Related papers: Minimal thermodynamic cost of computing with circu…
Mismatch cost (MMC) is a universally applicable lower bound on the entropy production (EP) of any fixed physical process across a given time interval. In the first part of the paper, we establish results concerning MMC to prove that it…
Digital computers implement computations using circuits, as do many naturally occurring systems (e.g., gene regulatory networks). The topology of any such circuit restricts which variables may be physically coupled during the operation of a…
Thermodynamic cost of communication is a major factor in the thermodynamic cost of real-world computers, both biological and digital. Despite its importance, the fundamental principles underlying this cost remain poorly understood. This…
Measures of circuit complexity are usually analyzed to ensure the computation of Boolean functions with economy and efficiency. One of these measures is energy complexity, which is related to the number of gates that output true in a…
We analyze a token-based Brownian circuit in which Brownian particles, coined `tokens,' move randomly by exploiting thermal fluctuations, searching for a path in multi-token state space corresponding to the solution of a given problem. The…
In this work we investigate into energy complexity, a Boolean function measure related to circuit complexity. Given a circuit $\mathcal{C}$ over the standard basis $\{\vee_2,\wedge_2,\neg\}$, the energy complexity of $\mathcal{C}$, denoted…
$\newcommand{\EC}{\mathsf{EC}}\newcommand{\KW}{\mathsf{KW}}\newcommand{\DT}{\mathsf{DT}}\newcommand{\psens}{\mathsf{psens}} \newcommand{\calB}{{\cal B}} $ For a Boolean function $f:\{0,1\}^n \to \{0,1\}$ computed by a circuit $C$ over a…
The construction of quantum computers is based on the synthesis of low-cost quantum circuits. The quantum circuit of any Boolean function expressed in a Positive Polarity Reed-Muller $PPRM$ expansion can be synthesized using…
In this work, we initiate the study of the Minimum Circuit Size Problem (MCSP) in the quantum setting. MCSP is a problem to compute the circuit complexity of Boolean functions. It is a fascinating problem in complexity theory -- its…
Using a thermodynamically consistent, mesoscopic model for modern complementary metal-oxide-semiconductor transistors, we study an array of logical circuits and explore how their function is constrained by recent thermodynamic uncertainty…
In this paper, we investigate computational power of threshold circuits and other theoretical models of neural networks in terms of the following four complexity measures: size (the number of gates), depth, weight and energy. Here the…
A notorious open question in circuit complexity is whether Boolean operations of arbitrary arity can efficiently be expressed using modular counting gates only. H{\aa}stad's celebrated switching lemma yields exponential lower bounds for the…
Clocks are inherently out-of-equilibrium because, due to friction, they constantly consume free energy to keep track of time. The Thermodynamic Uncertainty Relation (TUR) quantifies the trade-off between the precision of any…
Quantum circuit complexity quantifies the minimal number of gates needed to realize a unitary transformation and plays a central role in quantum computation. In this work, we investigate the complexity of quantum circuits through coherence…
Irreversible information processing cannot be carried out without some inevitable thermodynamical work cost. This fundamental restriction, known as Landauer's principle, is increasingly relevant today, as the energy dissipation of computing…
We investigate the fundamental limitations imposed by thermodynamics for creating correlations. Considering a collection of initially uncorrelated thermal quantum systems, we ask how much classical and quantum correlations can be obtained…
In classical thermodynamics the work cost of control can typically be neglected. On the contrary, in quantum thermodynamics the cost of control constitutes a fundamental contribution to the total work cost. Here, focusing on quantum…
Turing Machines (TMs) are the canonical model of computation in computer science and physics. We combine techniques from algorithmic information theory and stochastic thermodynamics to analyze the thermodynamic costs of TMs. We consider two…
The presence of correlations in physical systems can be a valuable resource for many quantum information tasks. They are also relevant in thermodynamic transformations, and their creation is usually associated to some energetic cost. In…
The Landauer principle bridges the energetic cost and information processing, showing that irreversible computation inevitably demands energy dissipation. As energy demands from computation continue to rise, approximate computing has…