Universal Adiabatic Quantum Computation via the SpaceTime CircuittoHamiltonian Construction
Abstract
We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a twodimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic X X Z chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q deformed version of SU(2) symmetry. We also discuss a related timeindependent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.
 Publication:

Physical Review Letters
 Pub Date:
 April 2015
 DOI:
 10.1103/PhysRevLett.114.140501
 arXiv:
 arXiv:1409.7745
 Bibcode:
 2015PhRvL.114n0501G
 Keywords:

 03.67.Ac;
 03.65.Vf;
 03.67.Lx;
 05.50.+q;
 Quantum algorithms protocols and simulations;
 Phases: geometric;
 dynamic or topological;
 Quantum computation;
 Lattice theory and statistics;
 Quantum Physics;
 Mathematical Physics
 EPrint:
 Phys. Rev. Lett. 114, 140501 (2015)