Related papers: Tensor Networks and Quantum Error Correction
The quantum computing devices of today have tens to hundreds of qubits that are highly susceptible to noise due to unwanted interactions with their environment. The theory of quantum error correction provides a scheme by which the effects…
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…
Parallel tensor network contraction algorithms have emerged as the pivotal benchmarks for assessing the classical limits of computation, exemplified by Google's demonstration of quantum supremacy through random circuit sampling. However,…
Topological quantum field theories (TQFT) encode quantum correlations in topological features of spaces. In this work, we leverage this feature to explore how information encoded in TQFTs can be stored and retrieved in the presence of local…
Active quantum error correction is a central ingredient to achieve robust quantum processors. In this paper we investigate the potential of quantum machine learning for quantum error correction in a quantum memory. Specifically, we…
Tensor network methods are taking a central role in modern quantum physics and beyond. They can provide an efficient approximation to certain classes of quantum states, and the associated graphical language makes it easy to describe and…
Quantum error correction (QEC) is essential for achieving low error rates required for fault-tolerant quantum computation. In stabilizer-based codes such as the surface code, errors are inferred from repeated syndrome measurements and…
Quantum error correction was invented to allow for fault-tolerant quantum computation. Systems with topological order turned out to give a natural physical realization of quantum error correcting codes (QECC) in their groundspaces. More…
Large-scale, fault-tolerant quantum computations will be enabled by quantum error-correcting codes (QECC). This work presents the first systematic technique to test the accuracy and effectiveness of different QECC decoding schemes by…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard…
Exact many-body quantum problems are known to be computationally hard due to the exponential scaling of the numerical resources required. Since the advent of the Density Matrix Renormalization Group, it became clear that a successful…
Quantum error-correcting codes (QECC's) are needed to combat the inherent noise affecting quantum processes. Using ZX calculus, we represent QECC's in a form called a ZX diagram, consisting of a tensor network. In this paper, we present…
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…
Quantum replacer codes are codes that can be protected from errors induced by a given set of quantum replacer channels, an important class of quantum channels that includes the erasures of subsets of qubits that arise in quantum error…
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…
We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. The…
Noise is one of the central obstacles to building useful quantum computers, and quantum error correction (QEC) provides the framework for protecting quantum information against it. Unlike classical error correction, QEC must preserve…
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…
Quantum Tanner codes constitute a family of quantum low-density parity-check (LDPC) codes with good parameters, i.e., constant encoding rate and relative distance. In this article, we prove that quantum Tanner codes also facilitate…