Related papers: Bounds on quantum evolution complexity via lattice…
The minimum distance is one of the most important combinatorial characterizations of a code. The maximum likelihood decoding problem is one of the most important algorithmic problems of a code. While these problems are known to be hard for…
Classical probabilistic models of (noisy) quantum systems are not only relevant for understanding the non-classical features of quantum mechanics, but they are also useful for determining the possible advantage of using quantum resources…
In a topological dynamical system the complexity of an orbit is a measure of the amount of information (algorithmic information content) that is necessary to describe the orbit. This indicator is invariant up to topological conjugation. We…
Low check weight is practically crucial code property for fault-tolerant quantum computing, which underlies the strong interest in quantum low-density parity-check (qLDPC) codes. Here, we explore the theory of weight-constrained stabilizer…
The existence of complex (multiple-step) genetic adaptations that are "irreducible" (i.e., all partial combinations are less fit than the original genotype) is one of the longest standing problems in evolutionary biology. In standard…
Quantum circuit complexity-a measure of the minimum number of gates needed to implement a given unitary transformation-is a fundamental concept in quantum computation, with widespread applications ranging from determining the running time…
Communication complexity is a fundamental aspect of information science, concerned with the amount of communication required to solve a problem distributed among multiple parties. The standard quantification of one-way communication…
Krylov complexity is an attractive measure for the rate at which quantum operators spread in the space of all possible operators under dynamical evolution. One expects that its late-time plateau would distinguish between integrable 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…
Inspired by the close relationship between Kolmogorov complexity and unsupervised machine learning, we explore quantum circuit complexity, an important concept in quantum computation and quantum information science, as a pivot to understand…
We study the computability and complexity of the exploration problem in a class of highly dynamic graphs: periodically varying (PV) graphs, where the edges exist only at some (unknown) times defined by the periodic movements of carriers.…
We develop the first steps towards an analysis of geometry on the quantum spacetime proposed in [1]. The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum…
Is undecidability a requirement for open-ended evolution (OEE)? Using methods derived from algorithmic complexity theory, we propose robust computational definitions of open-ended evolution and the adaptability of computable dynamical…
We provide a framework to determine the upper bound to the complexity of a computing a given observable with respect to a Hamiltonian. By considering the Heisenberg evolution of the observable, we show that each Hamiltonian defines an…
Many computational problems are subject to a quantum speed-up: one might find that a problem having an O(n^3)-time or O(n^2)-time classic algorithm can be solved by a known O(n^1.5)-time or O(n)-time quantum algorithm. The question…
Noise is ubiquitous in quantum systems and is a major obstacle for the advancement of quantum information science. Noise-robust quantum control achieves high-fidelity operations by engineering the evolution path so that first-order noise…
Evolutionary complexity is here measured by the number of trials/evaluations needed for evolving a logical gate in a non-linear medium. Behavioural complexity of the gates evolved is characterised in terms of cellular automata behaviour. We…
We develop an intuitive geometric picture of quantum states, define a particular state distance, and derive a quantum speed limit (QSL) for open systems. Our QSL is attainable because any initial state can be driven to a final state by the…
We present a method for obtaining a hierarchy of rigorous bounds on the time-evolution of a quantum mechanical system from an arbitrary initial state, systematically generalizing Mandelstam-Tamm-like relations. For any fixed level in the…
The unitary dynamics of quantum systems can be modeled as a trajectory on a Riemannian manifold. This theoretical framework naturally yields a purely geometric interpretation of computational complexity for quantum algorithms, a notion…