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

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. 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.

Planck-scale discretization envisioned by QMM.

Historical background

• 2024 (December). Publication of "The Quantum Memory Matrix" introduces the hypothesis and local imprint operators, and addresses the Black hole information paradox.
• 2024 (December). An IBM Quantum experiment demonstrates reversible imprinting and retrieval.
• 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.

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:

• Popular Mechanics dubbed QMM “memory cells of space-time”.

• New Scientist ran both a feature story and a follow-up letters page on its cosmological implications.

• Further commentary appeared in ScienceReader, Rude Baguette, and The Quantum Insider.

• International outlets also reported on the hypothesis:
  • Géo (France) called it “la théorie qui pourrait absolument tout bouleverser.”
  • Courrier International featured the question “L'espace-temps est-il une mémoire ?” on its front page.
  • Yahoo Actualités (France) summarized the idea for a general audience.
  • 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
• Unified field theory
• Grand unified theory
• Loop quantum gravity
• Quantum error correction