Quantum Memory Matrix

Quantum Memory Matrix

QMM_space_time_cells.png Planck-scale lattice of “memory cells” (schematic)
Fields	Quantum gravity · Quantum information science
Authors	Florian Neukart, Valerii Vinokur, Reuben Brasher, Eike Marx
Year proposed	2024
Related topics	Black hole information paradox · Loop quantum gravity · Quantum error correction

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.

Planck-scale discretization envisioned by QMM.

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.
• 2024 (December). An IBM Quantum experiment demonstrates reversible imprinting and retrieval.
• 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.
• 2025 (February). Two companion preprints extend QMM to electromagnetism and to the strong and weak sectors.
• 2025 (April). A study applies the framework to cosmological structure formation and PBH production.
• 2025 (May). Advanced Quantum Technologies reports QMM-enhanced error-correction fidelities.

Theoretical framework

Lattice structure

• Cells and topology. QMM discretizes space-time as a four-dimensional cubic lattice ${\mathcal {X}}\simeq \mathbb {Z} ^{4}$ with spacing $a\approx \ell _{P}$. Each site x hosts a finite Hilbert space ${\mathcal {H}}_{x}\cong \mathbb {C} ^{d}$, so the global kinematic space factorizes into ${\mathcal {H}}_{\text{QMM}}=\bigotimes _{x\in {\mathcal {X}}}{\mathcal {H}}_{x}$. Local imprint generators commute at space-like separation, ensuring microcausality; information spreads through a nearest-neighbor Hamiltonian ${\hat {H}}=\sum _{\langle x,y\rangle }J\,{\hat {\sigma }}_{x}{\hat {\sigma }}_{y}+\sum _{x}\lambda \,{\hat {\phi }}(x)\otimes {\hat {\sigma }}_{x}$.
• Emergent metric. Lattice connectivity is encoded in an adjacency matrix $A_{xy}$ (equal to 1 for nearest neighbors). On coarse scales the block-averaged metric is

$g_{\mu \nu }(X)=\alpha \sum _{x,y\in {\mathcal {B}}(X)}A_{xy}(\Delta x)_{\mu }(\Delta x)_{\nu }$ where ${\mathcal {B}}(X)$ is an $L^{4}$ block centered on macroscopic coordinate X and α is a normalization constant.

Imprint and retrieval maps

A local field interaction ${\hat {\phi }}(x)$ is encoded by the unitary imprint

${\hat {I}}_{x}=\exp \!{\bigl (}i\,\lambda \,{\hat {\phi }}(x)\otimes {\hat {\sigma }}_{x}{\bigr )},$

with inverse ${\hat {I}}_{x}^{\dagger }$. The map is reversible, and finite d supplies an ultraviolet cutoff.

• Quantum-circuit implementation. The IBM demonstration realizes ${\hat {I}}_{x}$ as two CNOTs; retrieval fidelity is $F_{\text{exp}}=0.74\pm 0.01$ for five-qubit cycles.
• Black-hole unitarity. In Hawking evaporation the partner mode is imprinted on horizon cells and later retrieved into outgoing radiation, giving a unitary S-matrix.

Gauge-field embedding

Gauge fields reside on links. A U(1) holonomy is

$U_{xy}=\exp \!{\bigl (}i\,e\,{\hat {A}}_{\mu }(x)\,\Delta x^{\mu }{\bigr )},$

and the gauge-invariant imprint operator is

${\hat {I}}_{x}=\exp \!{\Bigl (}i\,g\,\operatorname {Re} \![\operatorname {Tr} {\hat {U}}_{\square }(x)]\otimes {\hat {\sigma }}_{x}{\Bigr )},$

with ${\hat {U}}_{\square }(x)$ the plaquette loop (U(1), SU(2)_L, SU(3)_c). The Kogut–Susskind expansion recovers the Yang–Mills action.

Effective imprint-entropy field

Tracing out all but cell x defines

$S(x)=-\operatorname {Tr} _{{\mathcal {H}}_{x}}[\rho _{x}\ln \rho _{x}]$. Coarse-graining gives a scalar field S with action

$S_{\text{eff}}=\int d^{4}X{\sqrt {-g}}{\bigl [}R/(16\pi G)+\eta (\nabla S)^{2}-V(S){\bigr ]}$.

For V = 0 the field mimics cold dark matter; blue-tilted fluctuations trigger PBH production for $\delta S/S\gtrsim 0.3$.

Color confinement

Sequential imprints along a q\bar q line yield a linear potential,

$V(R)\simeq \sigma R$ with tension $\sigma \approx g_{s}^{2}/(4\pi a^{2})$, mirroring SU(3) confinement.

Color-flux tube realized as a chain of local imprints.

Quantum-error-correction analogy

The imprint map factorizes into a data qubit and two memory qubits: ${\hat {I}}=\mathrm {CNOT} _{12}\mathrm {CNOT} _{13}$. After idle time τ, logical recovery

${\hat {R}}={\hat {I}}^{\dagger }e^{-iH_{\text{noise}}\tau }{\hat {I}}$

raises fidelity to $F_{\text{logical}}\approx 0.94$, 32% above the bare code.

Information-well cosmology

The imprint-entropy stress tensor is

$T_{\mu \nu }^{({\text{QMM}})}=\eta [(\nabla _{\mu }S)(\nabla _{\nu }S)-{\tfrac {1}{2}}g_{\mu \nu }(\nabla S)^{2}+g_{\mu \nu }\Box S-\nabla _{\mu }\nabla _{\nu }S]$.

