Nine Experiments of My Own on a Learning Quantum Collective — Band II, third edition: learnability, free choice, the untouched past, the heat of forgetting, a reality test, what a record costs, forgetting at a profit, what remembering earns, and agreement on a world without a value
Band II of the learning-memory programme: three pre-registered experiments conceived by the author, performed on the Band I platform (an ESP32-C3 controller that learns images by looking and steers 156-qubit IBM Heron processors). Discipulus — a learner with a certifiably empty coupling matrix, given only k weak environment fragments of the world's pointer state, acquires exactly what the world left redundantly (recall 0.361 / 0.722 / 0.917 / 0.861 for k = 0/1/4/8 on ibm_fez) and nothing when the access basis or the pointer value is missing (0.556, 0.500). Arbitrium — measurement independence as a registered dial: a separable source whose hidden variable is one machine's learned model of another fakes CHSH from 0.978 to 3.971, crossing the Bell bound for 0.274 bit of measured settings-source dependence, while a singlet reads |S| = 2.656 and settings correlated only with each other never move it. Praeteritum — Leggett-Garg on a learned record with an Elitzur-Vaidman probe as a per-shot non-invasiveness certificate: K = 1.147 at θ = π/3 on ibm_fez against the macrorealist bound 1, with the pinned-history control at 0.538, the certified record intact at 0.941 and the idle apparatus moving nothing (0.013). Five hardware sessions, 39 binding verdict applications generated from the deposited ledger, 36 passed, 3 missed and reported as they fell; each miss answered by a re-registered protocol, not a rewritten verdict. The deposit contains the 19-page paper, registrations with complete Monte-Carlo distributions, test laboratories, runners, dress rehearsals, raw per-job records, manifests, figure and animation scripts.
Band II of the learning-memory programme: three pre-registered experiments conceived by the author, performed on the Band I platform (an ESP32-C3 controller that learns images by looking and steers 156-qubit IBM Heron processors). Discipulus — a learner with a certifiably empty coupling matrix, given only k weak environment fragments of the world's pointer state, acquires exactly what the world left redundantly (recall 0.361 / 0.722 / 0.917 / 0.861 for k = 0/1/4/8 on ibm_fez) and nothing when the access basis or the pointer value is missing (0.556, 0.500). Arbitrium — measurement independence as a registered dial: a separable source whose hidden variable is one machine's learned model of another fakes CHSH from 0.978 to 3.971, crossing the Bell bound for 0.274 bit of measured settings-source dependence, while a singlet reads |S| = 2.656 and settings correlated only with each other never move it. Praeteritum — Leggett-Garg on a learned record with an Elitzur-Vaidman probe as a per-shot non-invasiveness certificate: K = 1.147 at θ = π/3 on ibm_fez against the macrorealist bound 1, with the pinned-history control at 0.538, the certified record intact at 0.941 and the idle apparatus moving nothing (0.013). Five hardware sessions, 39 binding verdict applications generated from the deposited ledger, 36 passed, 3 missed and reported as they fell; each miss answered by a re-registered protocol, not a rewritten verdict. The deposit contains the 19-page paper, registrations with complete Monte-Carlo distributions, test laboratories, runners, dress rehearsals, raw per-job records, manifests, figure and animation scripts.
