Quantum Memory Matrix

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Originally proposed in 2024, the Quantum Memory Matrix (QMM) is a discretized, Planck-scale framework that models space-time as a four-dimensional lattice of finite-dimensional Hilbert "memory cells." Each cell can imprint the complete quantum state of any field that traverses it and later retrieve that information through a complementary unitary map.^[1] Because information is never destroyed—only redistributed among cells—the framework offers a unitary resolution of the black-hole information paradox, a natural ultraviolet cutoff, and a platform for unifying gravity with the Standard Model via gauge-invariant imprint operators. QMM also serves as a hardware-inspired blueprint for fault-tolerant quantum memory. The framework was initially developed by physicist Florian Neukart.

• 2024 (December). Publication of "The Quantum Memory Matrix" introduces the hypothesis and local imprint operators, and addresses the Black hole information paradox.^[1]
• 2024 (December). An IBM Quantum experiment demonstrates reversible imprinting and retrieval.^[2]
• 2025 (February). Two companion preprints extend QMM to electromagnetism^[3][4] and to the strong and weak sectors.^[5]
• 2025 (April). A study applies the framework to cosmological structure formation and PBH production.^[6]
• 2025 (May). Advanced Quantum Technologies reports QMM-enhanced error-correction fidelities.^[7]

• Cells and topology. QMM discretizes space-time as a four-dimensional cubic lattice ${\displaystyle {\mathcal {X}}\simeq \mathbb {Z} ^{4}}$ with spacing ${\displaystyle a\approx \ell _{P}}$. Each site x hosts a finite Hilbert space ${\displaystyle {\mathcal {H}}_{x}\cong \mathbb {C} ^{d}}$, so the global kinematic space factorizes into ${\displaystyle {\mathcal {H}}_{\text{QMM}}=\bigotimes _{x\in {\mathcal {X}}}{\mathcal {H}}_{x}}$. Local imprint generators commute at space-like separation, ensuring microcausality; information spreads through a nearest-neighbor Hamiltonian ${\displaystyle {\hat {H}}=\sum _{\langle x,y\rangle }J\,{\hat {\sigma }}_{x}{\hat {\sigma }}_{y}+\sum _{x}\lambda \,{\hat {\phi }}(x)\otimes {\hat {\sigma }}_{x}}$.

• Emergent metric. Lattice connectivity is encoded in an adjacency matrix ${\displaystyle A_{xy}}$ (equal to 1 for nearest neighbors). On coarse scales the block-averaged metric is

${\displaystyle g_{\mu \nu }(X)=\alpha \sum _{x,y\in {\mathcal {B}}(X)}A_{xy}(\Delta x)_{\mu }(\Delta x)_{\nu }}$ where ${\displaystyle {\mathcal {B}}(X)}$ is an ${\displaystyle L^{4}}$ block centered on macroscopic coordinate X and α is a normalization constant.^[1]

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

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

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

• Quantum-circuit implementation. The IBM demonstration realizes ${\displaystyle {\hat {I}}_{x}}$ as two CNOTs; retrieval fidelity is ${\displaystyle F_{\text{exp}}=0.74\pm 0.01}$ for five-qubit cycles.^[2]
• 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.^[1]

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

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

and the gauge-invariant imprint operator is

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

with ${\displaystyle {\hat {U}}_{\square }(x)}$ the plaquette loop (U(1), SU(2)_L, SU(3)_c). The Kogut–Susskind expansion recovers the Yang–Mills action.^[5]

Tracing out all but cell x defines

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

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

For V = 0 the field mimics cold dark matter; blue-tilted fluctuations trigger PBH production for ${\displaystyle \delta S/S\gtrsim 0.3}$.^[6]

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

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

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

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

raises fidelity to ${\displaystyle F_{\text{logical}}\approx 0.94}$, 32 % above the bare code.^[7]

The imprint-entropy stress tensor is

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

Regions with ${\displaystyle \partial _{X}S<0}$ act as “information wells,” collapsing into PBHs after horizon re-entry.^[6]

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

• Informational fixed point. Running couplings obey ${\displaystyle \beta _{G}=-2G+{\mathcal {O}}(G^{2})}$ and ${\displaystyle \beta _{\lambda }=0}$, yielding an interacting GIFP at ${\displaystyle (G_{\star },\lambda _{\star })}$; gravity and imprint kinetics therefore share the same asymptotic-safety basin.
• Dimensional transmutation. Below ${\displaystyle \Lambda _{\star }\sim M_{P}}$ the theory produces effective constants ${\displaystyle G_{\text{IR}}}$ and ${\displaystyle \Lambda _{\text{IR}}}$, while the imprint sector becomes scale-invariant, explaining how lattice QMM reproduces classical GR + SM in the infrared.