Regions with $\partial _{X}S<0$ act as “information wells,” collapsing into PBHs after horizon re-entry.

Growth of information-well depth leading to PBH collapse.

Hilbert-space capacity and holographic bound

• Finite cell dimension. Each Planck cell carries a Hilbert space of fixed size $\dim {\mathcal {H}}_{x}=d_{\max }\simeq \exp \!{\bigl [}A_{\text{cell}}/(4\ell _{P}^{2}){\bigr ]}\approx 5\times 10^{121}$, 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 $S(X)$, providing a microscopic origin for the thermodynamic arrow without breaking Lorentz symmetry at long wavelengths.

Renormalization-group completion

• Informational fixed point. Running couplings obey $\beta _{G}=-2G+{\mathcal {O}}(G^{2})$ and $\beta _{\lambda }=0$, yielding an interacting GIFP at $(G_{\star },\lambda _{\star })$; gravity and imprint kinetics therefore share the same asymptotic-safety basin.
• Dimensional transmutation. Below $\Lambda _{\star }\sim M_{P}$ the theory produces effective constants $G_{\text{IR}}$ and $\Lambda _{\text{IR}}$, 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 $\rho _{\text{vac}}=d_{\max }^{-1}M_{P}^{4}/16\pi ^{2}\approx (2\times 10^{-3}\,{\text{eV}})^{4}$, naturally reproducing the observed cosmological constant.
• Slow-roll entropy field. If imprint writing remains overdamped (${\ddot {S}}\ll H{\dot {S}}$), the kinetic term $\lambda (\partial S)^{2}$ gives an equation-of-state $w(a)\simeq -1+\lambda {\dot {S}}^{2}/\rho _{\text{vac}}$, predicting $w(z)+1\propto (1+z)^{6}$.

Emergent Lorentz symmetry

• Causal microstructure. Local commutators vanish outside the discrete light cone; at scales $\gg \ell _{P}$ the lattice dispersion approaches $E^{2}-p^{2}\approx m^{2}$ up to ${\mathcal {O}}\!{\bigl (}p^{4}\ell _{P}^{2}{\bigr )}$.
• Boost invariance from RG. Coarse-graining drives the dynamical exponent to $z\to 1$; 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 $\Delta S/S\sim 10^{-9}$ biases sphaleron transitions, producing the observed baryon-to-photon ratio $\eta _{B}\approx 6\times 10^{-10}$.
• No BSM fields required. The mechanism uses only Standard-Model CP violation and finite-Hilbert-space bookkeeping; it disappears in the continuum limit $d_{\max }\to \infty$, 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 $S_{\max }=A_{H}/4\ell _{P}^{2}$; unitary shuffling then resets curvature while preserving quantum coherence.
• Information-well collapse. Blue-tilted imprint fluctuations ($P_{S}\!\propto k^{n_{S}-1}$ with $n_{S}>1$) re-enter the horizon during radiation domination; regions with $\delta S/S\gtrsim 0.3$ form PBHs of mass $M_{\mathrm {PBH} }\simeq \gamma M_{H}(k/aH)^{-2}$, spanning $10^{-16}\!-\!10^{3}\,M_{\odot }$ 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.

• The baseline three-qubit cycle reached a retrieval fidelity of $F_{\text{retr}}=0.732\pm 0.012$.
• Adding a second, independent memory cell preserved fidelity within 3% (five-qubit dual cycle, $F=0.704\pm 0.014$).
• Phase-evolution and controlled-error runs confirmed reversibility: deliberate phase errors (δ = π⁄8) were corrected to $F=0.684\pm 0.014$, 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.

• The hybrid “QMM + Rep-3” block achieved a logical fidelity of $F_{\text{logical}}=0.941\pm 0.004$, 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

• Hawking radiation – Late-time, non-thermal correlations carrying imprint information.
• μ-distortions and PTA background – Spectral CMB distortions and a nanohertz gravitational-wave background from imprint-seeded PBHs.
• Small CP-phase shifts – ${\mathcal {O}}(10^{-4})$ corrections to CKM/PMNS phases from imprint loops.
• LISA-band gravitational waves – A predicted stochastic signal at 0.1–1 Hz from an imprint-driven phase transition.
• Ultra-high-energy cosmic rays – Spectral suppression above 5 × 10¹⁹ eV due to the Planck-cell cutoff.

Reception

Mainstream coverage (2024–25) includes:

• New Scientist ran a feature story written by Neukart which was covered by Popular Mechanics and The Quantum Insider.
• A summary and commentary of a video by new scientist was put out by ScienceReader
• International outlets also reported on the hypothesis and covered the New Scientist article:
  • Géo (France) called it "la théorie qui pourrait absolument tout bouleverser."
  • Courrier International explained that the New Scientist article is on the front page of the New Scientist.
  • FocusTech (Italy) wrote that it "riscrive le leggi della fisica."
  • Xataka Brasil explored quantum-gravity ramifications.
  • Levante-EMV (Spain) reported new hints that "el espacio-tiempo estaría memorizando información."
  • Mystery Planet (Argentina) said the universe might possess "su propia memoria."

See also

• Black hole information paradox
• Quantum information
• Unified field theory
• Grand unified theory
• Loop quantum gravity
• Quantum error correction