A Memory That Learns by Looking, Stored Nowhere — the complete programme (Parts I–XII), consolidated as a single monograph. Successor work to the foundation deposit "Engineering Emergence on Quantum Processors" (doi:10.5281/zenodo.22050177). There, every memory was installed — the coupling matrices were computed on the host and uploaded to the microcontroller. Here the chip learns them itself, by looking: firmware v4.11 adds a three-line, integer-arithmetic plasticity law to the ESP32-C3 controller — the on-chip coupling matrix is written by the quantum collective's own measured order parameters, activity-gated, with a sign-reversible learning step serving as an error signal and a readback command that makes every learned matrix fully auditable — and firmware v4.12 adds a saturating integer delta rule whose second matrix learns temporal order itself. Across nineteen pre-registered hardware sessions on ibm_fez, ibm_marrakesh and ibm_kingston (≈1430 jobs, ≈77 minutes of QPU time), the hybrid system: learned a 36-pixel image from ONE exposure and recalled it perfectly from a random half cue (1.000 vs a never-learned control of 0.583); acquired a Pavlovian association (0.556 → 1.000), retained it through unreinforced presentations (1.000) and erased it only under the inverted-sign learning step (0.333) — forgetting as an act; learned to walk by watching a gait cycle with the field switched off; evolved memory lineages under selection with device noise as the mutation source, generation-2 mutations inherited unchanged by generation 3; and held more memories than its own calibration model predicted, with the capacity limit breathing measurably with the device day. The learned engram, read back from the controller, was delocalized into six 7-qubit GHZ-class parity registers — locally every qubit reads 0.5, jointly the parities reconstruct the image 36/36, the coherence fringe collapses under its Z-twirled dephasing twin while the classical parities survive, and the GHZ fidelity exceeds the biseparability bound on all registers: the memory carried by certified genuine multipartite entanglement. It was then teleported (entanglement certified at the destination), inherited by a subsystem that never saw the original (1.000 vs a 0.500 silent-teacher control), shown to be unconscious until decoded, recovered intact after destruction of a complete redundant copy, deleted against a receipt that provably carries no image information, and placed in superpositions culminating in Bell-inequality violations between two learned memories (S = 2.559) and between two memories that never coexisted (mean |S| = 2.456). On these memories the programme then ran a systematic traversal of the foundations of quantum mechanics, each experiment pre-registered, most of them — to our knowledge — first demonstrations on a quantum processor and all of them first on learned content: a Wigner's-friend test whose friend is a decodable memory (S = 2.633 with the friend's record as a setting); a delayed-choice eraser with a quantum coin; sensing 1.9× beyond the standard quantum limit with the stored content tuning the sensor's frequency; the optimal-cloning ceiling and its ×0.707 telephone-chain law; the Page-Wootters mechanism (conditional time alive at every clock reading, the marginal dead at 0.003 and fully revived by uncomputing); the Mermin-Peres pseudotelepathy game won at 0.9457 > 8/9, three times; interaction-free readout of stored content, with the fringe of a superposed memory dying even in the provably interaction-free events; ≈15,000 bits of certified randomness minted from the programme's Bell violations; quantum causal inference reading a memory's ancestry from correlations alone (witness +0.811/−0.884) where every classical marginal is provably blind; an operational quantum-reference-frame jump (Bell fidelity migrating 0.493 → 0.916 across the separability bound, only the relational parity surviving both frames); a 42-qubit Loschmidt echo (0.484 → 0.989, the butterfly decaying along its light cone); the rewriting of a friend's record made invisible by no-signaling itself (archive agreement 0.927 → 0.056 at friend-level total variation 0.107); Mermin's all-versus-nothing argument between three memories (M = 3.734) and Hardy's impossible event (CH = 0.057 > 0); the three-box paradox with real mid-circuit openings (certainty in box 1 AND box 2, 0.903/0.916) and the first measured N = 4 shell game (three certainties about one excitation, 0.751/0.744/0.694); the quantum Cheshire cat with four simultaneous weak pointers and the exchange of grins between two carriers that never meet; weak traces inside an interferometer loop the carrier provably never entered