Related papers: Logical network implementation for cluster states …

We present the Lukasiewicz logic as a viable system for an implication algebra on a system of qubits. Our results show that the three valued Lukasiewicz logic can be embedded in the stabilized space of an arbitrary quantum error correcting…

A universal set of gates for (classical or quantum) computation is a set of gates that can be used to approximate any other operation. It is well known that a universal set for classical computation augmented with the Hadamard gate results…

Complex networks structures have been extensively used for describing complex natural and technological systems, like the Internet or social networks. More recently complex network theory has been applied to quantum systems, where complex…

Constructing quantum codes with good parameters and useful transversal gates is a central problem in quantum error correction. In this paper, we continue our work in arXiv:2502.01864 and construct the first family of asymptotically good…

Logical gates constitute the building blocks of fault-tolerant quantum computation. While quantum error-corrected memories have been extensively studied in the literature, explicit constructions and detailed analyses of thresholds and…

A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices. The boundary of the lattice consists of…

Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation…

We consider the task of secure multi-party distributed quantum computation on a quantum network. We propose a protocol based on quantum error correction which reduces the number of necessary qubits. That is, each of the $n$ nodes in our…

Topological error correction--a novel method to actively correct errors based on cluster states with topological properties--has the highest order of tolerable error rates known to date (10^{-2}). Moreover, the scheme requires only…

Suppressing errors is the central challenge for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected ``logical'' qubits, where information is…

In this paper, we propose and study a master-equation based approach to drive a quantum network with $n$ qubits to a consensus (symmetric) state introduced by Mazzarella et al. The state evolution of the quantum network is described by a…

Quantum networks are important for quantum communication, enabling tasks such as quantum teleportation, quantum key distribution, quantum sensing, and quantum error correction, often utilizing graph states, a specific class of multipartite…

A successful quantum error correction protocol would allow quantum computers to run algorithms without suffering from the effects of noise. However, fully fault-tolerant quantum error correction is too resource intensive for existing…

Based on a quantum analysis of two capacitively coupled current-biased Josephson junctions, we propose two fundamental two-qubit quantum logic gates. Each of these gates, when supplemented by single-qubit operations, is sufficient for…

We present a fault-tolerant universal quantum computing architecture based on a code concatenation of biased-noise qubits and the parity architecture. The parity architecture can be understood as an LDPC code tailored specifically to obtain…

Fault-tolerant quantum computing hinges on efficient logical compilation, in particular, translating high-level circuits into code-compatible implementations. Gate-by-gate compilation often yields deep circuits, requiring significant…

Using an algebraic framework we solve a problem posed in [5] and [7] about the axiomatizability of a quantum computational type logic related to fuzzy logic. A Hilbert-style calculus is developed obtaining an algebraic strong completeness…

In quantum computing, the connectivity of qubits placed on two-dimensional chips limits the scalability and functionality of solid-state quantum computers. This paper presents two approaches to constructing complex quantum networks from…

We develop a point of view on reduction of multiplicative proof nets based on quantum error-correcting codes. To each proof net we associate a code, in such a way that cut-elimination corresponds to error correction.

Any 8-qubit graph state belongs to one of the 101 equivalence classes under local unitary operations within the Clifford group. For each of these classes we obtain a representative which requires the minimum number of controlled-Z gates for…