QPC Holographic Memory

Generate a binary pattern, encode it into a QPC circuit (superposition + phase encoding + spreading layers), then measure only k of N qubits on real hardware. From the k-bit outcome distribution, compute marginals and infer the full N-bit pattern. Compare reconstructed to original; report full, observed-only, and unobserved-only accuracy.

Standard benchmarks measure all qubits. Here we show that QPC can support a different regime: partial observation with full reconstruction. That is a distinct architectural layer—distributed storage and holographic-style recovery—aligned with research directions in quantum holography, associative memory, and distributed representation (including ideas from brain microtubule and interference-based memory models).

In optical holography, a 3D scene is encoded into an interference pattern on a plate. Even a fragment of the hologram can reconstruct the full image when illuminated. Here we do the computational analog: the pattern is encoded into the quantum interference field; we measure only a subset of qubits (a “fragment” of the full state). The decoder recovers the full pattern from that partial signal. So the test is a proof of concept for any application where full information must be recoverable from partial readout—imaging, compressed sensing, or redundant distributed storage.

In Hopfield-like associative memory, patterns are stored in a distributed way across many units; presenting a partial or noisy cue can recall the full pattern. The holographic benchmark implements a similar idea in a QPC circuit: the pattern is spread across qubits via phases and entanglement; partial measurement (a “cue”) is used to reconstruct the full pattern. So the capability is relevant for associative recall, content-addressable memory, or any setting where “full state from partial view” is required.

Theories of quantum cognition and brain microtubule models propose that neural information can be represented in a distributed, interference-based way—closer to holographic storage than to local registers. The QPC holographic benchmark is a computational analog: it shows that a quantum circuit can store a pattern in a distributed manner and recover it from partial observation. So it fits the research direction of quantum-inspired or quantum-supported distributed representation and holographic information processing.

In sensor or agent networks, you often have access only to a subset of nodes (failed links, limited bandwidth, or privacy). The question is: can we still infer the full system state? The benchmark demonstrates that QPC can encode a full pattern and then “observe” only part of the system (k qubits) and still reconstruct the whole. So it is a proof of concept for full-state inference from partial sensors when the encoding is distributed and interference-based.

In holographic storage, redundancy means that damage to part of the medium does not destroy the stored information—the rest can still reconstruct it. Here, “measuring only k qubits” simulates having access to only part of the stored state. If reconstruction accuracy remains meaningful, the architecture supports robustness to partial loss or partial access, useful for fault-tolerant or distributed memory designs.

Bottom line: The holographic memory test shows that QPC supports a distinct capability layer: distributed encoding and full-pattern reconstruction from partial measurement. The same idea applies to holography-style imaging, associative memory, quantum-inspired distributed representation, sensor-network inference, and robust storage.

The QPC holographic script is a computational analog of a possible holographic process. Here we explain how you can interpret and use it in a brain-inspired model where information is stored in tubulins and microtubules (e.g. as in quantum cognition and microtubule-based memory theories), using the QPC notions of Kenograms (contextual units / state carriers) and Contextures (distinct logical layers). We map each step of the script to this model and clarify entanglement and transitions between contextures. This is a theoretical and computational mapping—not a claim that the brain runs this exact circuit.

Inside neurons, microtubules are cylindrical polymers made of tubulin subunits. In some theories (e.g. Orch-OR, quantum cognition), tubulins can occupy different conformational or dipole states and may sustain quantum coherence over short times and distances. Information is then not stored in a single tubulin but distributed across many tubulins along a microtubule (and possibly across microtubules). The system behaves more like a hologram: the “pattern” is written into the collective phase and entanglement of many units, so that partial observation (e.g. only some tubulins coupled to the environment or “read” by downstream biochemistry) could in principle still allow reconstruction of the full pattern. The holographic script implements this idea in a minimal quantum circuit.

Kenograms (in QPC) are the minimal contextual units that carry state and participate in logical operations—here they correspond to sites that can hold a binary or phase state. In the script, each qubit is one such site (N qubits = N sites). In the tubulin model, each tubulin (or each lattice site along a microtubule) is one Kenogram: it can be in different states (e.g. 0/1 or phase-encoded), and the pattern is the initial configuration of these states (which tubulins are “on” or “phase-marked”).

Contextures are distinct logical or operational layers that coexist and interact. In the script there are three contextural layers (three “contexts”): (0) pattern as phase on a superposition, (1) spreading along the chain, (2) a second phase layer. In the tubulin/microtubule model you can think of them as follows. Contexture 0 (Kenogrammatic): Initial state preparation—the “pattern” is written as phases (or conformational/dipole states) on the tubulins, after a global superposition (all sites in a coherent mix). Contexture 1 (Spreading / morphogrammatic): Information is spread along the microtubule by entangling neighboring tubulins (the chain of CX gates in the script). This creates correlations so that the pattern is no longer local but distributed across the chain. Contexture 2: A second phase layer adds another contextual interference; the full state is then a polycontextural interference field. Transitions between contextures are the passage from one layer to the next (e.g. from “pattern written” to “spreading” to “second phase”)—in the circuit these are the barriers between layers; in the biological analogy they could be thought of as temporal or structural transitions (e.g. conformational waves or coupling changes along the microtubule).