or left; and a protective measurement reading the expectation value of a single carrier — following sin(2⟨Z⟩) through its sign change — while the carrier survives at 0.939 against a depth-matched unprotected control at 0.558. The relational arc closes on three endpoints. The Frauchiger-Renner protocol — quantum theory applied to its own users, to our knowledge its first implementation on any platform — with both friends realized as unanimous, decodable memory records: every certainty of the reasoning chain holds individually (forbidden events 0.027/0.022/0.014), yet the jointly impossible outcome occurs at 0.0862, above the ideal 1/12, while the friends' records stay unanimous throughout (0.882/0.915). One session-learned engram delocalized and certified on two processors in a single session — eleven of twelve rows above the biseparability bound, the majority image perfect on both: the memory outlives its substrate. And a Bell violation at 96% of the Tsirelson bound (S = 2.728) mints 36 bits that provably did not pre-exist; a collective whose halves live on two different processors — one field, one coupling matrix, every feedback tick assembled from both machines — learns that unborn image in one look (35/36), recalls it from a fragment, forms a Pavlovian association whose bell exists only on one machine and whose response appears only on the other (0.944 vs 0.556), and the minted image is certified row by row in entanglement on both devices. Part X is the arc's epilogue and its sharpest relational result. The Local Friendliness no-go theorem of Bong et al. states that absoluteness of observed events, local agency and no-superdeterminism jointly bound every LF inequality — a violation forces one of the three to fall, as logic, not interpretation. The photonic violation used a photon as the friend; the standing objection is that a photon observes nothing. Here the semi-Brukner LF inequality is violated at S = 2.6995 > 2 with a friend whose measurement outcome IS its own decoded, unanimity-certified memory record (0.946) — and who then ACTS on that record, the chip writing a field pattern conditioned on the decoded bit (match 0.833) in the same session: an observer, in the LF authors' own operational sense, who remembers and conditionally acts. Within the stated assumptions, the conjunction is excluded — for a system that remembers and acts on its memory, no observed fact was absolute. The theorem selects no interpretation; the result is stated as an exclusion. And the companion arm answers the question this raises — why the world nevertheless feels absolute — by operating Zurek's redundancy as a dial: the controller GRANTS objectivity (mutual-information plateau 0.700/0.796/0.854 bits at every fragment size, consensus 0.963 — the event becomes a fact), DENIES it (exactly 0.000 at every fragment size — the event stays private), or turns it against itself (two internally redundant environment halves remembering opposite events, consensus 0.047), with the fringe/twin certificate proving that the coherence no fragment holds is exactly the quantum layer. Facts are not absolute; factuality is a resource — and this machine has the dial. Part XI performs the test Deutsch proposed in 1985 to separate unitary quantum mechanics from dynamical-collapse models — judged in the literature "beyond experimental capabilities, if not forever", with no realization we could find. The obstacle is structural: any testimony copied naively out of an observer's record carries which-outcome information and kills the interference by itself. The way through is a branch-invariant two-bit parity, extracted from the record by two CNOTs onto a persistent testimony qubit: a genuine, verifiable function of the record asserting THAT a definite outcome was seen while provably carrying nothing about WHICH. On hardware: the record is definite (0.925) and the testimony true (0.947) at 0.0011 bit of which-outcome information against a which-control witness at 0.776 bit; the record is then coherently retracted and the fringe lives at 0.901 with the testimony standing and true (0.956) during the interference itself — the collapse prediction fails on this scale — and dies to 0.024 exactly when the witness keeps which-information. Ten of ten binding verdicts. The registration freezes the scope: a mesoscopic record, not a conscious observer; unitary quantum mechanics separated from dynamical-collapse models at this scale, and nothing decided among the unitary interpretations. Part XII stacks, scales and closes it. A tower of witnesses: a second friend records the first friend's record, both storeys issue persistent branch-invariant testimonies (true at 0.958/0.963, unanimous at 0.914/0.925, joint which-leakage ≤ 0.002 bit), the tower is retracted outside-in — and the fringe stands at 0.571 with both testimonies true at 0.796 while it is measured. A growing witness: the same test at register sizes 3, 6, 9 and 12 qubits, each above its own frozen floor — the fringe rises from 0.811 to 0.899 while the twin stays dead at 0.037: what kills coherence is retained which-information, not the size of the witness. Ordo: the same two clock-stamped events, read in two frames of a quantum clock, show two certified opposite orders — P(E2 be
