Related papers: Quantum Process Realization of LDPC Code Dualities…
We explain the use of quantum process calculus to describe and analyse linear optical quantum computing (LOQC). The main idea is to define two processes, one modelling a linear optical system and the other expressing a specification, and…
Equivalence checking of quantum circuits is a central verification task in quantum computing, ensuring the correctness of circuit optimizations, hardware mappings, and compilation pipelines. Among the primary symbolic methods for this…
It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…
Quantum computers have the potential to solve certain problems faster than classical computers by exploiting quantum mechanical effects such as superposition. However, building high-quality quantum software is challenging due to the…
In the present paper, the first in a series of two, we propose a model of universal quantum computation using a fermionic/bosonic multi-particle continuous-time quantum walk with two internal states (e.g., the spin-up and down states of an…
A systematic approach to dualities in symmetric (1+1)d quantum lattice models has recently been proposed in terms of module categories over the symmetry fusion categories. By characterizing the non-trivial way in which dualities intertwine…
The Kramers-Wannier self-duality of critical quantum chains is examined from the perspective of model wave functions. We demonstrate, using the transverse-field Ising chain and the $3$-state Potts chain as examples, that the symmetry…
In this paper, a new method is given for counting cycles in the Tanner graph of a (Type-I) quasi-cyclic (QC) low-density parity-check (LDPC) code which the complexity mainly is dependent on the base matrix, independent from the CPM-size of…
This invited paper presents an overview of an ongoing research program aimed at extending the Curry-Howard-Lambek correspondence to quantum computation. We explore two key frameworks that provide both logical and computational foundations…
Complex quantum circuits are constituted by combinations of quantum subroutines. The computation is possible as long as the quantum data encoding is consistent throughout the circuit. Despite its fundamental importance, the formalization of…
In the iconic measurements of atomic spin-1/2 or photon polarization, one employs two spatially separated and noninteracting detectors. Each detector is binary, registering the presence or absence of the atom or the photon. For measurements…
We propose a method for constructing quantum error-correcting codes based on non-binary low-density parity-check codes with Tanner graph girth 16. While conventional constructions using circulant permutation matrices are limited to girth…
The transition from quantum to classical behavior is a central question in modern physics. How can we rationalize everyday classical observations from an inherently quantum world? For instance, what makes two people, each absorbing an…
Quantum low-density parity-check codes reduce quantum error correction overhead but require dense, long-range connectivity that challenges hardware implementation, particularly for superconducting processors. We address this problem by…
The techniques of distance verification known for general linear codes are re-applied to quantum stabilizer codes. Then distance verification is addressed for classical and quantum LDPC codes. New complexity bounds for distance verification…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…
Quantum computing opens exciting opportunities for kernel-based machine learning methods, which have broad applications in data analysis. Recent works show that quantum computers can efficiently construct a model of a classifier by…
Quantum low-density parity check (qLDPC) codes offer higher encoding rate than topological codes, e.g. surface codes, making them favourable for practical, fault-tolerant quantum computing with low overhead. These codes are particularly…
Quantum and Classical computers continue to work together in tight cooperation to solve difficult problems. The combination is thus suggested in recent times for decoding the Low Density Parity Check (LDPC) codes, for the next generation…
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…