29 The confirmed empirical advantages – Quantum Computing, Information and Physics in qang Space

29.1 From the base: where the advantages come from

The book’s advantages have two origins, and they should not be mixed:

The weight filter (Chapters 20–25): if the circuit conserves the number of excitations, every shot with the wrong weight had an error and is discarded. It is symmetry verification, a known technique. The qang scale contributes the witness (the register’s mean readout, whose ideal value is known before running) and the rule for when it pays (Chapter 21).
The scale itself (Chapters 18, 23, 26, 27): readouts that separate things the raw readout mixes. Temperature from readout error, T1 from unital noise, thermal drift from an attack.

29.2 Exact restoration under T1

With the same T1 on every qubit, the filter returns exactly the noiseless readout in every sector (Chapter 21, checked to \(10^{-12}\) m-qg). In classification, the notes (§80) measured it over 60 paired runs (5 seeds, 3 splits, 4 datasets), with predictions committed before running:

with the weight-1 model, trained without noise and read under T1, qang recovers +2.5 points of accuracy (95% interval: +0.8 to +4.1), up to the exact accuracy of 0.952;
with the weight-2 model it recovers +16.5 points (+11.8 to +21.2), from 0.757 to 0.922;
with dephasing, +12.6 and +22.6 points;
when training under the noise, the difference vanishes (+0.1 and −0.1 points): the advantage is not having to train under the noise, not an accuracy higher than achievable.

All five predictions held. The index’s figures (“+2.5 and +16.5 over 60 runs”) are in §80 as stated.

The gradient, too (§112). Under equal T1 the filter returns the noiseless gradient exactly; without the filter, at weight 1 the gradient is \(K\) times smaller. This is the noise-induced barren plateau, and the filter trades it for shots: the cost of resolving the sign of the gradient grows like \(1/K\) instead of \(1/K^2\) (Section 23.8). In the notes the filter needed fewer shots in 10 of 12 cells; at half filling with \(K\le0.14\) it needed 1.3–2.2 times more (T5 failed).

29.3 Lower readout error on simulated devices

The script recomputes the error-reduction factor (raw over filter plus readout correction) on every device of every stored run:

Table 29.1: Raw error over error with filter plus readout, recomputed from the stored runs.

study	devices	min	median	max
10 weight-1 circuits (§137)	3	3.99	4.66	8.07
IBM fleet (§144)	17	2.45	3.12	6.11
PCA spectrum (§146)	21	1.57	4.63	7.67
XY Trotter, best error (§147)	21	1.59	2.04	2.82
inversion test (§149)	6	3.84	4.55	11.24
3-flavour neutrinos (§151)	3	2.97	3.43	3.83
sterile neutrino (§163)	3	5.55	5.61	5.68
neutrinos on IQM Garnet (§165, real hardware)	1	—	1.59	—

The filter never made the error worse in any of the 74 cases (the same simulated device appears in several studies). It cut it 1.6 to 11 times.
On real hardware it gained less (1.59 times): the chip was better than its simulated model (raw error 0.062 against 0.126), so fewer shots left the sector. The remaining error is inside the sector, where the filter does not see.
The IBM fleet, taking the better of filter alone and filter plus readout, gives 2.4 to 9.0 times (the notes: 2.4–8.9). The “2.7–3.6×” range the index announced is not in the notes: the figures are those of this table. For the §85 classifier the notes give 2.9–3.6 times on the readout error, with the same accuracy (0.933) with and without qang.

Figure 29.1: Error-reduction factor with the filter, device by device, in seven studies on simulated noise models and in the real run on IQM Garnet (star). The bars are medians.

29.4 In-sector errors: the echo

What the filter does not see, the echo measures (Chapter 22). With the weight-1 network on 189 inputs and 1000 shots, on five simulated devices, the decisions that differ from the noiseless network are 15 without qang, 7 with the filter and 3 with the filter plus the echo, over 945 readouts (§106). The echo removes 43 to 56% of the decision-value error the filter leaves. It does not help with narrow-margin inputs, when the filtered error is already close to its shot noise (§108).

29.5 Characterization and control

These advantages belong to the scale itself, without the filter (Chapter 27):

Temperature and readout: the heralded sweep measures the readout error without bias and the effective temperature to 1 mK, where the standard calibration inflates the error by \(p\cdot b\) and sees the qubit at 0 mK.
T1 diagnosis without classical simulation: the mean readout tells T1 from unital noise with 88% accuracy from 100 shots under strong noise, against 70–76% for XEB and HOP, which also need the ideal distribution. With realistic noise nothing tells the two apart on arbitrary circuits.
Control quantization: a grid even in qg lowers the total variation distance when loading a distribution in 43 of 45 cases (median 1.56 times), and the worst probability error by an exact factor \(\pi/2\). It loses in fidelity near the poles.