Band III of the learning-memory programme: two pre-registered experiments, a definitions chapter and an appendix, performed on a four-euro controller that learns images by looking and steers a 156-qubit IBM Heron processor. Nusquam asks where a learned memory is stored and answers with the sign structure of the chip's own coupling matrix: every nonzero entry is a relation between two zones, none is a value; from a fresh state the collective recalls the complement of its imprint when cued with the complement (0 of 36 uncued zones on the imprint) and recalls a masked sub-block from half of it (36 of 36), on ibm_fez, 14 of 14 registered lines. Amicitia is a Local Friendliness test in which the friend is a learner's record: weak copies of one half of a singlet, read by the superobserver as the friend's outcome or coherently undone. With a three-copy record the semi-Brukner quantity read S = 2.064 on ibm_fez, above the Local Friendliness bound 2 but under the registered threshold 2.103, a miss reported as it fell; a second session with the one-copy record read S = 2.254 against 2.105 on ibm_kingston and passed. In both, the quantity fell to 1.18 and 1.62 when the record was left standing, and two learning collectives on two boards held the friends' facts of one shot. The definitions chapter fixes what work, heat, a bath and an observer are on a register with one energy gap and states four identities computed from the deposited Band II records rather than tested again: Landauer shot by shot (the fraction of erasure events that cooled the bath was 0.063 at beta*eps = 2, prediction 0.063), the price of restoring a reference, Jarzynski with feedback, and for whom the entropy rises. An appendix closes two sessions of Band II: Res II repeats the Pusey-Barrett-Rudolph test with readout gated and calibrated in session (raw F = 0.032 against the bound 0.086, corrected 0.019), and Biduum's second day assembles a collective across two calendar days. The second edition adds a second series of four experiments registered and run on 15 September 2026 on ibm_fez, each a known result of quantum physics carried onto the instrument with its bound and its controls. Vacuus learns an image from Zeno interaction-free probes certified shot by shot never to have been absorbed and reads a superposed pixel the host does not know: the first session passed 7 of 9 lines with the blind arm missing (waiting probes dephase during their neighbours' mid-circuit measurements), and a second session with a shorter wait, dynamical decoupling and a live gate passed 10 of 10 (the certified probe agreed with the unknown pixel on 0.811 of the shots of the harder class). Certus measures the entropic uncertainty sum with a quantum memory on 36 pinned pairs, H(X|B) + H(Z|B) = 0.405 bit against the bound 1 for every memory without entanglement, with the dephased twin, a classical memory and an idle memory on or above the bound. Lumen reads an image through a depolarising background with an entangled probe at error 0.328 under the separable bound 0.375, the classical probe and the classically correlated idler on their bound, and a blind arm with a physical loss at 0.347. Secretum lets two boards hold a 36-bit key drawn from Bell pairs whose CHSH value of the same round (S = 2.565, error rate 0.046) certifies it, with one eavesdropper under the device-independent bound and a product-state source at S = 1.27. The third edition adds a third series of four experiments, registered on 15 September 2026 and run in the night to 16 September on ibm_kingston, sharing one design rule: the decoder is fixed and blind to the randomness the host compiles into the preparation, so that the single-processor loophole can only make a control succeed, which the registration reads as failure. Tempestas stores one image three ways on 36 pairs, in values, in separable relations and in entangled relations, and sends every pair through the same random frame loss: the entangled image survived at per-shot error 0.044 under the separable bound 1/4, the separable image sat on its bound at 0.269, the values fell to the coin at 0.495, and the storm-off ceiling