Related papers: Circuit Synthesis based on Prescribed Lagrangian
We conjecture that the proper-time series expansion of the one-loop effective Lagrangian of quantum electrodynamics can be summed in all terms containing the field-strength invariants $\mathcal{F} = \frac{1}{4} F_{\mu\nu}F^{\mu\nu} (x)$,…
The paper presents a novel approach to synthesize robust controllers for nonlinear systems along perturbed trajectories. The approach linearizes the system with respect to a reference trajectory. In contrast to existing methods rooted in…
In nonlinear electrodynamics, by implementing the causality principle as the requirement that the group velocity of elementary excitations over a background field should not exceed unity, and the unitarity principle as the requirement that…
In this paper, a library-based synthesis methodology for reversible circuits is proposed where a reversible specification is considered as a permutation comprising a set of cycles. To this end, a pre-synthesis optimization step is…
We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations, exploiting the inherent conservative structure to achieve stable long-range…
Implementing Boolean functions with circuits consisting of logic gates is fundamental in digital computer design. However, the implemented circuit must be exactly equivalent, which hinders generative neural approaches on this task due to…
The electromagnetic analog of an elastic spring-mass network is constructed. These electromagnetic circuits offer the promise of manipulating electromagnetic fields in new ways, and linear electrical circuits correspond to a subclass of…
The theory of circuit quantum electrodynamics has successfully analyzed superconducting circuits on the basis of the classical Lagrangian, and the corresponding quantized Hamiltonian, describing these circuits. In many simplified versions…
In recent years, AI-assisted IC design methods have demonstrated great potential, but the availability of circuit design data is extremely limited, especially in the public domain. The lack of circuit data has become the primary bottleneck…
We discuss the validity of close-to-equilibrium entropy production principles in the context of linear electrical circuits. Both the minimum and the maximum entropy production principle are understood within dynamical fluctuation theory.…
Traditional state estimation (SE) methods that are based on nonlinear minimization of the sum of localized measurement error functionals are known to suffer from non-convergence and large residual errors. In this paper we propose an…
We investigate the dynamical equivalence of quadratic Lagrangians and its relation to separation of variables. We show that requiring two quadratic Lagrangians to generate the same Euler--Lagrange equations imposes a compatibility condition…
A Lagrangian generalization of time-reversible Born-Oppenheimer molecular dynamics [Niklasson et al., Phys. Rev. Lett. vol. 97, 123001 (2006)] is proposed. The Lagrangian includes extended electronic degrees of freedom as auxiliary…
Symplectic integrators offer many advantages for the numerical solution of Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two of the central Hamiltonian systems encountered in…
We present an algorithm for the approximate decomposition of diagonal operators, focusing specifically on decompositions over the Clifford+$T$ basis, that minimize the number of phase-rotation gates in the synthesized approximation circuit.…
We show that logic computational circuits in gene regulatory networks arise from a fibration symmetry breaking in the network structure. From this idea we implement a constructive procedure that reveals a hierarchy of genetic circuits,…
In the low energy region chiral perturbation theory including virtual photons is used to derive the structure of the generating functional. The work we do is performed within the three flavor framework and reaches up to next-to-leading…
Exact synthesis provides unconditional optimality and canonical structure, but is often limited to small, carefully scoped regimes. We present an exact synthesis framework for two-qubit circuits over the Clifford+$T$ gate set that optimizes…
In the present work, a new time-dependent exchange theory is presented wherein the symmetry constraints, on a multi-electron wavefunction, are properly accounted for. In so doing, the equations of motion, incorporating the required…
This work propose an alternative and systematic way to obtain a canonical Lagrangian formulation for rotational systems. This will be done in the symplectic framework and with the introduction of extra variables which enlarge the phase…