Abstract
We present a Hamiltonian quantum-computation scheme universal for quantum computation. Our Hamiltonian is a sum of a polynomial number (in the number of gates in the quantum circuit) of constant-norm, time-independent, two-body interaction terms. Furthermore, each qubit in the system interacts only with a constant number of other qubits in a three-layer, geometrically local layout. The computer runs in three steps—it starts in a simple initial product state, evolves according to a time-independent Hamiltonian for time of order (up to logarithmic factors), and finishes with a two-qubit measurement. Our model improves previous universal two-local-Hamiltonian constructions, as it avoids using perturbation gadgets and large energy-penalty terms in the Hamiltonian, which would result in a large required run time.
- Received 22 November 2011
DOI:https://doi.org/10.1103/PhysRevA.85.032330
©2012 American Physical Society