• Residual cell energy. Fully saturated cells store a uniform zero-point density ${\displaystyle \rho _{\text{vac}}=d_{\max }^{-1}M_{P}^{4}/16\pi ^{2}\approx (2\times 10^{-3}\,{\text{eV}})^{4}}$, naturally reproducing the observed cosmological constant.
• Slow-roll entropy field. If imprint writing remains overdamped (${\displaystyle {\ddot {S}}\ll H{\dot {S}}}$), the kinetic term ${\displaystyle \lambda (\partial S)^{2}}$ gives an equation-of-state ${\displaystyle w(a)\simeq -1+\lambda {\dot {S}}^{2}/\rho _{\text{vac}}}$, predicting ${\displaystyle w(z)+1\propto (1+z)^{6}}$.

• Causal microstructure. Local commutators vanish outside the discrete light cone; at scales ${\displaystyle \gg \ell _{P}}$ the lattice dispersion approaches ${\displaystyle E^{2}-p^{2}\approx m^{2}}$ up to ${\displaystyle {\mathcal {O}}\!{\bigl (}p^{4}\ell _{P}^{2}{\bigr )}}$.
• Boost invariance from RG. Coarse-graining drives the dynamical exponent to ${\displaystyle z\to 1}$; Lorentz symmetry thus emerges as an infrared fixed line rather than a fundamental postulate.

• CP-weighted imprints. During the electroweak crossover an initial entropy skew ${\displaystyle \Delta S/S\sim 10^{-9}}$ biases sphaleron transitions, producing the observed baryon-to-photon ratio ${\displaystyle \eta _{B}\approx 6\times 10^{-10}}$.
• No BSM fields required. The mechanism uses only Standard-Model CP violation and finite-Hilbert-space bookkeeping; it disappears in the continuum limit ${\displaystyle d_{\max }\to \infty }$, directly linking matter genesis to QMM discreteness.

• Bounce condition. A cosmological cycle ends when total imprint entropy approaches ${\displaystyle S_{\max }=A_{H}/4\ell _{P}^{2}}$; unitary shuffling then resets curvature while preserving quantum coherence.
• Information-well collapse. Blue-tilted imprint fluctuations (${\displaystyle P_{S}\!\propto k^{n_{S}-1}}$ with ${\displaystyle n_{S}>1}$) re-enter the horizon during radiation domination; regions with ${\displaystyle \delta S/S\gtrsim 0.3}$ form PBHs of mass ${\displaystyle M_{\mathrm {PBH} }\simeq \gamma M_{H}(k/aH)^{-2}}$, spanning ${\displaystyle 10^{-16}\!-\!10^{3}\,M_{\odot }}$ and seeding dark-matter and PTA signals across cycles.

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.^[8]

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

A follow-up experiment integrated a single-layer QMM dressing ahead of a length-3 repetition code on the same hardware.^[9]

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

• Hawking radiation – Late-time, non-thermal correlations carrying imprint information.^[1]
• μ-distortions and PTA background – Spectral CMB distortions and a nanohertz gravitational-wave background from imprint-seeded PBHs.^[6]
• Small CP-phase shifts – ${\displaystyle {\mathcal {O}}(10^{-4})}$ corrections to CKM/PMNS phases from imprint loops.^[5]
• LISA-band gravitational waves – A predicted stochastic signal at 0.1–1 Hz from an imprint-driven phase transition.^[6]
• Ultra-high-energy cosmic rays – Spectral suppression above 5 × 10¹⁹ eV due to the Planck-cell cutoff.^[1]

Mainstream coverage (2024–25) includes:

• Popular Mechanics dubbed QMM “memory cells of space-time”.^[10]

• New Scientist ran both a feature story^[11] and a follow-up letters page on its cosmological implications.^[12]

• Further commentary appeared in ScienceReader^[13], Rude Baguette^[14], and The Quantum Insider.^[15]

• International outlets also reported on the hypothesis:
  • Géo (France) called it “la théorie qui pourrait absolument tout bouleverser.”^[16]
  • Courrier International featured the question “L'espace-temps est-il une mémoire ?” on its front page.^[17]
  • Yahoo Actualités (France) summarized the idea for a general audience.^[18]
  • FocusTech (Italy) wrote that it “riscrive le leggi della fisica.”^[19]
  • Xataka Brasil explored quantum-gravity ramifications.^[20]
  • Levante-EMV (Spain) reported new hints that “el espacio-tiempo estaría memorizando información.”^[21]
  • Mystery Planet (Argentina) said the universe might possess “su propia memoria.”^[22]

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