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We introduce an asymmetric distance in the space of learning tasks, and a framework to compute their complexity. These concepts are foundational for the practice of transfer learning, whereby a parametric model is pre-trained for a task,…
In this paper we give an Immerman's Theorem for real-valued computation. We define circuits operating over real numbers and show that families of such circuits of polynomial size and constant depth decide exactly those sets of vectors of…
Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…
Circuit compilation, a crucial process for adapting quantum algorithms to hardware constraints, often operates as a ``black box,'' with limited visibility into the optimization techniques used by proprietary systems or advanced open-source…
We study properties of relational structures such as graphs that are decided by families of Boolean circuits. Circuits that decide such properties are necessarily invariant to permutations of the elements of the input structures. We focus…
We introduce "binding complexity", a new notion of circuit complexity which quantifies the difficulty of distributing entanglement among multiple parties, each consisting of many local degrees of freedom. We define binding complexity of a…
An investigation of Einstein's ``physical'' reality and the concept of quantum reality in terms of information theory suggests a solution to quantum paradoxes such as the Einstein-Podolsky-Rosen (EPR) and the Schroedinger-cat paradoxes.…
Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the…
Random instances of feedforward Boolean circuits are studied both analytically and numerically. Evaluating these circuits is known to be a P-complete problem and thus, in the worst case, believed to be impossible to perform, even given a…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…
Quantum resource analysis is crucial for designing quantum circuits as well as assessing the viability of arbitrary (error-corrected) quantum computations. To this end, we introduce QUANTIFY, which is an open-source framework for the…
In quantum computing the decoherence time of the qubits determines the computation time available and this time is very limited when using current hardware. In this paper we minimize the execution time (the depth) for a class of circuits…
This paper addresses a new approach to find a spectrum of information measures for the process of digital circuit synthesis. We consider the problem from the information engine point of view. The circuit synthesis as a whole and different…
Some quantum algorithms have "quantum speedups": improved time complexity as compared with the best-known classical algorithms for solving the same tasks. Can we understand what fuels these speedups from an entropic perspective? Information…
Reversible computation is gaining increasing relevance in the context of several post-CMOS technologies, the most prominent of those being Quantum computing. One of the key theoretical problem pertaining to reversible logic synthesis is the…
Folklore in complexity theory suspects that circuit lower bounds against $\mathbf{NC}^1$ or $\mathbf{P}/\operatorname{poly}$, currently out of reach, are a necessary step towards proving strong proof complexity lower bounds for systems like…
Research into active networking has provided the incentive to re-visit what has traditionally been classified as distinct properties and characteristics of information transfer such as protocol versus service; at a more fundamental level…
We establish a direct connection between spread complexity and quantum circuit complexity by demonstrating that spread complexity emerges as a limiting case of a circuit complexity framework built from two fundamental operations:…
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…
We examine the circuit complexity of coherent states in a free scalar field theory, applying Nielsen's geometric approach as in [1]. The complexity of the coherent states have the same UV divergences as the vacuum state complexity and so we…