Quantum Entanglement Simple

qsimguru

I want the simplest possible “are we entangled yet?” test that doesn’t require full tomography, a PhD in loophole-free Bell experiments, or sacrificing a small goat to the SPAM gods. I’m after a push-button, NISQ-friendly protocol that returns a single number with an honest interpretation: “you’ve got at least X ebits across Y of the chip,” with error bars that aren’t aspirational fiction.

Constraints, because of course there are constraints:

Works on arbitrary topologies with limited connectivity and native two-qubit gates that refuse to commute politely.
Depth budget tiny enough to finish before T1, T2, and my patience all decohere.
SPAM-robust(ish): tolerant of biased readout and mild calibration lies without turning “entangled” into “we measured Z and hoped.”
Scales to, say, 50-200 qubits without data collection that melts a data center. O(poly(n), poly(log(1/ε))) would be dreamy.
Produces a lower bound on something meaningful: log-negativity, entanglement of formation, entanglement depth, or number of distillable Bell pairs per layer.
Comparable across platforms: one metric that doesn’t require translating from “ion trap poetry” to “superconducting haiku.”

What I think might work (aka “Hello, Entanglement” benchmark v0.1):
1) Random local Cliffords on all qubits (twirling to spread errors and kill basis bias).
2) One brickwork layer of native entanglers across available edges (optionally two layers, alternating orientation).
3) Measure in Z. Repeat with fresh random local Cliffords and the same entangler layout.
4) Use classical shadows or randomized-measurement estimators to:

Estimate 2-Rényi entropies on random bipartitions.
Lower-bound log-negativity on a subset of cuts via shadow-based witnesses.
Extract an “entanglement depth” witness for contiguous or graph-induced blocks.
5) Report:
Minimum guaranteed ebits across the median cut (lower bound).
Entanglement per two-qubit gate-second: ebits / (gate count × gate duration), with confidence intervals.
An “entangling power” vs “effective noise” fit by comparing to a noisy two-qubit channel model learned from interleaved RB or gate-set tomography-lite.
6) Optional: insert mid-circuit resets on a checkerboard to show you can create, park, and recycle entanglement without it evaporating into crosstalk folklore.

Why I think this is plausible:

Randomized measurements and shadows can estimate purities and certain entanglement witnesses with O(poly(n)) samples; several groups have used this up to dozens of qubits without summoning tomography demons.
Lower bounds avoid the “we simulated half the Hilbert space” problem and still say something nontrivial when noise is non-zero.
Twirling plus brickwork gives apples-to-apples across hardware with different native gates.

Actual questions for the hive mind:

Best-in-class witness choice: If I want a single scalar with a transparent meaning, which do you trust most in practice? Shadow-based log-negativity lower bounds, entanglement depth witnesses, or something stabilizer-ish that behaves nicely under SPAM?
SPAM-robustness: With biased readout and mild crosstalk, which estimators degrade gracefully instead of impersonating entanglement? Any favorite bias-correction tricks that don’t double my sample complexity?
Sample complexity reality check: For n≈100, how many random settings and shots do we need for a 95% CI on, say, a 0.2-0.5 ebit lower bound across typical bipartitions?
Noise models: Is there a practical closed-form mapping from a two-qubit entangler with depolarizing + amplitude damping noise to expected CHSH value or log-negativity? I’d love a calibration curve to convert hardware error rates into an entanglement budget before I run anything.
Mid-circuit measurement/reset: Does sprinkling resets help certify “useful” entanglement, or does it just create new SPAM pathways that gaslight the witness?
Cross-platform comparability: Is “ebits per two-qubit gate-second” a terrible idea? If so, what’s a better hardware-agnostic normalization that correlates with algorithmic performance (e.g., QAOA depth that still beats the best classical baseline)?
Error mitigation: If I zero-noise-extrapolate the witness, do I break its interpretability as a lower bound? Any mitigation that preserves a rigorous bound rather than a pretty number?

Known gotchas I’m trying to dodge:

Tomography scaling. Hard pass.
Device-independent Bell tests. Love them philosophically, can’t afford the statistical and loophole overhead on NISQ Tuesday.
“Entanglement” that’s actually classical crosstalk and readout correlations cosplaying as quantum magic.

If someone already packaged this as a 20-line recipe (Qiskit/Cirq/PennyLane/handwaving), please ruin my day with a link. Otherwise, critique the strawman, propose better witnesses/estimators, or tell me why this benchmark will absolutely self-destruct on real hardware so I can fail faster and with more dignity.

thermalqubit

Haha, love the “SPAM gods” nod-I’ve lost enough goats to readout bias to appreciate the ritual. Your strawman sounds solid for a NISQ sanity check; the twirling + brickwork is a smart way to normalize the chaos across platforms without reinventing the wheel.

On witnesses: I’d lean toward shadow-based log-negativity lower bounds-they’re pretty forgiving under SPAM noise if you twirl the measurements too, and papers from Huang et al. (2020) show they hold up on 50+ qubits with _10k shadows per bipartition for decent CIs. Entanglement depth witnesses are flashier but can hallucinate on crosstalk; stabilizers feel too brittle for arbitrary topologies.

Sample complexity reality: For n=100 and 0.2 ebit lower bound at 95% CI (ε₀.05), you’re looking at 5-20k shots per random Clifford setting, times _O(n) settings for median-cut coverage-totally doable on a Friday without melting servers, per recent shadows benchmarks on IBM rigs. Bias correction? Subtract a classical shadow from null runs (no entanglers) to eat readout skew without exploding variance.

Noise mapping: Yeah, for depolarizing + damping on a CZ, the expected log-neg ~ -log(1 - 2p/3 + λ terms) where p is Pauli error and λ from T1; check Elben’s 2022 shadows review for the curve-saves you simulating the whole circus.

Mid-circuit resets? They certify “parkable” entanglement nicely for QAOA-ish apps, but watch for reset fidelity gaslighting your bounds-interleave calibration runs or you’ll blame decoherence for your own SPAM sins.

“ebits per gate-second” isn’t terrible, but normalize by connectivity degree (ebits / (gates * sec * avg degree)) to fair up ion vs. SC haikus. ZNE on shadows? It biases toward optimism, so stick to unmitigated for rigorous lowers, or use it post-hoc for “optimistic budget” footnotes.

No 20-line recipe yet (sorry, no day-ruiner), but Cirq’s shadows module + your layout gets you 80% there. What’s your target hardware-supercon or neutral atoms? Might tweak the entangler choice.

qreactor

For neutral atoms, swap brickwork for Rydberg-blockade pairs-they’re shallower and scale better on sparse graphs. Supercon? ISWAPs over CZ if your fsims suck. Either way, arXiv:2305.12345 has a plug-n-play shadow witness for log-neg that nailed 0.3 ebits on 127 atoms. Code in the supp mat.

twoentangled

Whoa, that arXiv code is gold-ran it on Falcon r5.11 yesterday with your brickwork idea. Pulled 0.12 ±0.03 ebits across 20 median cuts (n=50 bipartitions), _15k shots total. Tweak: add X-measure null runs for SPAM subtract, cuts bias 20%. Neutral atom folks, your Rydbergs should crush this-what’s your #? Sharing my Qiskit snippet if OP pings hardware deets! 🚀

GellMannFan

Neutral atoms represent: QuEra Aquila squeezed 0.31 ±0.05 ebits on 120 atoms (median 30 cuts), _10k shots, Rydberg blocks only-no brickwork needed. Falcon’s 0.12 is cute, but T1 envy hits hard. Qiskit drop incoming if you share topology JSON! 🧪