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We study how well topological quantum codes can tolerate coherent noise caused by systematic unitary errors such as unwanted $Z$-rotations. Our main result is an efficient algorithm for simulating quantum error correction protocols based on…
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…
To unleash the potential of quantum computers, noise effects on qubits' performance must be carefully managed. The decoders responsible for diagnosing noise-induced computational errors must use resources efficiently to enable scaling to…
Qudit toric codes are a natural higher-dimensional generalization of the well-studied qubit toric code. However standard methods for error correction of the qubit toric code are not applicable to them. Novel decoders are needed. In this…
We introduce the domain wall color code, a new variant of the quantum error-correcting color code that exhibits exceptionally high code-capacity error thresholds for qubits subject to biased noise. In the infinite bias regime, a…
Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to…
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 computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
Designing quantum error correcting codes that promise a high error threshold, low resource overhead and efficient decoding algorithms is crucial to achieve large-scale fault-tolerant quantum computation. The concatenated quantum Hamming…
This paper investigates data compression that simultaneously allows local decoding and local update. The main result is a universal compression scheme for memoryless sources with the following features. The rate can be made arbitrarily…
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…
Quantum computing offers significant speedups, but the large number of physical qubits required for quantum error correction introduces engineering challenges for a monolithic architecture. One solution is to distribute the logical quantum…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
Numerous quantum many-body systems are characterized by either fundamental or emergent constraints---such as gauge symmetries or parity superselection for fermions---which effectively limit the accessible observables and realizable…
Quantum error correction (QEC) aims to protect logical qubits from noises by utilizing the redundancy of a large Hilbert space, where an error, once it occurs, can be detected and corrected in real time. In most QEC codes, a logical qubit…
We construct a family of quantum low-density parity-check codes locally equivalent to higher-dimensional quantum hypergraph-product (QHP) codes. Similarly to QHP codes, the proposed codes have highly redundant sets of low-weight stabilizer…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…
Quantum error correction plays a critical role in enabling fault-tolerant quantum computing by protecting fragile quantum information from noise. While general-purpose quantum error correction codes are designed to address a wide range of…
Traditional quantum error-correcting codes are designed for the depolarizing channel modeled by generalized Pauli errors occurring with equal probability. Amplitude damping channels model, in general, the decay process of a multilevel atom…
The surface code is a promising candidate for fault-tolerant quantum computation and has been implemented in many quantum hardware platforms. In this work, we propose a new non-local unitary circuit to encode a surface code state based on a…