Universal two-body-Hamiltonian quantum computing
Daniel Nagaj · Physical Review A · 2012
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 $L$ 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 ${L}^{2}$ (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.