Heurémen

Superconducting qubits on seven IBM processors and Rigetti Cepheus-1-108Q. Every finding links to its data.

One event, read from three positions, and the disagreement kept: EL MIRÓN the observer, EL TESTIGO the witness, EL TIEMPO time. Two readings can never say which of them is wrong — that information is not in a pair. Pointed at three things: what a measurement costs, how far it reaches, and how long it took.

New here? What we measured, in plain words — no background assumed. The technical version is here.

Superposition — what a measurement costs beyond the clock

we stateMeasuring a qubit costs the qubits around it more than the time it occupies — once there are more than nine measurements. Below that, the cost is the clock.
standard viewA spectator qubit's coherence decays with elapsed time. A measurement occupies time, so it costs what that time costs and nothing more.
what we foundAgainst the same span of idle: 0.99–1.03 up to 9 measurements, then 1.16–1.18 at 27. And at 128 the measured qubit passes fully mixed at 25.5 and reaches 0.067 of where it started, where 40 µs of plain idle leaves it at 0.661. Repeated measurement drives a qubit through the middle rather than letting it settle there.
the run11 October, ibm_fez, three separate jobs: a free spectator through 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128 measurements — 4,179 measurements in all. One three-parameter stretched exponential passes every point in all six fits, worst χ²/dof 1.38. The two seats fall in different shapes: 0.823 ± 0.013 for the measured qubit against 1.381 ± 0.074 for the spectators, 7.4 widths apart. all three reads, verbatim · the_count.py

Entanglement — how far a measurement reaches

we stateMeasuring one qubit disturbs qubits nobody touched, and the disturbance behaves like something radiated rather than something wired.
standard viewCrosstalk follows the wiring. A disturbance on an unmeasured qubit should track its wired neighbours, or the nearest measured one.
what we foundNeither predictor wins. Σ1/r² over every measured qubit orders the spectators best — better than counting neighbours, better than nearest distance. It fades with separation (1.03 → 1.02 → under 1.01 against an idle control of 0.99), it grows with how many measured qubits sit in range (1.039 → 1.181, reproduced on a redrawn layout on a second processor), and ringing one qubit with measurement multiplies it to 2.07 / 2.29 / 3.25 against 1.04 in the open.
the runAnd the correlation itself, measured both ways in one session: two entangled qubits rotated by θ, against a single qubit measured–rotated–measured. The same cos θ, at all seven angles including both nulls. Separation in time does the work of separation in space. No-signaling held on a first run and a balanced rerun. space and time, the runs · the reach

Time — one event, three seats, three answers

we stateA duration is not a fact. It is a reading, and whoever takes it is part of it. One operation, timed from three positions, gives three answers in a fixed order.
standard viewA readout takes the duration the scheduler says it takes. A discrepancy is calibration error or crosstalk.
what we foundOne readout timed three ways in the same job, on seven processors: the chip's spec sheet says 2.18 µs, an untouched qubit's accumulated phase says 2.32, the measured qubit's own decay says 3.79. The order is the same on 7 of 7 while every value moves chip to chip. Witness over maker is one constant: 1.0331 ± 0.0083, 4.0σ from no effect. And the clock is a qubit too: a slower spectator reports a longer event, on every processor tested.
the runThe figure is a slope, not a ratio of levels: the spectator's phase against measurement count, so anything added to every point equally cannot move it. Fed a dataset built with a pure overhead and no effect, planted costs of 0, 0.2, 1.0 and 5.0 µs return slope/L of 1.0007, 1.0011, 1.0026, 0.9994, while the cost itself is recovered to the digit. The intercept that fit always discarded, now printed per spectator on all seven processors — 21 runs, 767 spectators — is −0.036 ± 0.038 µs, one constant at χ²/dof 0.18. The two durations differ by a factor, not by a constant. the run, verbatim · split_seven_chips.py

The apparatus, and the floor under it

An idle qubit keeps its books — three parking methods, residual against its own decay
±0.002
detail
A 4 % stretch planted in simulated qubits reads back 1.037–1.039; with nothing planted, 1.000
1.000
verify
Decay is not a single exponential, per qubit: population below its own 300 µs extrapolation at 30 µs
62–84 %
detail

The discarded half, on a chip

A three-box weak measurement: the corner that should hold a negative number of particles does, 9σ below zero. Real boxes +0.773, +0.763
−0.506 ± 0.057
code

The processors themselves

T1 drifts up to 10 µs between jobs and holds steady within one
174/177/181 µs
code
The effect sorts processors into two groups matching the manufacturer's own T2:T1 ordering; survives re-reading on blind and on seeing clocks (+0.98, +0.93)
1.22–1.35 / 1.45–1.78
detail
Each push costs more than stated and the cost is negative — second and third chip, all three rulers, every read, 54–70 % of individual qubits carry it
−0.0014 to −0.0020
per push
detail
Zero on the one processor with a square lattice instead of heavy-hex
−0.00002
detail
Each push costs this multiple of the manufacturer's stated gate error
4 – 8.5×
detail

The clock is a qubit too

Weakly-detuned spectator qubits report a longer measurement, on all seven processors — Spearman
−0.17 to −0.56
verify
A measurement we laid ourselves on a second vendor, no manufacturer number in it — a tone of known length swept over four lengths, no-tone control 0.99. Fitting rate and offset together per clock
slope 1.0114 ± 0.0045
offset +0.035 ± 0.015 µs
Rigetti

Light — a ruler for relative error

Where the rulers come from: x² = x + 1 has two roots, and we keep both. The one that grows, φ = 1.6180339887, carries magnitudes — what every instrument reports — and closes on π = 10 · arcsin(1/2φ), exact, because 1/2φ = sin 18°. The one that shrinks, ψ = −0.6180339887, carries signs, and |·|² deletes them — so the discarded half is read as data: the absence, the edge, the null. And φ − ψ = √5 never closes. That gap is not an error to calibrate out; it is why there is a clock at all. Las Ecuaciones

Ramanujan's 1/π series gains about eight digits per term — per-term ratio 256/396⁴. Its own errors make a ladder any relative error can be placed on
1.0410×10⁻⁸
La Siete
That ladder's first two rungs, as relative error — which is why it cannot resolve anything between 10⁻² and 10⁻⁶: one step is 7.6 decades wide
2.43×10⁻⁸ · 2.04×10⁻¹⁶
La Siete
φ is the worst-approximable irrational — every partial quotient is 1, the slowest-converging continued fraction. Its Fibonacci convergents are simultaneously the best approximations to it and the hardest rationals to tell apart from it
[1; 1, 1, 1, …]
El Reloj
The width needed to exclude each convergent — 3/2, 5/3, 8/5, 13/8, 21/13, 34/21
3.65 % → 0.031 %
table
A nonlinearity makes only 2f, 3f, f+g, f−g — integer combinations. No integer combination ever equals f·φ, so an irrational leg is the one corner an apparatus cannot forge
f : f·12/11 : f·φ
El Picnic
Coherence time from a linewidth, which is a difference — how long a phase may be carried before it is noise
τ = 1/(π·Δν)
equations

Full write-up with charts · 305 runs with their data, and verify.py — recomputes every qubit figure from 34 KB in one command, no account, no network · Rigetti · entanglement across time · calls already tested · Seven · El Reloj · Las Ecuaciones · El Bonefish · Las Fallas · Las Guardas
Raw shot data ~22 GB on request.  Heuremen LLC  “We found it.”