Related papers: Average-Case Complexity of Quantum Stabilizer Deco…
Quantum error correction (QEC) enables reliable computation on noisy hardware by encoding logical information across many physical qubits and periodically measuring parities to detect errors. A decoder is the classical algorithm that uses…
Several recently proposed code-based cryptosystems base their security on a slightly generalized version of the classical (syndrome) decoding problem. Namely, in the so-called restricted (syndrome) decoding problem, the error values stem…
Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
In adversarial settings, where attackers can deliberately and strategically corrupt quantum data, standard quantum error correction reaches its limits. It can only correct up to half the code distance and must output a unique answer.…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number…
Classical data encoding is usually treated as a black-box in the oracle-based quantum algorithms. On the other hand, their constructions are crucial for practical algorithm implementations. Here, we open the black-boxes of data encoding and…
Efficient and accurate decoding of quantum error-correcting codes is essential for fault-tolerant quantum computation, however, it is challenging due to the degeneracy of errors, the complex code topology, and the large space for logical…
The complexity of maximal likelihood decoding of the Reed-Solomon codes $[q-1, k]_q$ is a well known open problem. The only known result in this direction states that it is at least as hard as the discrete logarithm in some cases where the…
The stabiliser formalism plays a central role in quantum computing, error correction, and fault tolerance. Conversions between and verifications of different specifications of stabiliser states and Clifford gates are important components of…
Classical $(r,\delta)$-locally recoverable codes are designed for avoiding loss of information in large scale distributed and cloud storage systems. We introduce the quantum counterpart of those codes by defining quantum…
Recent years have seen significant activity on the problem of using data for the purpose of learning properties of quantum systems or of processing classical or quantum data via quantum computing. As in classical learning, quantum learning…
A quantum computer needs the assistance of a classical algorithm to detect and identify errors that affect encoded quantum information. At this interface of classical and quantum computing the technique of machine learning has appeared as a…
Stabilizer states are a prime resource for a number of applications in quantum information science, such as secret-sharing and measurement-based quantum computation. This motivates us to study the entanglement of noisy stabilizer states…
Scrambling of quantum information is an important feature at the root of randomization and benchmarking protocols, the onset of quantum chaos, and black-hole physics. Unscrambling this information is possible given perfect knowledge of the…
Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be…
We investigate layer codes, a family of three-dimensional stabilizer codes that can achieve optimal scaling of code parameters and a polynomial energy barrier, as candidates for self-correcting quantum memories. First, we introduce two…
We investigate dense coding by imposing various locality restrictions to our decoder by employing the resource theory of asymmetry framework. In this task, the sender Alice and the receiver Bob share an entangled state. She encodes the…
In Part II we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent.The lower (existence) bound for stabilizer codes is proved by a…