Related papers: Quantum weight enumerators and tensor networks

We provide the first tensor network method for computing quantum weight enumerator polynomials in the most general form. If a quantum code has a known tensor network construction of its encoding map, our method is far more efficient, and in…

In a recent paper ([quant-ph/9610040]), Shor and Laflamme define two ``weight enumerators'' for quantum error correcting codes, connected by a MacWilliams transform, and use them to give a linear-programming bound for quantum codes. We…

Throughout its history, the theory of quantum error correction has heavily benefited from translating classical concepts into the quantum setting. In particular, classical notions of weight enumerators, which relate to the performance of an…

A promising new algebraic approach to weighted model counting makes use of tensor networks, following a reduction from weighted model counting to tensor-network contraction. Prior work has focused on analyzing the single-core performance of…

In this paper, we consider codes over finite fields, finite abelian groups, and finite Frobenius rings. For such codes, the complete weight enumerator and the Hamming weight enumerator serve as powerful tools. These two types of weight…

We construct a class of linear codes by choosing a proper defining set and determine their complete weight enumerators and weight enumerators. The results show that they are at most three-weight codes and they are suitable for applications…

We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…

Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine…

We propose a method to enhance the performance of Large Language Models (LLMs) by integrating quantum computing and quantum-inspired techniques. Specifically, our approach involves replacing the weight matrices in the Self-Attention and…

Once developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum machine learning to assess problems…

Quantum kernel methods are promising candidates for achieving a practical quantum advantage for certain machine learning tasks. Similar to classical machine learning, an exact form of a quantum kernel is expected to have a great impact on…

Most research in quantum computing today is performed against simulations of quantum computers rather than true quantum computers. Simulating a quantum computer entails implementing all of the unitary operators corresponding to the quantum…

We extend the recently introduced notion of tensor enumerator to the circuit enumerator. We provide a mathematical framework that offers a novel method for analyzing circuits and error models without resorting to Monte Carlo techniques. We…

Semiring parsing is an elegant framework for describing parsers by using semiring weighted logic programs. In this paper we present a generalization of this concept: latent-variable semiring parsing. With our framework, any semiring…

In a recent paper [quant-ph/9610040], Shor and Laflamme define two ``weight enumerators'' for quantum error correcting codes, connected by a MacWilliams transform, and use them to give a linear-programming bound for quantum codes. We extend…

In this paper we present a new method for finding the weight enumerator of binary linear block codes by using genetic algorithms. This method consists in finding the binary weight enumerator of the code and its dual and to create from the…

Gleason's 1970 theorem on weight enumerators of self-dual codes has played a crucial role for research in coding theory during the last four decades. Plenty of generalizations have been proved but, to our knowledge, they are all based on…

Running quantum algorithms often involves implementing complex quantum circuits with such a large number of multi-qubit gates that the challenge of tackling practical applications appears daunting. To date, no experiments have successfully…

Quantum weight enumerators are fundamental tools for analyzing quantum error-correcting codes and multipartite entanglement, offering insights into the existence of quantum error-correcting codes and $k$-uniform states. In this work, we…

In this note we show that the weight enumerators of a real quantum error correcting code with $ X $ and $ Z $ exactly transversal must satisfy certain identities. One consequence of these identities is that if the code is error detecting…