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Journal of Operator Theory, 2021 We reconcile, at the semi-classical level, the original spectral realization of zeros of the Riemann zeta function as an ``absorption'' picture using the ad\`ele class space, with the ``emission'' semi-classical computations of Berry and Keating. We then use the quantized calculus to analyse the recent attempt of X.-J.~Li at proving Weil's positivity ...
Connes, Alain, Consani, Caterina
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Random Compiler for Fast Hamiltonian Simulation. [PDF]
Physical Review Letters, 2018 The dynamics of a quantum system can be simulated using a quantum computer by breaking down the unitary into a quantum circuit of one and two qubit gates.
E. Campbell
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On learning Hamiltonian systems from data. [PDF]
Chaos, 2019 Concise, accurate descriptions of physical systems through their conserved quantities abound in the natural sciences. In data science, however, current research often focuses on regression problems, without routinely incorporating additional assumptions ...
Tom S. Bertalan +3 more
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The Fibonacci Hamiltonian [PDF]
Inventiones mathematicae, 2016 We consider the Fibonacci Hamiltonian, the central model in the study of electronic properties of one-dimensional quasicrystals, and provide a detailed description of its spectrum and spectral characteristics (namely, the optimal H lder exponent of the integrated density of states, the dimension of the density of states measure, the dimension of the ...
Damanik, David +2 more
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Time-dependent Hamiltonian simulation with $L^1$-norm scaling [PDF]
Quantum, 2019 The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously.
D. Berry +4 more
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Shadow hamiltonian simulation. [PDF]
Nat CommunSimulating quantum dynamics is one of the most important applications of quantum computers. Traditional approaches for quantum simulation involve preparing the full evolved state of the system and then measuring some physical quantity. Here, we present a different and novel approach to quantum simulation that uses a compressed quantum state that we ...
Somma RD +4 more
europepmc +5 more sources
Coupling and convergence for Hamiltonian Monte Carlo [PDF]
The Annals of Applied Probability, 2018 Based on a new coupling approach, we prove that the transition step of the Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed Kantorovich (L1 Wasserstein) distance. The lower bound for the contraction rate is explicit.
Nawaf Bou-Rabee +2 more
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Hamiltonian Thermodynamics [PDF]
Nelineinaya Dinamika, 2020 It is believed that thermodynamic laws are associated with random processes occurring in the system and, therefore, deterministic mechanical systems cannot be described within the framework of the thermodynamic approach. In this paper, we show that thermodynamics (or, more precisely, a thermodynamically-like description) can be constructed even for ...
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A Hamiltonian Approach to Fault Isolation in a Planar Vertical Take–Off and Landing Aircraft Model
International Journal of Applied Mathematics and Computer Science, 2015 The problem of fault detection and isolation in a class of nonlinear systems having a Hamiltonian representation is considered. In particular, a model of a planar vertical take-off and landing aircraft with sensor and actuator faults is studied.
Rodriguez-Alfaro Luis H. +3 more
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Model of a three-qubit cluster in a thermal bath
Физико-химические аспекты изучения кластеров, наноструктур и наноматериалов, 2023 This work studies a mathematical model of a quantum cluster consisting of three qubits and being in thermal equilibrium with the environment. The effective Hamiltonian is invariant under permutations of qubits and consists of two parts. The first part is
E. Andre, A.N. Tsirulev
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