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{{Short description|Emerging theory of quantum information}}
{{Infobox
| title = Quantum Memory Matrix
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}}
The '''Quantum Memory Matrix''' ('''QMM''') is a proposed framework in quantum gravity and unified-field research that models space-time as a discrete lattice of Planck-scale “memory cells”.
Each cell possesses a finite-dimensional Hilbert space and can record, in the form of a reversible ''quantum imprint'', the full quantum state of any field that interacts with it. Because the imprints can later be retrieved through unitary operations, QMM aims to preserve unitarity in extreme scenarios such as black-hole evaporation and cosmic bounces, while simultaneously furnishing an ultraviolet cut-off and a natural route to unification of the four fundamental interactions.
[[File:QMM_space_time_cells.png|thumb|upright=1.20|Planck-scale discretization envisioned by QMM.<ref name="Neukart2024" />]]
==Historical background==
* '''2024 (November).''' Publication of ''The Quantum Memory Matrix: A Unified Framework for the Black Hole Information Paradox'' lays out the Planck-scale “memory-cell” hypothesis, introduces local imprint operators, and proposes a unitary resolution of the [[Black hole information paradox]].<ref name="Neukart2024">{{cite journal |last1=Neukart |first1=Florian |last2=Brasher |first2=Reuben |last3=Marx |first3=Eike |title=The Quantum Memory Matrix: A Unified Framework for the Black Hole Information Paradox |journal=Entropy |volume=26 |issue=12 |pages=1039 |year=2024 |doi=10.3390/e26121039 |arxiv=2504.00039 |bibcode=2024Entrp..26.1039N |doi-access=free }}</ref>
* '''2024 (December).''' An IBM Quantum experiment demonstrates reversible imprinting and retrieval.<ref name="Arxiv2502">{{cite arXiv |last1=Neukart |first1=Florian |last2=Marx |first2=Eike |last3=Vinokur |first3=Valerii |eprint=2502.15766 |title=Reversible Imprinting and Retrieval of Quantum Information: Experimental Verification of the QMM Hypothesis |date=2025 |class=physics.gen-ph }}</ref>
* '''2025 (January).''' ''Annals of Physics'' publishes the '''Geometry-Information Duality (GID)''' paper, providing the theoretical foundation that links local imprint entropy to space-time curvature and unifies QMM with black-hole thermodynamics.<ref name="GID">{{cite journal |last=Neukart |first=Florian |title=Geometry–Information Duality and Black-Hole Entropy |journal=Annals of Physics |year=2025 |volume=475 |pages=125392 |doi=10.1016/j.aop.2025.125392 |doi-broken-date=22 July 2025 |url=https://www.sciencedirect.com/science/article/pii/S0003491625001253 |doi-access=free }}</ref>
* '''2025 (February).''' Two companion preprints extend QMM to electromagnetism<ref>{{cite journal |last=Neukart |first=F. |title=Planck-Scale Electromagnetism in the Quantum Memory Matrix: A Discrete Approach to Unitarity |journal=Preprints |year=2025 |number=2025030551 |doi=10.20944/preprints202503.0551.v1 |doi-access=free |url=https://www.preprints.org/manuscript/202503.0551/v1}}</ref><ref>{{cite arXiv |last1=Neukart |first1=Florian |last2=Marx |first2=Eike |last3=Vinokur |first3=Valerii |eprint=2502.15766v2 |title=Integrating Electromagnetic Interactions into the QMM Framework |date=2025 |class=physics.gen-ph }}</ref> and to the strong and weak sectors.<ref name="Neukart2025SW">{{cite journal |last=Neukart |first=F. |title=Extending the Quantum Memory Matrix Framework to the Strong and Weak Interactions |journal=Entropy |volume=27 |issue=2 |pages=153 |year=2025 |doi=10.3390/e27020153 |pmid=40003150 |pmc=11854125 |doi-access=free }}</ref>
* '''2025 (April).''' A study applies the framework to cosmological structure formation and PBH production.<ref name="PBH">{{cite arXiv |last1=Neukart |first1=Florian |last2=Marx |first2=Eike |last3=Vinokur |first3=Valerii |eprint=2506.13816 |title=Information Wells and the Emergence of Primordial Black Holes in a Cyclic Quantum Universe |date=2025 |class=physics.gen-ph }}</ref>
* '''2025 (May).''' ''Advanced Quantum Technologies'' reports QMM-enhanced error-correction fidelities.<ref name="AQT">{{cite journal |last1=Neukart |first1=Florian |last2=Marx |first2=Eike |last3=Vinokur |first3=Valerii |last4=Titus |first4=Jeff |title=QMM-Enhanced Error Correction: Demonstrating Reversible Imprinting and Retrieval for Robust Quantum Computation |journal=Adv. Quantum Technol. |year=2025 |article-number=e2500262 |doi=10.1002/qute.202500262 |url=https://advanced.onlinelibrary.wiley.com/doi/10.1002/qute.202500262|url-access=subscription }}</ref>
==Theoretical framework==
===Lattice structure===
* '''Cells and topology.''' QMM discretizes space-time as a four-dimensional cubic lattice <math>\mathcal{X}\simeq\mathbb{Z}^4</math> with spacing <math>a\approx\ell_P</math>. Each site ''x'' hosts a finite Hilbert space <math>\mathcal{H}_x\cong\mathbb{C}^d</math>, so the global kinematic space factorizes into <math>\mathcal{H}_{\text{QMM}}=\bigotimes_{x\in\mathcal{X}}\mathcal{H}_x</math>. Local imprint generators commute at space-like separation, ensuring microcausality; information spreads through a nearest-neighbor Hamiltonian <math>\hat H=\sum_{\langle x,y\rangle}J\,\hat\sigma_x\hat\sigma_y+\sum_x\lambda\,\hat\phi(x)\otimes\hat\sigma_x</math>.
