Quantum brachistochrone problem for two spins-1/2 with anisotropic Heisenberg interaction

Abstract

We study the quantum brachistochrone evolution for a system of two spins-$\frac{1}{2}$ described by an anisotropic Heisenberg Hamiltonian without $zx$, $zy$ interacting couplings in magnetic field directed along the z-axis. This Hamiltonian realizes quantum evolution in two subspaces spanned by $\Vert \uparrow \uparrow ⟩$, $\Vert \downarrow \downarrow ⟩$ and $\Vert \uparrow \downarrow ⟩$, $\Vert \downarrow \uparrow ⟩$ separately and allows to consider the brachistochrone problem on each subspace separately. Using the evolution operator for this Hamiltonian we generate quantum gates, namely an entangler gate, SWAP gate, iSWAP gate et al.

17 pages

References in corpus (10)

• Quantum Computation as Geometry
• Faster than Hermitian Quantum Mechanics
• Optimal control, geometry, and quantum computing
• Speed limits for quantum gates in multi-qubit systems
• Entanglement and the Lower Bounds on the Speed of Quantum Evolution
• Lower bounds on the complexity of simulating quantum gates
• Quantum brachistochrone problem for spin-1 in a magnetic field
• Time-optimal synthesis of unitary transformations in coupled fast and slow qubit system
• Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain
• Genuine tripartite entanglement in quantum brachistochrone evolution of a three-qubit system

Cited by in corpus (11)

• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Entanglement and quantum state geometry of spin system with all-range Ising-type interaction
• Quantum Speed Limit under Brachistochrone Evolution
• Preparation of quantum states of two spin-$\frac{1}{2}$ particles in the form of the Schmidt decomposition
• Quantum adiabatic brachistochrone for open systems
• Geometry and speed of evolution for a spin-s system with long-range zz-type Ising interaction
• Probing the geometry of two-qubit state space by evolution
• Impacts of Intrinsic Noise and Quantum Entanglement on the Geometric and Dynamical Properties of the XXZ Heisenberg Interacting Spin Model
• Geometry of quantum state manifolds generated by the Lie algebra operators
• Implementation of a two-qubit state by an auxiliary qubit on the three-spin system
• Preparation of two-qubit entangled states on a spin-1/2 Ising-Heisenberg diamond spin cluster by controlling the measurement