29.6 Neutrinos: mitigation without extra circuits

Neutrino oscillations in a circuit conserve the weight, so the filter applies without adding any circuit. With three flavours (§151), the error falls 3.4 times in the median of three simulated devices (the index said 3 times); with a sterile neutrino (§163), 5.6 times, and the survival dip appears at the right energy on all three. On IQM Garnet (§165), on real hardware, the filter cuts the error 1.59 times and puts the oscillation maximum back at 2.6 GeV (exact 2.63), where the raw readout placed it at 0.8 GeV. It is the only one of these advantages confirmed on hardware. The other two Garnet runs (§168 and §170, 8 of 9 predictions) tested the scale and the reading, not an advantage: they show that the milli-qang measures a real chip, not that qang improves it.

29.7 BB84: fewer false alarms under thermal drift

In BB84, the sum \(qg(0)+qg(1)\) of the states sent in Z is a T1 witness: relaxation produces only 1→0 errors, and an intercept-resend attack produces symmetric errors (notes §40, Chapter 17). With windows of 2000 bits and 1% false alarms on the baseline:

Table 29.2: Fraction of windows with an alarm (notes §40, from the Chapter 17 cache).

scenario	QBER monitor	qg monitor
baseline	0.007	0.006
T1 drift, \(\gamma\) 0.02 → 0.04	0.478	0.009
T1 drift, \(\gamma\) 0.02 → 0.06	0.962	0.006
intercept-resend, \(f=0.05\)	0.861	0.823
intercept-resend, \(f=0.10\)	1.000	0.994
T1-mimicking attack	0.962	0.006

The qg monitor detects the attack as well as the QBER monitor and does not fire when only the memory’s T1 worsens, where the QBER monitor fires in 48–96% of windows. The price is written down: an attacker who mimics T1 goes unnoticed by the qg monitor and not by the QBER one. The two are complementary, and there is no security gain: the key rate falls the same way in both cases.

Figure 29.2: Fraction of windows with an alarm for the QBER monitor and the qg monitor in six BB84 scenarios with 2000 bits; the qg monitor does not fire under thermal drift, nor under an attack that mimics it.

29.8 What remains open

Of all these advantages, only the neutrino one is confirmed on real hardware, once, with 300 shots per circuit. The ones most worth taking to a device are the heralded characterization (thermal population does not exist in simulators) and the filter on a circuit with several excitations.

29.9 Without qang and with qang

Table 29.3: The confirmed advantages and their limits.

advantage	without qang	with qang	size	where it stops holding
accuracy under T1 without retraining	0.928 / 0.757 (weight 1 / 2)	0.952 / 0.922	+2.5 / +16.5 points	with unequal T1 it loses ≤ 1 point; training under noise, none
readout error (simulated)	raw	filter + readout	1.6 to 11 times, never worse	error inside the sector
error on real hardware	0.062	0.039	1.59 times	chips better than their model gain less
gradient under T1	\(K\) times smaller	exact with the filter	shots from \(1/K^2\) to \(1/K\); 10 of 12 cells	half filling with \(K\le0.14\) (§112)
a classifier’s decisions	15 of 945 differ	3 with filter and echo	5 times fewer	narrow margin (§108)
readout and temperature	\(e_{01}\) inflated, 0 mK	unbiased, to 1 mK	—	needs mid-circuit measurement
T1 diagnosis	0.70–0.76 with ideal simulation	0.88 from counts only	+12–18 points	realistic noise: chance
loading distributions	grid in \(\theta\)	grid in qg	43 of 45, median 1.56 times	fidelity near the poles
BB84 alarms	48–96% false alarms from drift	0.6–0.9%	—	an attack that mimics T1

Balance. The advantages are real and measured, but of two kinds. Those of the filter are the largest (up to 11 times in simulation) and belong to symmetry verification, which is known; qang contributes the witness and the rule. Those of the scale itself are smaller and more its own: separating temperature from readout, T1 from unital noise and drift from attack. Only one advantage has been through real hardware, and there it gained less than in simulation. That is the figure to look at first.

29.10 In code

import json

d = json.load(open("examples/data/iqm_neutrino_qg_run.json"))
d["raw_error"] / d["filtered_error"]      # 1.59: the filter on IQM Garnet, real hardware
d["kept"]                                 # 0.88 of the shots kept

29.11 Summary

Under equal T1, qang recovers the noiseless accuracy without retraining: +2.5 points with weight 1 and +16.5 with weight 2 over 60 runs.
The filter cuts the readout error 1.6 to 11 times in 74 simulated-device cases, never making it worse; on real hardware, 1.59 times.
Against the T1 noise plateau, the filter returns the exact gradient and lowers the shot cost from \(1/K^2\) to \(1/K\).
The echo brings wrong decisions from 15 to 3 over 945 readouts.
The scale itself separates temperature from readout error, T1 from unital noise, and thermal drift from an attack in BB84.
Each advantage has written down where it stops holding; Chapter 30 gathers the negative results.

Bibliographic notes

The restoration under T1 is a symmetry verification (Bonet-Monroig et al. 2018; McArdle et al. 2019); the echo, Hahn (1950). The neutrino results use the parameters of Esteban et al. (2020), and the BB84 monitor, the protocol of Bennett and Brassard (2014) and the proof of Shor and Preskill (2000). The numbered research notes (§) cited in this chapter and the scripts that check it are in the repository (Monteverde 2026a); the definition of the qang unit is in Monteverde (2026b).