* '''Emergent metric.''' Lattice connectivity is encoded in an adjacency matrix <math>A_{xy}</math> (equal to 1 for nearest neighbors). On coarse scales the block-averaged metric is
::<math>g_{\mu\nu}(X)=\alpha\sum_{x,y\in\mathcal{B}(X)}A_{xy}(\Delta x)_{\mu}(\Delta x)_{\nu}</math> where <math>\mathcal{B}(X)</math> is an <math>L^{4}</math> block centered on macroscopic coordinate ''X'' and α is a normalization constant.<ref name="Neukart2024" />
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The imprint map factorizes into a data qubit and two memory qubits: <math>\hat I=\mathrm{CNOT}_{12}\mathrm{CNOT}_{13}</math>. After idle time ''τ'', logical recovery
:<math>\hat R=\hat I^{\dagger}e^{-iH_{\text{noise}}\tau}\hat I</math>
raises fidelity to <math>F_{\text{logical}}\approx0.94</math>, 32
===Information-well cosmology===
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[[File:QMM_information_wells_PBH.png|thumb|upright=1.15|Growth of information-well depth leading to PBH collapse.<ref name="PBH" />]]
===Hilbert-space capacity and holographic bound===
* '''Finite cell dimension.''' Each Planck cell carries a Hilbert space of fixed size <math>\dim\mathcal H_x=d_{\max}\simeq\exp\!\bigl[A_{\text{cell}}/(4\ell_P^2)\bigr]\approx5\times10^{121}</math>, which follows from the covariant Bekenstein–Hawking relation and sets the ultimate UV cutoff.
* '''Arrow of time.''' Because the imprint map is CP-T odd, every interaction increases the coarse-grained entropy field <math>S(X)</math>, providing a microscopic origin for the thermodynamic arrow without breaking Lorentz symmetry at long wavelengths.
===Renormalization-group completion===
* '''Informational fixed point.''' Running couplings obey <math>\beta_G=-2G+\mathcal O(G^2)</math> and <math>\beta_\lambda=0</math>, yielding an interacting GIFP at <math>(G_\star,\lambda_\star)</math>; gravity and imprint kinetics therefore share the same asymptotic-safety basin.
* '''Dimensional transmutation.''' Below <math>\Lambda_\star\sim M_P</math> the theory produces effective constants <math>G_{\text{IR}}</math> and <math>\Lambda_{\text{IR}}</math>, while the imprint sector becomes scale-invariant, explaining how lattice QMM reproduces classical GR + SM in the infrared.
===Vacuum-imprint energy and late-time acceleration===
* '''Residual cell energy.''' Fully saturated cells store a uniform zero-point density <math>\rho_{\text{vac}}=d_{\max}^{-1}M_P^4/16\pi^2\approx(2\times10^{-3}\,\text{eV})^4</math>, naturally reproducing the observed cosmological constant.
* '''Slow-roll entropy field.''' If imprint writing remains overdamped (<math>\ddot S\ll H\dot S</math>), the kinetic term <math>\lambda(\partial S)^2</math> gives an equation-of-state <math>w(a)\simeq-1+\lambda\dot S^2/\rho_{\text{vac}}</math>, predicting <math>w(z)+1\propto(1+z)^6</math>.
