Scale from one entangled pair to a computation. Qubit placement programs the interaction graph (edge iff $r_{ij} < R_b$), the problem's solution is encoded in the ground state of the resulting many-body Hamiltonian, and an adiabatic sweep steers the register toward it; a computational-basis measurement returns the answer as a bitstring — a maximum independent set of the graph. Embed the target graph, then beat the linear ramp's success probability.
SYSTEM. Four to five atoms; positions are free parameters. The register induces a unit-disk graph $G$: vertices are atoms, and $(i,j)$ is an edge iff $r_{ij} < R_b$.
TASK. Choose positions so that $G$ equals a target graph below, then design a global sweep $\Omega(t)$, $\delta(t)$ from $|g \cdots g\rangle$ such that a final measurement returns a maximum independent set of $G$ — atoms found in $|r\rangle$ form the candidate set.
TARGET GRAPHS. Solve either (or both — score is per graph):
| Graph |
Edges |
$\alpha(G)$ |
Embedding hint |
|
$G_A$: star $K_{1,3}$
|
$\lbrace (0,1), (0,2), (0,3)\rbrace$ |
3 |
center atom plus three atoms at 120° and radius $\rho$, with $\rho < R_b < \sqrt{3}\rho$
|
|
$G_B$: cycle $C_5$
|
$\lbrace (0,1), (1,2), (2,3), (3,4), (4,0)\rbrace$ |
2 |
regular pentagon of side $s$, with $s < R_b < 1.618\ s$ (the diagonal) |
BASELINE (THE RAMP TO BEAT). A linear detuning sweep at constant amplitude, on the starter-kit registers ($\rho = s = 5.5\ \mu\mathrm{m}$), total $T = 4\ 000$ ns:
$$
\Omega(t):\quad 0 \ \xrightarrow{\ 252\ \mathrm{ns\ rise}\ }\ \Omega_b \ \xrightarrow{\ 3\ 496\ \mathrm{ns\ hold}\ }\ \Omega_b \ \xrightarrow{\ 252\ \mathrm{ns\ fall}\ }\ 0, \qquad \Omega_b = 6.283\ \mathrm{rad}/\mu\mathrm{s}\ (2\pi \times 1.0\ \mathrm{MHz}),
$$
$$
\delta(t):\quad \delta_0 = -12.57\ \mathrm{rad}/\mu\mathrm{s} \ \xrightarrow{\ \mathrm{linear\ over\ the}\ 3\ 496\ \mathrm{ns\ hold}\ }\ \delta_f = +12.57\ \mathrm{rad}/\mu\mathrm{s} \quad (\mp 2\pi \times 2.0\ \mathrm{MHz}),
$$
with $\delta$ held at $\delta_0$ during the rise and $\delta_f$ during the fall. Sanity check on the pentagon at $s = 5.5\ \mu\mathrm{m}$: nearest-neighbor interaction $U_{\mathrm{nn}} = 31.3\ \mathrm{rad}/\mu\mathrm{s} > \delta_f$, diagonal interaction $U_{\mathrm{diag}} = 1.7\ \mathrm{rad}/\mu\mathrm{s} < \delta_f$ — the final detuning sits inside the MIS window.
SCORE. $P_{\mathrm{MIS}}$: the probability that the measured Rydberg configuration is an independent set of $G$ of maximum size $\alpha(G)$, from the same shot budget (recommended: 500 shots).
SUCCESS. $P_{\mathrm{MIS}}$ strictly above the baseline ramp on the same graph.
Submission (Discord team channel by 16:30)
Device limits: see the device envelope — and verify Device.specs at runtime.
SYSTEM. Four to five atoms; positions are free parameters. The register induces a unit-disk graph$G$ : vertices are atoms, and $(i,j)$ is an edge iff $r_{ij} < R_b$ .
TASK. Choose positions so that$G$ equals a target graph below, then design a global sweep $\Omega(t)$ , $\delta(t)$ from $|g \cdots g\rangle$ such that a final measurement returns a maximum independent set of $G$ — atoms found in $|r\rangle$ form the candidate set.
TARGET GRAPHS. Solve either (or both — score is per graph):
BASELINE (THE RAMP TO BEAT). A linear detuning sweep at constant amplitude, on the starter-kit registers ($\rho = s = 5.5\ \mu\mathrm{m}$ ), total $T = 4\ 000$ ns:
with$\delta$ held at $\delta_0$ during the rise and $\delta_f$ during the fall. Sanity check on the pentagon at $s = 5.5\ \mu\mathrm{m}$ : nearest-neighbor interaction $U_{\mathrm{nn}} = 31.3\ \mathrm{rad}/\mu\mathrm{s} > \delta_f$ , diagonal interaction $U_{\mathrm{diag}} = 1.7\ \mathrm{rad}/\mu\mathrm{s} < \delta_f$ — the final detuning sits inside the MIS window.
SCORE.$P_{\mathrm{MIS}}$ : the probability that the measured Rydberg configuration is an independent set of $G$ of maximum size $\alpha(G)$ , from the same shot budget (recommended: 500 shots).
SUCCESS.$P_{\mathrm{MIS}}$ strictly above the baseline ramp on the same graph.
Submission (Discord team channel by 16:30)
Device limits: see the device envelope — and verify
Device.specsat runtime.