Fast simulation of a quantum phase transition in an ion-trap realisable unitary map

Abstract

We demonstrate a method of exploring the quantum critical point of the Ising universality class using unitary maps that have recently been demonstrated in ion trap quantum gates. We reverse the idea with which Feynman conceived quantum computing, and ask whether a realisable simulation corresponds to a physical system. We proceed to show that a specific simulation (a unitary map) is physically equivalent to a Hamiltonian that belongs to the same universality class as the transverse Ising Hamiltonian. We present experimental signatures, and numerical simulation for these in the six-qubit case.

12 pages, 6 figures

References in corpus (8)

• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement in a simple quantum phase transition
• On the Power of One Bit of Quantum Information
• A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
• Entanglement and quantum computation with ions in thermal motion
• Direct detection of quantum entanglement
• Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field
• Generation of eigenstates using the phase-estimation algorithm

Cited by in corpus (10)

• Quantum Simulations with Cold Trapped Ions
• Mesoscopic Spin-Boson Models of Trapped Ions
• Limitations of Quantum Simulation Examined by Simulating a Pairing Hamiltonian using Nuclear Magnetic Resonance
• Multipartite Entanglement in a One-Dimensional Time Dependent Ising Model
• Entanglement in a periodic quench
• Quantum phases of interacting phonons in ion traps
• A Two-Dimensional Lattice Ion Trap for Quantum Simulation
• Evolution of pairwise entanglement in a coupled n-body system
• Quenching and generation of random states in a kicked Ising model
• One, Two, and $n$ Qubit Decoherence