Hardware Sheet — Platforms, Metrics, and the Materials Connection (L07, L13, L17) - Quantum Computing & Quantum Information

Platform Comparison (orders of magnitude, mid-2020s)¶

	Supercond.	Ions	Neutral atoms	Si spins	Photons
Qubit	transmon	hyperfine	Rydberg	QD/donor	dual-rail
1Q gate time	10–50 ns	1–10 $\mu$ s	$\mu$ s	10–100 ns	fs (passive)
2Q gate time	30–300 ns	10–300 $\mu$ s	$\sim\mu$ s	100 ns	prob. fusion
2Q fidelity	99–99.9%	99.9%	99–99.5%	99–99.5%	heralded
$T_2$	10–500 $\mu$ s	s–min	ms–s	ms	loss-limited
Connectivity	2D lattice	all-to-all (chain)	reconfigurable	1D/2D	network-native
Temp.	10–20 mK	RT trap, laser-cooled	$\mu$ K atoms	mK–1 K	RT

Always divide $T_2$ by the 2Q gate time: that ratio (10³–10⁵) bounds useful circuit depth.

Key Metrics Dictionary¶

$T_1$ energy relaxation ( $|1\rangle\to|0\rangle$ ) $\to$ amplitude damping, $\gamma=1-e^{-t/T_1}$ .
$T_2$ dephasing (phase randomization) $\to$ phase damping; $T_2\le2T_1$ ; $T_2^*$ includes slow drift, $T_2^{\text{echo}}$ removes it.
Gate fidelity from randomized benchmarking: average error per Clifford.
Readout error: confusion matrix $M_{ij}$ ; mitigate by inverting (L17).
Quantum volume $2^n$ : largest square random circuit passing a heavy-output test.
Crosstalk: unwanted coupling during parallel gates — why calibration data is per-pair.

Materials Physics of Decoherence (L07)¶

Transmons: TLS defects in amorphous oxides (junction barrier, surfaces, substrate interface) dominate $T_1$ ; quasiparticles and flux noise add in.
Materials wins: Ta films, sapphire substrates, surface passivation $\Rightarrow$ order-of-magnitude $T_1$ gains.
Si spins: isotopic purification to $^{28}$ Si removes nuclear-spin bath $\Rightarrow$ ms coherence.
Ions/atoms: qubits are perfect; the trap (anomalous heating from electrode surfaces) and lasers are the materials/engineering battle.

Datasheet $\to$ Simulation Recipe¶

Read $T_1, T_2$ , gate times $t_g$ , readout error per qubit.
Per gate: amplitude damping $\gamma=1-e^{-t_g/T_1}$ ; phase damping from $T_\phi$ : $\frac{1}{T_\phi}=\frac{1}{T_2}-\frac{1}{2T_1}$ .
Add depolarizing channel matching reported gate infidelity.
Apply confusion matrix to final counts.
Predict, run, compare — discrepancies = crosstalk/drift.

Choosing a Backend (rules of thumb)¶

Deep, few qubits (QPE): ions. Shallow, many shots (VQE): superconducting.
Lattice-geometry simulation: neutral atoms. Communication/QKD: photonics.
Long-term embedded/cryo-CMOS integration: Si spins.

Fault-Tolerance Numbers to Remember (L13)¶

Surface code threshold $\sim1\%$ physical error; logical error $\propto (p/p_{\text{th}})^{(d+1)/2}$ .
Overhead: $\sim2d^2$ physical qubits per logical (distance $d$ ); $d\sim20$ –30 for chemistry-grade runs $\Rightarrow$ 10²–10³ physical per logical.

Hardware Sheet — Platforms, Metrics, and the Materials Connection (L07, L13, L17)