Interfacing with Hamiltonian dynamics

Simple constructions and protocols are demonstrated to allow the implementation of universal quantum computation on an arbitrarily large quantum system by controlling a fixed number of spins within a noiseless setting. Pulse sequences are derived for deterministic gate operation and system cooling, which only require pulse strengths that are comparable to the intrinsic Hamiltonian of the system. The analyticity of these protocols allows insights into, for example, scalability, which are not present in the numerical results derived from control theoretic solutions.

Figure 1

(Color online) Plot, as a function of time for a chain of $102\left(N=100\right)$ spins, for (a) fidelity of arrival and departure of states $|\underset{̱}{101}⟩$ and $|\underset{̱}{0}⟩$, respectively, for $f=3$ and $\Delta =10$, giving an arrival fidelity of 99.45% and (b) coupling strengths ${\Omega }_0$ and ${\Omega }_N$. The final fidelity can be increased by increasing $\Delta$.

Figure 2

(Color online) Arrival fidelity as a function of timing error, $t_N-t_0$, for a chain of 100 spins, $\Delta =30$, $f=3$.

Figure 3

(Color online) Plot, as a function of time, for (a) fidelity of arrival and departure of states $|\underset{̱}{101}⟩$ and $|\underset{̱}{0}⟩$, respectively, for $f=3$ and $\Delta =10$, giving arrival fidelity of 99.37% and (b) coupling strengths ${\tilde{\Omega }}_0$ and ${\tilde{\Omega }}_N$, which are randomly varied from their ideal forms (Fig. 1) within the range $\pm 10\%$.

Figure 4

(a) Time-controlled spin chain, used to simulate the fixed spin chain depicted in (b), where $\dots$ indicates the presence of a chain of $N_A$ (left) or $N_B$ (right) qubits, either of which may be taken to $\infty$.