===Emergent Lorentz symmetry===
* '''Causal microstructure.''' Local commutators vanish outside the discrete light cone; at scales <math>\gg\ell_P</math> the lattice dispersion approaches <math>E^2-p^2\approx m^2</math> up to <math>\mathcal O\!\bigl(p^4\ell_P^2\bigr)</math>.
* '''Boost invariance from RG.''' Coarse-graining drives the dynamical exponent to <math>z\to1</math>; Lorentz symmetry thus emerges as an infrared fixed line rather than a fundamental postulate.
===Baryogenesis by entropy bias===
* '''CP-weighted imprints.''' During the electroweak crossover an initial entropy skew <math>\Delta S/S\sim10^{-9}</math> biases sphaleron transitions, producing the observed baryon-to-photon ratio <math>\eta_B\approx6\times10^{-10}</math>.
* '''No BSM fields required.''' The mechanism uses only Standard-Model CP violation and finite-Hilbert-space bookkeeping; it disappears in the continuum limit <math>d_{\max}\to\infty</math>, directly linking matter genesis to QMM discreteness.
===Cyclic bounce cosmology and primordial black holes===
* '''Bounce condition.''' A cosmological cycle ends when total imprint entropy approaches <math>S_{\max}=A_H/4\ell_P^2</math>; unitary shuffling then resets curvature while preserving quantum coherence.
* '''Information-well collapse.''' Blue-tilted imprint fluctuations (<math>P_S\!\propto k^{n_S-1}</math> with <math>n_S>1</math>) re-enter the horizon during radiation domination; regions with <math>\delta S/S\gtrsim0.3</math> form PBHs of mass <math>M_{\mathrm{PBH}}\simeq\gamma M_H(k/aH)^{-2}</math>, spanning <math>10^{-16}\!-\!10^{3}\,M_\odot</math> and seeding dark-matter and PTA signals across cycles.
==Experimental verification==
A dedicated hardware study on IBM’s 127-qubit '''ibm_kyiv''' and '''ibm_brisbane''' devices implemented five imprint–retrieval circuits that scale from a minimal three-qubit cell to a dual five-qubit cycle.<ref>{{cite arXiv |last1=Neukart |first1=Florian |last2=Marx |first2=Eike |last3=Vinokur |first3=Valerii |eprint=2502.15766v2 |title=Reversible Imprinting and Retrieval of Quantum Information: Experimental Verification of the Quantum Memory Matrix Hypothesis |date=2025 |class=physics.gen-ph }}</ref>
* The baseline three-qubit cycle reached a retrieval fidelity of <math>F_{\text{retr}} = 0.732 \pm 0.012</math>.
* Adding a second, independent memory cell preserved fidelity within 3% (five-qubit dual cycle, <math>F = 0.704 \pm 0.014</math>).
* Phase-evolution and controlled-error runs confirmed reversibility: deliberate phase errors (δ = π⁄8) were corrected to <math>F = 0.684 \pm 0.014</math>, while control runs without injected noise restored the baseline value.
Mutual-information analyses and Pearson correlations between field and output registers excluded classical leakage, establishing unitary, local storage and recovery of quantum information as predicted by QMM.
==QMM-enhanced error correction==
A follow-up experiment integrated a '''single-layer QMM dressing''' ahead of a length-3 repetition code on the same hardware.<ref>{{cite journal |last=Neukart |first=Florian |title=QMM-Enhanced Error Correction: Demonstrating Reversible Imprinting and Retrieval for Robust Quantum Computation |journal=Advanced Quantum Technologies |volume=?? |year=2025 |article-number=e2500262 |doi=10.1002/qute.202500262 |url=https://advanced.onlinelibrary.wiley.com/doi/10.1002/qute.202500262|url-access=subscription }}</ref>
* The hybrid “QMM + Rep-3” block achieved a logical fidelity of <math>F_{\text{logical}} = 0.941 \pm 0.004</math>, a '''32 % improvement''' over the bare repetition code at identical two-qubit-gate cost.
* Noise-calibrated simulations showed that stacking three QMM layers brings the logical error rate to within 20% of a distance-three surface code while using an order of magnitude fewer qubits.
Because the imprint layer is fully unitary and measurement-free, it operates as a lightweight "booster" compatible with architectures where rapid stabilizer read-out is impractical, providing empirical support for the broader claim that space-time may function as a distributed quantum memory.