In the script, entanglement is created by the chain of two-qubit (CX) gates in Contexture 1: each site is coupled to its neighbor, so the state of one qubit depends on the others. In the tubulin model, entangled tubulins would mean that the state of one tubulin is quantum-correlated with others (e.g. along the same microtubule or across junctions). The script thus gives a concrete recipe: a linear chain of sites (one microtubule, or one strand of tubulins) with nearest-neighbor coupling that spreads the initial pattern into a distributed, non-local state. The more the information is spread, the more “holographic” the storage: no single tubulin holds the full pattern; the pattern is in the joint state. That is why partial readout can still recover it—the statistics of the observed sites (marginals) carry information about the whole.

The script measures only k of N qubits (e.g. 16 of 32). In the brain model, not all tubulins are “observed” at once—only a subset might couple to the environment, to molecular motors, or to downstream signaling at a given time. So partial measurement in the script models this: only k sites (tubulins) are “read”; the rest remain unobserved. The device returns a distribution over k-bit outcomes (e.g. 4096 shots). From that we compute marginals—the probability that each observed site is in state 1—and from marginals we decode the full N-bit pattern (observed sites from marginals, unobserved by interpolation from nearest observed). That decoding step is the holographic reconstruction: full pattern from partial readout. In the biological analogy, “reconstruction” would be the process by which the rest of the pattern (the state of unobserved tubulins) is inferred or functionally recovered from the partial signal.

Transitions between contextures in the script are the step from one layer to the next (Contexture 0 → 1 → 2). In the tubulin model these can be interpreted as (a) temporal transitions—the system first writes the pattern (kenogrammatic), then spreads it (entanglement along the microtubule), then adds the second phase (another contexture)—or (b) structural transitions—different segments or modes of the same microtubule (or different microtubules) acting as different contextures that interact. Transitions between states (e.g. tubulin conformational change, or 0↔1 flip) are not explicitly modeled as gates in this script; the script encodes a fixed pattern and then spreads and measures it. But the phase rotations (RZ) in each contexture can be seen as setting the “state” or phase of each Kenogram; changing those phases would correspond to different patterns or different moments in time. So you can use the same circuit structure with different pattern inputs (or different RZ angles) to model transitions from one stored pattern to another—e.g. one pattern per “memory” or per time step.

To use the holographic script as a computational model of tubulin/microtubule holographic storage:

• N qubits = N tubulin sites (e.g. one microtubule segment, or N sites across several). Use --qubits 32 or 64, 128 as a proxy for the number of sites.
• Pattern = initial configuration of tubulin states (which are “on” or phase-marked). You can fix a pattern (seed) or sweep many to study robustness.
• Three contextures = Kenogrammatic (phase encoding), Spreading (chain entanglement), Second phase. These are the three “layers” in the script; keep them to match the Kenogram/Contexture picture.
• k observed = number of tubulins that are “read” (coupled to environment or measurement). Use --observe 16 for half, or fewer/more to study how reconstruction degrades with less partial readout.
• Marginals → decode = the holographic reconstruction step: from the statistics of the k observed sites, infer the full N-site pattern. Accuracy (ideal vs hardware) tells you how well the distributed encoding survives noise (device noise in the lab; in the brain, decoherence or biochemical noise).

Running ./run_holographic.sh --qubits 32 --observe 16 --compare-simulator gives you (1) ideal reconstruction accuracy (noiseless) and (2) hardware accuracy (noise-limited). The gap illustrates that the logic of holographic storage and reconstruction works; the limit is the “environment” (noise). In the tubulin model, that would correspond to the idea that the architecture can in principle support full-pattern recovery from partial observation, while real biological noise and decoherence limit the fidelity.

So you can use this script and computation as a concrete implementation of a tubulin/microtubule hologram model where Kenograms are the tubulin sites, Contextures are the three encoding layers (with entanglement and transitions between them), and partial observation leads to full-pattern reconstruction—with the caveat that this is a computational and theoretical analog, not a literal claim about biophysical implementation.

• 1. Generate a random N-bit pattern (e.g. N=32).
• 2. Build QPC circuit: H on all, phase encode pattern (RZ on 1s), spreading (chain CX+RZ), second phase layer. Three polycontextural layers.
• 3. Measure only k qubits (e.g. k=16) to a classical register—real partial measurement on device.
• 4. Run on noiseless simulator (ideal) and on IBM hardware (e.g. Fez, Torino, Pittsburgh). From k-bit counts compute marginals; decode full pattern (observed qubits from marginals, unobserved by interpolation from nearest observed).
• 5. Report full, observed-only, and unobserved-only accuracy. Compare ideal vs hardware; gap interpreted as device noise.

./run_holographic.sh --qubits 32 --observe 16 --compare-simulator -o qhm_compare.json or python3 qpc_holographic_memory.py --qubits 32 --observe 16 --compare-simulator -o qhm_compare.json

PQST-64 shows supremacy-style output. QPC Crash Detection shows cascade detection. PRCBS and RICT encode–decode show relational encoding and graph reconstruction from full measurement. All run on real hardware.

This test adds a distinct capability: partial measurement with full-pattern reconstruction. It does not replace the others; it demonstrates a different architectural layer—distributed, holographic-style storage and recovery—that aligns with optical holography, associative memory, distributed representation, and quantum-inspired cognition research. Ideal vs hardware comparison (Fez, Torino, Pittsburgh) shows the task is mastered in principle, with outcomes on current IBM hardware restricted by device noise.

Together, PQST-64, Crash Detection, PRCBS, RICT encode–decode, and QPC Holographic Memory give a consistent story: supremacy-style output, application (crash), relational decode (full measurement), and holographic reconstruction from partial measurement as a distinct capability layer.