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We introduce a classical algorithm to approximate the free energy of local, translation-invariant, one-dimensional quantum systems in the thermodynamic limit of infinite chain size. While the ground state problem (i.e., the free energy at…
Quantum complexity measures the difficulty of realizing a quantum process, such as preparing a state or implementing a unitary. We present an approach to quantifying the thermodynamic resources required to implement a process if the…
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…
Framing computation as the transformation of metastable memories, we explore its fundamental thermodynamic limits. The true power of information follows from a novel decomposition of nonequilibrium free energy derived here, which provides a…
In this paper, we explore statistical versus computational trade-off to address a basic question in the application of a distributed algorithm: what is the minimal computational cost in obtaining statistical optimality? In smoothing spline…
Perfectly rational decision-makers maximize expected utility, but crucially ignore the resource costs incurred when determining optimal actions. Here we propose an information-theoretic formalization of bounded rational decision-making…
We present an algorithm that prepares thermal Gibbs states of one dimensional quantum systems on a quantum computer without any memory overhead, and in a time significantly shorter than other known alternatives. Specifically, the time…
We show that every quantum computation can be described by Bayesian update of a probability distribution on a finite state space. When applied to the model of quantum computation with magic states, the size of this state space only depends…
Simulating mantle convection often requires reaching a computationally expensive steady-state, crucial for deriving scaling laws for thermal and dynamical flow properties and benchmarking numerical solutions. The strong temperature…
This paper extends the core results of discrete time infinite horizon dynamic programming to the case of state-dependent discounting. We obtain a condition on the discount factor process under which all of the standard optimality results…
We present a perturbative approach to the problem of computation of mixed-state fidelity susceptibility (MFS) for thermal states. The mathematical techniques used provides an analytical expression for the MFS as a formal expansion in terms…
Classical thermodynamics treats temperature as a state variable characterizing systems in equilibrium with idealized infinite reservoirs. We argue that this framing, while computationally exact, obscures an essential physical reality: any…
The processing of quantum information always has a cost in terms of physical resources such as energy or time. Determining the resource requirements is not only an indispensable step in the design of practical devices - the resources need…
Recently the regular conditional distributions of max-infinitely divisible processes were derived by \citet{Dombry2011} and although these conditional distributions have complicated closed forms, \citet{Dombry2011b} introduce an algorithm…
Physical systems driven away from equilibrium by an external controller dissipate heat to the environment; the excess entropy production in the thermal reservoir can be interpreted as a "cost" to transform the system in a finite time. The…
In this paper we develop a new technique, called \textit{state redistribution}, that allows the use of explicit time stepping when approximating solutions to hyperbolic conservation laws on embedded boundary grids. State redistribution is a…
The construction of models from data is a significant contributor to the energetic costs of computation. Because of this, understanding how foundational thermodynamic bounds apply to modeling algorithms will be increasingly important. Here,…
Inference in dynamic probabilistic models is a complex task involving expensive operations. In particular, for Hidden Markov Models, the whole state space has to be enumerated for advancing in time. Even states with negligible probabilities…
Scientific explanation often requires inferring maximally predictive features from a given data set. Unfortunately, the collection of minimal maximally predictive features for most stochastic processes is uncountably infinite. In such…
We provide necessary and sufficient conditions for separability of mixed states of n-particle systems. The conditions are formulated in terms of maps which are positive on product states of $n-1$ particles. The method of providing of the…