==Potential observational signatures==
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* '''μ-distortions and PTA background''' – Spectral CMB distortions and a nanohertz gravitational-wave background from imprint-seeded PBHs.<ref name="PBH" />
* '''Small CP-phase shifts''' – <math>\mathcal{O}(10^{-4})</math> corrections to CKM/PMNS phases from imprint loops.<ref name="Neukart2025SW" />
* '''LISA-band gravitational waves''' – A predicted stochastic signal at 0.1–1
* '''Ultra-high-energy cosmic rays''' – Spectral suppression above 5 × 10<sup>19</sup> eV due to the Planck-cell cutoff.<ref name="Neukart2024" />
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Mainstream coverage (2024–25) includes:
* ''
* A summary and commentary of a video by ''New Scientist'' was put out by ''ScienceReader''<ref name="ScienceReader">{{cite web |title=Does Space-Time Remember? |website=ScienceReader |date=18 June 2025 |url=https://sciencereader.com/florian-neukart-does-space-time-remember/ |access-date=13 July 2025}}</ref>
* International outlets also reported on the hypothesis and covered the ''New Scientist'' article: ▼
** ''Géo'' (France) called it
** ''Courrier International''
** ''FocusTech'' (Italy) wrote that it
▲* International outlets also reported on the hypothesis:
▲** ''Géo'' (France) called it “la théorie qui pourrait absolument tout bouleverser.”<ref>{{cite web |title=Et si l'espace-temps était doté d'une mémoire ? La théorie qui pourrait absolument tout bouleverser |website=Géo |date=17 Jun 2025 |url=https://www.geo.fr/sciences/et-si-lespace-temps-etait-dote-dune-memoire-la-theorie-qui-pourrait-absolument-tout-bouleverser-227116}}</ref>
▲** ''Courrier International'' featured the question “L'espace-temps est-il une mémoire ?” on its front page.<ref>{{cite web |title=L'espace-temps est-il une mémoire ? |website=Courrier International |date=18 Jun 2025 |url=https://www.courrierinternational.com/une/une-du-jour-l-espace-temps-est-il-une-memoire_232202}}</ref>
▲** ''FocusTech'' (Italy) wrote that it “riscrive le leggi della fisica.”<ref>{{cite web |title=L'universo potrebbe avere una memoria ? La teoria che riscrive le leggi della fisica |website=FocusTech |language=it |date=20 Jun 2025 |url=https://focustech.it/news/luniverso-potrebbe-avere-una-memoria-la-teoria-che-riscrive-le-leggi-della-fisica/}}</ref>
** ''Xataka Brasil'' explored quantum-gravity ramifications.<ref>{{cite web |title=A coisa mais chocante que a física tem a oferecer é a possibilidade de um entrelaçamento quântico reescrever a gravidade |website=Xataka Brasil |language=pt |date=22 Jun 2025 |url=https://www.xataka.com.br/ciencia/a-coisa-mais-chocante-que-a-fisica-tem-a-oferecer-e-a-possibilidade-um-entrelacamento-quantico-reescrever-a-gravidade}}</ref>
** ''Levante-EMV'' (Spain) reported new hints that
** ''Mystery Planet'' (Argentina) said the universe might possess
** ''Anomalien'' reported on the idea in an article titled "The universe may have its own memory, physicists say."<ref>{{cite web |title=The universe may have its own memory, physicists say |website=Anomalien |date=27 Jun 2025 |url=https://anomalien.com/the-universe-may-have-its-own-memory-physicists-say/ |access-date=13 July 2025}}</ref>
* Coverage specific to the QMM-enhanced error-correction experiments:
** ''HPCwire'': "Terra Quantum Reports Hardware-Validated QMM Layer for Enhancing Quantum Computation Fidelity".<ref>{{cite web |title=Terra Quantum Reports Hardware-Validated QMM Layer for Enhancing Quantum Computation Fidelity |website=HPCwire |url=https://www.hpcwire.com/off-the-wire/terra-quantum-reports-hardware-validated-qmm-layer-for-enhancing-quantum-computation-fidelity/ |access-date=14 August 2025}}</ref>
** ''KRON4'' (EIN Presswire syndication): "Terra Quantum brings quantum gravity to quantum computing: new breakthrough reduces errors without added complexity".<ref>{{cite web |title=Terra Quantum brings quantum gravity to quantum computing: new breakthrough reduces errors without added complexity |website=KRON4 |url=https://www.kron4.com/business/press-releases/ein-presswire/839754888/terra-quantum-brings-quantum-gravity-to-quantum-computing-new-breakthrough-reduces-errors-without-added-complexity/ |access-date=14 August 2025}}</ref>
==See also==
* [[Black hole information paradox]]
* [[Quantum information]]
* [[Unified field theory]]
* [[Grand
* [[Loop quantum gravity]]
* [[Quantum error correction]]
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