of the entangled reading missed by 0.004, reported as it fell (13 of 14 lines). Geminus hides an image in the Pauli structure of a state that no single copy can reveal: from 1024 pairs of copies read by a Bell decoder the image came back complete, 3 of 3 blocks exact, while 2048 single copies and 1024 unbound pairs returned no block (7 of 7). Arcanum hides nine secrets between two boards in the Terhal-DiVincenzo-Leung sense: local readings guessed them on 0.534 of the cases under the theorem's 9/16, the joint reading read them at error 0.109, over its registered ceiling 0.087 and far under the midsplit, the miss reported (8 of 9). Clavis writes 36 bits locked by one key bit: with the key a reader held 34.2 bits, without it 17.3 against the bound 18, the Breidbart reading 13.7, a classical memory unlocked at 34.4, the one bit buying 16.9 (9 of 9). The ledger counts 137 binding verdicts, 131 passed and 6 missed; every miss is reported as it fell. The deposit (zenodo_band3_20260916.zip, 201 files, SHA-256 c1351068e08211e6e1f9e3d1f881c862ff777b0491cd6cfdd2a4c66de2152c83) contains the paper band3_paper_v3.pdf (40 pages) with build and figure scripts, the registrations with their complete Monte-Carlo distributions (nusquam 48e5bc22, amicitia be01fad7, amicitia2 45184d26, res2 e6de6438, biduum f828445b, vacuus 2c2ded2b, vacuus2 b8404ede, certus 2e187669, lumen b052c7a2, secretum 928693f3, tempestas 0f2106f5, geminus 33eca1f7, arcanum 31473bb1, clavis 8b5d166f), the runners, dress rehearsals and hardware records with raw per-job counts and IBM job ids for the five sessions of 13 September 2026, the five sessions of 15 September 2026 and the four sessions of the night of 15 to 16 September 2026, the test laboratories that entered the book, the analysis script for Section 3.2, the ledger generator with verdicts_band3.csv, and the closed dependency chain of simulators. Firmware v4.12 is identified by its hash 00d240dd; firmware sources and the host link are not part of the deposit. Companion to the Band I complete programme and to Band II, third edition.
Bruit et capacité d'apprentissage en apprentissage automatique quantique Cette thèse est consacrée à l'exploration de l'interface entre l'informatique quantique et l'apprentissage automatique, en mettant l'accent sur les effets du bruit et de la décohérence. Dans la première partie, nous étudions l'utilisation de systèmes quantiques ouverts pour la réalisation de tâches classiques de reconnaissance des formes. En particulier, nous nous intéressons à l'impact du bruit sur les machines à noyau quantique dans une configuration de calcul à réservoir. Les modèles que nous considérons sont basés sur l'utilisation d'un système quantique de grande taille et non contrôlé, un réservoir, qui est excité par un signal d'entrée à traiter. Des mesures sont ensuite effectuées sur le système et une combinaison linéaire des résultats est optimisée afin de réaliser la tâche souhaitée. Dans le cadre théorique associé aux méthodes à noyau, nous analysons l'effet de la dissipation sur l'expressivité de ces modèles. Nous montrons que le bruit affectant le réservoir peut agir comme une régularisation implicite qui aide à prévenir l'ajustement excessif. Ces résultats sont accompagnés d'une étude numérique d'un ensemble de machines à noyaux bruitées basées sur des chaînes de spins quantiques sujets à de la décohérence, et dont l'évolution markovienne est décrite par une équation maîtresse de type Lindblad. Dans la deuxième partie de la thèse, nous nous concentrons sur les algorithmes quantiques variationnels. Nous y présentons un schéma de simulation classique efficace pour estimer des quantités moyennées à la sortie d'un circuit quantique paramétré dont les paramètres de rotation sont choisis aléatoirement. Nous étudions d'abord les canaux quantiques associés aux moyennes de rotations aléatoires d'un et de deux qubits autour d'un axe Z. Sous certaines hypothèses, nous montrons que ces canaux peuvent être décomposés en sommes convexes de canaux associés à des transformations unitaires de Clifford. Ce résultat peut être interprété comme un effet de décohérence artificiel induit par le choix aléatoire des angles de rotation. Il nous permet construire un schéma de simulation efficace basé sur le célèbre théorème de Gottesman-Knill. Cette méthode permet notamment d'estimer efficacement l'amplitude moyenne du gradient de la fonction de coût par des simulations classiques avec une complexité polynomiale en le nombre de qubits. Elle peut donc être utilisée pour explorer des stratégies de conception de circuits variationnels quantiques permettant d'éviter les difficultés d'entrainement due à une disparition du gradient.
