crossbars, which can accelerate vector-matrix multiplication for machine learning. Unlike traditional communication or storage channels, this…
We analyze the long time behavior of a quantum computer running a quantum error correction (QEC) code in the presence of a correlated environment. Starting from a Hamiltonian formulation of realistic noise models, and assuming that QEC is…