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Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes…
We give a quantum reduction from finding short codewords in a random linear code to decoding for the Hamming metric. This is the first time such a reduction (classical or quantum) has been obtained. Our reduction adapts to linear codes…
Quantum error correction codes are usually designed to correct errors regardless of their physical origins. In large-scale devices, this is an essential feature. In smaller-scale devices, however, the main error sources are often…
Benchmarking the performance of quantum error correction codes in physical systems is crucial for achieving fault-tolerant quantum computing. Current methodologies, such as (shadow) tomography or direct fidelity estimation, fall short in…
Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…
We describe a general method for turning quantum circuits into sparse quantum subsystem codes. The idea is to turn each circuit element into a set of low-weight gauge generators that enforce the input-output relations of that circuit…
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…
Realizing the full potential of quantum computation requires Quantum Error Correction (QEC). QEC reduces error rates by encoding logical information across redundant physical qubits, enabling errors to be detected and corrected. A common…
Model quantization enables the deployment of deep neural networks under resource-constrained devices. Vector quantization aims at reducing the model size by indexing model weights with full-precision embeddings, i.e., codewords, while the…
We introduce the concept of quantum weight as a ground state property of quantum many-body systems that is encoded in the static structure factor and characterizes density fluctuation at long wavelengths. The quantum weight carries a wealth…
Quantum counting is the task of determining the dimension of the subspace of states that are accepted by a quantum verifier circuit. It is the quantum analog of counting the number of valid solutions to NP problems -- a problem well-studied…
Topological quantum error correction codes have high thresholds and are well suited to physical implementation. The minimum weight perfect matching algorithm can be used to efficiently handle errors in such codes. We perform a timing…
Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and good code distance scaling, providing a promising route to low-overhead fault-tolerant quantum computing. However, the long-range connectivity required to…
In this work, we investigate the possibility of compressing a quantum system to one of smaller dimension in a way that preserves the measurement statistics of a given set of observables. In this process, we allow for an arbitrary amount of…
Quantum error correction plays a prominent role in the realization of quantum computation, and quantum low-density parity-check (qLDPC) codes are believed to be practically useful stabilizer codes. While qLDPC codes are defined to have…
We introduce a new weight and corresponding metric over finite extension fields for asymmetric error correction. The weight distinguishes between elements from the base field and the ones outside of it, which is motivated by asymmetric…
The surface code is a powerful quantum error correcting code that can be defined on a 2-D square lattice of qubits with only nearest neighbor interactions. Syndrome and data qubits form a checkerboard pattern. Information about errors is…
It is a major challenge to construct good quantum codes supporting fault-tolerant (e.g. transversal) non-Clifford gates with low-weight parity-check measurements. In this paper, we construct the first known quantum codes with linear…
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…
Although quantum machine learning has shown great promise, the practical application of quantum computers remains constrained in the noisy intermediate-scale quantum era. To take advantage of quantum machine learning, we investigate the…