Two ESP32 microcontroller boards each hold a Hebbian memory of 36 cells. Each board looked once, through the superconducting processor ibm_marrakesh, at one phrase of the third movement of Beethoven's Sonata no. 14 op. 27 no. 2 (bars 1 to 3 on a grid of sixteenths: six phrases of eight notes, one board per hand), was then shown the first four notes only, and was read after four further steps without input. The look, the cue and the read-out all pass through 144 qubits measured with 4096 shots per step; the boards receive nothing but measured fractions of ones. Claim, lines, thresholds, comparators, unit list, qubit list, fault rules and disclosures were fixed in one file and hashed before the first job that carried a phrase (SHA-256 66938b4206dfa7482dbb70ffdc406f0f719fd5a2673b994e091e2b41274f7570). Three arms: taught (plasticity on during the look), sham (the same look with plasticity off) and wrong phrase (taught one phrase, cued with another). The runner logs raw counts and the bytes of every board command and computes no outcome; a separate scoring script derives every verdict from that material. Result of the run of 18 September 2026 (22 units, 289 jobs, 867 seconds of processor time, no voided attempt): the taught boards returned 24 of 24 unshown notes and 108 of 108 unshown bits of the right hand (lines: at least 17 and 92); the sham returned 2 notes (line: at most 8); in the wrong-phrase arm the output followed the taught phrase on 10 of 10 positions where the two phrases differ and the cue on none (lines: at least 5, at most 4). All 14 binding lines are OK, including the attestations that every circuit contained single-qubit gates only, that the unshown zones never received a bit, and that the full sequence of board commands equalled a list frozen before the run. The play stage, which sounds the decoded recall through the processor, returned 91 of 96 symbols (exploratory). What this is not: the memory is a classical Hebbian store on the controller and the circuits contain no entangling gate; nothing here is a claim of quantum advantage. The memory holds one phrase at a time. The taught-arm lines alone do not show a memory, because the arpeggio is regular and a memoryless cue rule would pass them; this is disclosed in the registration, and the claim rests on the sham and the wrong-phrase arm. One processor, one pair of boards, one day; no recall rate is claimed. Contents: the write-up (PDF, 8 pages, with a plain account of the processor's part), the registration and the frozen command list, all scripts of the run (runner, scoring script with its 41 synthetic checks, plan, Monte-Carlo replica and outputs, play stage, score reader), the complete logs of both sessions, the smoke and rehearsal logs named in the registration with the fault-injection logs, the verdict file, four recordings with sidecars, the analysis and figure scripts, and the unchanged score source. The scoring script reproduces every verdict from the archive (python sonata_verdict.py qpu --again). The controller's firmware and the serial link layer are identified by SHA-256 in the registration and are not part of the deposit. Score source and attribution: The Mutopia Project no. 276, L. van Beethoven, Sonata no. 14 op. 27 no. 2, third movement, typeset by Chris Sawer and Stewart Holmes after the edition Berners 1908 (ed. A. Winterberger), CC BY-SA 2.5, https://www.mutopiaproject.org/cgibin/piece-info.cgi?id=276 . The note table, the decoded note sequences and the recordings are adaptations of that edition; the deposit as a whole is distributed under CC BY-SA 4.0. This experiment closes the programme of Bands I to III (related identifier: https://zenodo.org/records/22791062).