Elliptic functions and efficient control of Ising spin chains with unequal couplings
arXiv:0710.0075 · doi:10.1103/PhysRevA.77.032340
Abstract
In this article, we study optimal control of dynamics in a linear chain of three spin 1/2, weakly coupled with unequal Ising couplings. We address the problem of time-optimal synthesis of multiple spin quantum coherences. We derive time-optimal pulse sequence for creating a desired spin order by computing geodesics on a sphere under a special metric. The solution to the geodesic equation is related to the nonlinear oscillator equation and the minimum time to create multiple spin order can be expressed in terms of an elliptic integral. These techniques are used for efficient creation of multiple spin coherences in Ising spin-chains with unequal couplings.
References in corpus (11)
- Time Optimal Control in Spin Systems
- Quantum Computation as Geometry
- Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer
- Optimal control, geometry, and quantum computing
- Optimal simulation of two-qubit Hamiltonians using general local operations
- Characterization of non-local gates
- Interaction cost of non-local gates
- Time Optimal Control of Coupled Qubits Under Non-Stationary Interactions
- Broadband Geodesic Pulses for Three Spin Systems: Time-Optimal Realization of Effective Trilinear Coupling Terms and Indirect SWAP Gates
- Geodesics for Efficient Creation and Propagation of Order along Ising Spin Chains
- Gate simulation and lower bounds on the simulation time
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