Quantum Institute: Visitor Schedule

The Quantum Lunch is regularly held on Thursdays in the Theoretical Division Conference Room, TA-3, Building 123, Room 121. For more information, contact Diego Dalvit.

August 16, 2007
Thursday, 12:30PM to 2 PM
T-DO Conference Room, TA-3-123-121

Andrew John Landahl,
University of New Mexico

One-Dimensional, Time-Independent, Nearest-Neighbor Hamiltonians are Universal for Quantum Computation

Abstract

In 1984, Feynman proved that continuous-time quantum walks are universal for quantum computation. The Hamiltonian he used in his proof is spatially nonlocal and requires four-body interactions. In this talk, I will describe how one can simplify his proof using modern concepts in quantum information science. In particular, I will describe a time-independent, nearest-neighbor Hamiltonian on a one-dimensional ring of eight-state systems that can efficiently simulate an arbitrary quantum computation. Moreover, I will describe how Hamiltonian "gadget" perturbation theory can map this architecture onto one involving only qubits that interact locally on a two-dimensional grid. The motivation for these constructions is that such Hamiltonians or variants thereof may be constructible in a real laboratory setting. Operating a computer built according to this architecture would be a simple process of preparing the input, waiting, and measuring the output. As a side result of these investigations, I will outline how we can also prove that adiabatic quantum computing with these Hamiltonians is also universal for quantum computation.

This talk represents joint work with Brad Chase.