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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…
In this paper we study the quantum graphs of mixed-unitary channels generated by tensor products of Pauli operators, which we call Pauli channels. We show that most quantum graphs arising from Pauli channels have non-trivial quantum cliques…
Mapping an error syndrome to the error operator is the core of quantum decoding network and is also the key step of recovery. The definitions of the bit-flip error syndrome matrix and the phase-flip error syndrome matrix were presented, and…
The quantum capacity captures the value of a quantum channel for transmitting quantum information, establishing the fundamental limits on quantum communication. In spite of its central role in quantum information theory, the quantum…
Coherent errors, which arise from collective couplings, are a dominant form of noise in many realistic quantum systems, and are more damaging than oft considered stochastic errors. Here, we propose integrating stabilizer codes with…
We consider a molecular channel, in which messages are encoded to the frequency of objects in a pool, and whose output during reading time is a noisy version of the input frequencies, as obtained by sampling with replacement from the pool.…
Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily…
An important outstanding challenge that must be overcome in order to fully utilize the XY surface code for correcting biased Pauli noise is the phenomena of fragile temporal boundaries that arise during the standard logical state…
Motivated by estimation of quantum noise models, we study the problem of learning a Pauli channel, or more generally the Pauli error rates of an arbitrary channel. By employing a novel reduction to the "Population Recovery" problem, we give…
In fault-tolerant quantum computation, the preparation of logical states is a ubiquitous subroutine, yet significant challenges persist even for the simplest states required. In the present work, we present a unitary, scalable,…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
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 provide a purely quantum version of polar codes, achieving the symmetric coherent information of any qubit-input quantum channel. Our scheme relies on a recursive channel combining and splitting construction, where a two-qubit gate…
Polar codes are a family of capacity-achieving codes that have explicit and low-complexity construction, encoding, and decoding algorithms. Decoding of polar codes is based on the successive-cancellation decoder, which decodes in a bit-…
The GKP encoding is a top contender among bosonic codes for fault-tolerant quantum computation. Analysis of the GKP code is complicated by the fact that finite-energy code states leak out of the ideal GKP code space and are not orthogonal.…
We discuss the estimation of channel parameters for a noisy quantum channel - the so-called Pauli channel - using finite resources. It turns out that prior entanglement considerably enhances the fidelity of the estimation when we compare it…
Statistical verification of a quantum state aims to certify whether a given unknown state is close to the target state with confidence. So far, sample-optimal verification protocols based on local measurements have been found only for…
Quantum error correction represents a significant milestone in large-scale quantum computing, with the surface code being a prominent strategy due to its high error threshold and experimental feasibility. However, it is challenging to…
We show that a simple modification of the surface code can exhibit an enormous gain in the error correction threshold for a noise model in which Pauli Z errors occur more frequently than X or Y errors. Such biased noise, where dephasing…
Classical coding theory contains several techniques to obtain new codes from other codes, including puncturing and shortening. For quantum codes, a form of puncturing is known, but its description is based on the code space rather than its…