Synopsis: A resource state for one-way quantum computation

Synopsis Image
Illustration: Alan Stonebraker

Gapped Two-Body Hamiltonian Whose Unique Ground State Is Universal for One-Way Quantum Computation

Xie Chen, Bei Zeng, Zheng-Cheng Gu, Beni Yoshida, and Isaac L. Chuang

Published June 5, 2009

In the one-way quantum computation model, unitary operations that perform logic gates are replaced by measurements on single particles, which are much easier to implement. This scheme requires an initial state, called a resource state, which has entanglement distributed among its many particles.

Do many-body entangled states with the right properties already exist in some known condensed matter system? Researchers are investigating ways to find physically realizable states. Writing in Physical Review Letters, Xie Chen and co-workers from MIT in the US construct a resource state and Hamiltonian, which correspond to particles on a hexagonal lattice, each of which can adopt six possible states. This resource state possesses many sought after properties. For one, it is universal, meaning that the state and the appropriate measurements are enough to efficiently simulate any quantum circuit. It is also the exact and unique ground state of a Hamiltonian, making it stable for performing the necessary operations, as the system cannot transition to a lower energy state. The Hamiltonian for the system has a fixed energy gap between its ground state and its first excited state, so it is robust to thermal noises. Finally, the Hamiltonian involves only two-body nearest-neighbor interactions, which create the necessary entanglement among the particles.

The tools used to construct this state open the way for simpler versions and link the fields of condensed matter and quantum information. – Sonja Grondalski