Regular programs and formulae of the dynamic logic language are de ﬁned by mutual induction.
Logic-Based Specification Languages for Intelligent Software Agents
For example, this is the case in circuits of ﬂux qubits coupled by a mutual inductance that is controlled by the circulating current in a DC Superconducting QUantum Interference Device (SQUID) .
Generation of quantum logic operations from physical Hamiltonians
Note that, by induction hypothesis (iii), we know {e(k) 11, qk ; k ≥ 1} is a family of mutually orthogonal projections in M.
Singly Generated II_1 Factors
By induction, one may ﬁnd a maximal set of mutually commuting orthogonal pro jectors Pj, all commuting with h: If there exists one P commuting with h, one may start with the set {P, 1−P }.
Analysis of quantum semigroups with GKS-Lindblad generators I. Simple generators
Finally, Figure 3c shows two ﬂux qubits coupled through a mutual inductance M .
Superconducting qubits
The proof uses induction and follows directly from the mutually inverse functors of the duality between ordinals and intervals.
On the duality between trees and disks
We denote by F (P (t)) the set of predicates that are mutually inductive with P (t).
Cyclic and Inductive Calculi are equivalent
The set of inductive predicates occurring in the antecedents of sequents of a proof tree may be partitioned into several disjoint families of mutually inductive, identically tagged predicates.
Cyclic and Inductive Calculi are equivalent
Given a cyclic proof D, and a family of tagged mutually inductive predicates Ψ, consider the result of removing from D all the dc-trees whose root Θ has the property that cs(Θ) ∈ Ψ.
Cyclic and Inductive Calculi are equivalent
By employing the magnetic ﬁeld produced by the current, the ﬂux qubit can strongly couple to the LC circuit via a large mutual inductance between them.
Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems
There is, of course, a presentation of rose trees by mutual recursion as well, but this doesn’t give the expected induction rule in Coq either.
Generic Fibrational Induction
The two qubits are directly coupled by a mutual inductance Mqq, and also via the dynamical inductance of a DC-SQUID which depends on the bias current Ib at ﬁxed ﬂux bias.
Parametric coupling for superconducting qubits
Two ﬂux-qubits of persistent currents Iq,i and energy gaps ∆i (i = 1, 2) are inductively coupled by a mutual inductance Mqq .
Parametric coupling for superconducting qubits
They are also inductively coupled to a DC-SQUID with a mutual inductance Mqs .
Parametric coupling for superconducting qubits
At typical experimental temperatures, the low frequency available in techniques like mutual inductance measurements allows almost the DC limit of quantities like the superﬂuid density in superconductors to be measured.
Electrodynamics of correlated electron systems
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