Related papers: A Combinatorial Approach to Quantum Error Correcti…
The quantum approximate optimisation ansatz (QAOA) is one of the flagship algorithms used to tackle combinatorial optimisation on graphs problems using a quantum computer, and is considered a strong candidate for early fault-tolerant…
In an undirected graph, a proper (k,i)-coloring is an assignment of a set of k colors to each vertex such that any two adjacent vertices have at most i common colors. The (k,i)-coloring problem is to compute the minimum number of colors…
In the Coloured Clustering problem, we wish to colour vertices of an edge coloured graph to produce as many stable edges as possible, i.e., edges with the same colour as their ends. In this paper, we reveal that the problem is in fact a…
Finding diverse solutions in combinatorial problems recently has received considerable attention (Baste et al. 2020; Fomin et al. 2020; Hanaka et al. 2021). In this paper we study the following type of problems: given an integer $k$, the…
Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore's law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world…
An important topic in quantum information is the theory of error correction codes. Practical situations often involve quantum systems with states in an infinite dimensional Hilbert space, for example coherent states. Motivated by these…
The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…
We systematically study the fundamental competition between quantum error correction (QEC) and continuous symmetries, two key notions in quantum information and physics, in a quantitative manner. Three meaningful measures of approximate…
The surface code is a powerful quantum error correcting code that can be defined on a 2-D square lattice of qubits with only nearest neighbor interactions. Syndrome and data qubits form a checkerboard pattern. Information about errors is…
We present a novel algorithm that solves the turbo code LP decoding problem in a fininte number of steps by Euclidean distance minimizations, which in turn rely on repeated shortest path computations in the trellis graph representing the…
We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…
This paper proposes a framework that formulates a wide range of graph combinatorial optimization problems using permutation-based representations. These problems include the travelling salesman problem, maximum independent set, maximum cut,…
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…
A cube-like graph is a Cayley graph for the elementary abelian group of order $2^n$. In studies of the chromatic number of cube-like graphs, the $k$th power of the $n$-dimensional hypercube, $Q_n^k$, is frequently considered. This coloring…
Gaussian Boson Sampling (GBS) is a quantum computational model that leverages linear optics to solve sampling problems believed to be classically intractable. Recent experimental breakthroughs have demonstrated quantum advantage using GBS,…
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…
We explore the design of quantum error-correcting codes for cases where the decoherence events of qubits are correlated. In particular, we consider the case where only spatially contiguous qubits decohere, which is analogous to the case of…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
We study quantum analogs of graph colorings and chromatic number. Initially defined via an interactive protocol, quantum colorings can also be viewed as a natural operator relaxation of graph coloring. Since there is no known algorithm for…