Related papers: A combinatorial approach for the state complexity …

The complexity of quantum states under dynamical evolution can be investigated by studying the spread with time of the state over a pre-defined basis. It is known that this complexity is minimised by choosing the Krylov basis, thus defining…

Quantifying mixed-state entanglement in many-body systems has been a formidable task. In this work, we quantify the entanglement of states in unresolvable spin ensembles, which are inherently mixed. By exploiting their permutationally…

The paper focuses on a new class of combinatorial problems which consists in restructuring of solutions (as sets/structures) in combinatorial optimization. Two main features of the restructuring process are examined: (i) a cost of the…

We address the question of which quantum states can be inter-converted under the action of a time-dependent Hamiltonian. In particular, we consider the problem applied to mixed states, and investigate the difference between pure and…

We consider the problem of remote state preparation recently studied in several papers. We study the communication complexity of this problem, in the presence of entanglement and in the scenario of single use of the channel.

In recent years, the entanglement spectra of quantum states have been identified to be highly valuable for improving our understanding on many problems in quantum physics, such as classification of topological phases, symmetry-breaking…

Emerging computational paradigms, such as probabilistic and hybrid programming, introduce new primitive operations that often need to be combined with classic programming constructs. However, it still remains a challenge to provide a…

Topologically-ordered quantum states with Abelian excitations can host defects that obey effective non-Abelian statistics, in principle allowing for quantum information processing via defect braiding. These extrinsic defects (or twists) are…

Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely specified constraints of different importance, the available…

In this paper, we show that, due to the structural properties of the resulting automaton obtained from a prior operation, the state complexity of a combined operation may not be equal but close to the mathematical composition of the state…

Imagine an assembly line where a box with a lid and liquid in it enters in some unknown orientation. The box should leave the line with the open lid facing upwards with the liquid still in it. To save costs there are no complex sensors or…

In this paper, we investigate the rational synthesis problem for concurrent game structure for a variety of objectives ranging from reachability to Muller condition. We propose a new algorithm that establishes the decidability of the non…

We study the structure of dynamically generated bound states in the chiral unitary approach. The compositeness of a bound state is defined through the wavefunction renormalization constant in the nonrelativistic field theory. We apply this…

We investigate the reachability problem in symmetric vector addition systems with states (VASS), where transitions are invariant under a group of permutations of coordinates. One extremal case, the trivial groups, yields general VASS. In…

We consider the computational complexity of Hamiltonians which are sums of commuting terms acting on plaquettes in a square lattice of qubits, and we show that deciding whether the ground state minimizes the energy of each local term…

We study the computational complexity of quantum state isomorphism problems under group actions: given two quantum circuits that prepare pure or mixed states, decide whether the two states are related by a group action. This can be seen as…

We study the application of various forms of the coupled cluster method to systems with paired fermions. The novel element of the analysis is the study of the breaking and eventual restoration of particle number in the CCM variants. We…

Number partitioning is one of the classical NP-hard problems of combinatorial optimization. It has applications in areas like public key encryption and task scheduling. The random version of number partitioning has an "easy-hard" phase…

The topology of entanglement in multipartite states with translational invariance is discussed in this article. Two global features are foundby which one can distinguish distinct states. These are the cyclic unit and the quantised geometric…

We introduce algebraic sets in the products of complex projective spaces for the mixed states in multipartite quantum systems as their invariants under local unitary operations. The algebraic sets have to be the union of the linear…