Rydberg Blockade and Antiferromagnetic Order

Neutral-atom quantum computers do not run gates. They hold atoms in place with laser tweezers and drive them all at once, and the answer comes from where the atoms end up. The most quoted demonstration of this is antiferromagnetic order: a chain of atoms driven slowly enough settles into an alternating pattern, excited, ground, excited, ground.

Every explanation of that result says the alternation is caused by the Rydberg blockade. Almost none of them say how much blockade you need, or what you get when there is not enough. So we measured it: one chain, one pulse sequence, seven different atom spacings, 1000 shots each.

The one number that matters

An atom excited to a Rydberg state shifts the energy of its neighbours enough that the same laser can no longer excite them. The distance over which that holds is the blockade radius, written Rb. It is not a property of the atoms alone: it depends on how hard you are driving them, because a stronger drive is harder to suppress.

The quantity that decides the physics is the ratio of that radius to the spacing between atoms, Rb divided by a. If Rb/a is comfortably above 1, each atom blocks its neighbour and the only way to excite as many atoms as possible is to take every other one, which is the alternating pattern. If Rb/a falls below 1, neighbours stop blocking each other and there is nothing to enforce the alternation.

That is the theory. Here is what it does.

The measurement

Seven atoms in a line, driven by a global Rydberg beam through a 4000 ns adiabatic sweep: amplitude ramps up over 400 ns, detuning sweeps from -37.7 to +12.6 rad/us over 3200 ns, amplitude ramps down over 400 ns. The drive is fixed at 12.566 rad/us throughout, which puts the blockade radius at 6.40 um. Only the spacing changes.

A bit reads 1 when that atom finished in the Rydberg state, so perfect antiferromagnetic order is the bitstring 1010101.

spacing   Rb/a   top outcome   count   1010101 %   distinct outcomes
  5.0 um  1.28      1010101       899      89.9              12
  5.2 um  1.23      1010101       886      88.6              14
  5.6 um  1.14      1010101       849      84.9              23
  6.0 um  1.07      1010101       629      62.9              36
  6.4 um  1.00      1010101       369      36.9              64
  7.0 um  0.91      1010101        68       6.8              72
  8.0 um  0.80      1111111       479       0.0              36

The order does not switch off at a threshold. It decays, and the decay is steep: between Rb/a of 1.28 and 1.00, a spacing change of less than a third of a micrometre, the alternating state goes from nine runs in ten to fewer than four.

One caveat on reading that table. In the ordered rows the top outcome is solidly 1010101 and repeats run to run. In the disordered rows it is not stable: at 7.0 um the distribution is spread across about seventy bitstrings with no clear winner, and a rerun can put a different one on top with a similar count. The percentage column is the meaningful one there, not the identity of whichever string happened to lead.

Where it breaks, and what replaces it

The last column is the more interesting one. It counts how many different bitstrings appeared at all across 1000 shots, which is a crude but honest measure of how disordered the outcome is.

At tight spacing there are 12. The chain has essentially one answer, plus a handful of single-atom defects. As the blockade weakens that number climbs to 72, which is the system running out of any reason to prefer one arrangement over another. This is the disordered regime, and it is worth seeing quantified rather than described, because a paper that only reports the good spacing never shows you this half.

Then at 8.0 um something different happens. The distinct-outcome count falls back to 36 and the dominant state is no longer 1010101 at all. It is 1111111: every atom excited. The alternating state essentially stops appearing, turning up in nought to one shot per thousand depending on the run.

That is the blockade failing completely rather than weakening. With Rb/a at 0.80 no atom suppresses any other, so the detuning sweep does the simplest thing available and excites all of them. The system becomes ordered again, just into the wrong order. An experiment that measured only "is the outcome sharply peaked" would call this a success.

The device sets the floor

The tightest spacing in that table is 5.0 um, and that is not a choice. The device refuses to place atoms closer than 5 um, because tweezers that close cannot reliably hold separate atoms.

That matters more than it first appears. The blockade radius shrinks as the drive gets stronger, so you cannot simply turn up the laser to buy more Rb/a; you would have to move the atoms closer, and the hardware will not let you past 5 um. The usable window is bounded on one side by physics and on the other by engineering, and at this drive strength the whole interesting range fits between 5.0 and 8.0 um.

The certificate

One run at 5.2 um carries a public certificate: cb6bf9ecb491466d. It reports 909 shots of 1010101 out of 1000, on the exact-evolution engine, with the sequence hash and the full outcome distribution.

The sweep above records 886 at that same spacing. Those are two separate runs, and at 1000 shots the sampling spread is about one percentage point per standard deviation, so a couple of points between runs is ordinary. We are quoting both rather than the flattering one, because a single number with no sense of its own scatter is the thing that makes results irreproducible.

The certificate also states what it does not cover. The engine integrates the full state with no truncation, so there is no approximation error to report and only shot noise applies. That exactness is bought with a hard ceiling: the register is capped at 14 atoms, because the cost of an exact analog simulation grows with 2^n amplitudes carried through every timestep. Real neutral-atom hardware runs 100 atoms and more, and no exact classical simulation follows it there.

Reproducing this

The whole sweep runs on a laptop. Pulser builds the sequence, and the engine is free at these sizes:

import numpy as np, pulser
from pulser import Pulse, Register, Sequence
from pulser.devices import AnalogDevice
import qsim_sdk

omega = 4 * np.pi                  # 12.566 rad/us
spacing = 5.2                      # um; Rb is 6.40 um, so Rb/a = 1.23

coords = np.array([[i * spacing, 0.0] for i in range(7)])
coords -= coords.mean(axis=0)
reg = Register.from_coordinates(coords, prefix="q").with_automatic_layout(AnalogDevice)

seq = Sequence(reg, AnalogDevice)
seq.declare_channel("ising", "rydberg_global")
d0, df = -3 * omega, omega
seq.add(Pulse.ConstantDetuning(pulser.waveforms.RampWaveform(400, 0.0, omega), d0, 0.0), "ising")
seq.add(Pulse.ConstantAmplitude(omega, pulser.waveforms.RampWaveform(3200, d0, df), 0.0), "ising")
seq.add(Pulse.ConstantDetuning(pulser.waveforms.RampWaveform(400, omega, 0.0), df, 0.0), "ising")

client = qsim_sdk.Client(token="YOUR_TOKEN")
job = client.run_sequence(seq, shots=1000)
print(job["result"]["counts"])

Change `spacing` and rerun to reproduce any row of the table. The interesting values are the ones nobody publishes: set it to 8.0 and watch the chain excite everywhere.

You can also run it without writing anything. The sequence is a one-click template in the console, where the register is drawn with the blockade radius to scale, so you can see that it reaches the neighbour and stops short of the atom beyond.

Why publish the failures

The result everyone reports is the first row of that table. It is a real result and it reproduces. But quoting it alone implies the alternating state is what a Rydberg chain does, when what a Rydberg chain does depends on a ratio, and gets the answer badly wrong over most of the range we could physically test.

The 8.0 um row is the one worth remembering. A sharply peaked, highly reproducible, completely wrong answer looks exactly like a correct one if you are only checking whether the distribution is sharp. Knowing which regime you are in is not a detail of the setup. It is the result.