Quantum Logic + Max-Plus in Scheduling Problems ①🥇

I have compiled a report on the concept of "Quantum Logic-based Scheduling Emulation," born from the intersection of 40 years of Prolog experience and 27 years of on-site expertise.

Report: Quantum Logic Emulation in SCM Algebra

~ Abandoning sequential search for batch calculation via field interference ~

1. Background of the concept and paradigm shift

Conventional scheduling algorithms (sequential processing in Python, etc., or simple backtracking in Prolog) were particle-like searches, akin to a "mouse walking through a maze." This concept abandons that approach in favor of "field computation," where water is poured into the entire maze at once.

Core concepts

• From search to interference: Instead of "searching for the correct answer," we "carve the universe with a mold (mask) of constraints, and what remains is the correct answer."

• Spatialization of time: Trade off procedural if-then loops (time) for bit-width (space) to achieve simultaneous judgment of all solutions in a single clock cycle.

2. Three-layer hybrid architecture

To achieve both logical rigor and extreme computational speed, I propose the following three-layer structure.

① Symbolic Layer (CHR: Constraint Handling Rules)

An interface for describing on-site tacit knowledge and constraints (e.g., "A is before B").

• Role: Blueprint for quantum gates.

• Features: Defines irreversible "field rules" where the "state" is reactively rewritten the moment a constraint is injected.

② Bit-Parallel Layer (Emulating quantum superposition)

Packing parallel worlds using arbitrary-precision integers (infinite-precision bit strings).

• Mechanism: Expand all permutations of 5 items ($${5! = 120}$$ combinations) into a 120-bit register.

• Calculation: Generate constraints as "bitmasks" and interfere with all parallel worlds at once using a single logical AND operation.

• Benefits: By dividing a problem of $${50}$$ items into clusters of $${5}$$ items each, combinatorial explosion is contained within the bit-width.

③ Max-Plus Algebra Layer (Calculation of dynamic timing)

Elevating time calculation to "tropical geometry"-style matrix operations.

• Definition: * Addition: $${x \oplus y = \max(x, y)}$$ (synchronization/waiting)

  • Multiplication: $${x \otimes y = x + y}$$ (accumulation of work)

• Role: Eliminating sequential calculation and propagating the completion time of all tasks as a wave via the matrix product $${x(k+1) = A \otimes x(k)}$$.

3. Extension via "Bloch Sphere" tokens (innocent evolution)

Extending tokens on a Petri net from mere "points" to "Bloch spheres," and introducing the concept of **"Phase."**

Conceptual physical meaning Interpretation on scheduling State vector$${0\rangle}$$ and Phase ($${\phi}$$) Vector rotation "Fluctuations" in fine-grained timing on-site.Interference Wave cancellation; automatically eliminates routes where phases do not match (resource conflicts).

4. Conclusion: Why this is the "strongest"

• Redefining Prolog: Utilizing Prolog not merely as a "search engine," but as a **"compiler that burns logic into bitmasks."**

• Breaking away from Pythonic thinking: By eliminating conditional branching and replacing everything with logical and algebraic operations, computational efficiency accelerates to the physical limit (CPU register width).

• Instant annihilation of contradictions: Deadlocks and constraint contradictions are detected instantly when the bit string becomes 0 ("annihilation of the entire universe").

Based on this report, shall we move on to the implementation of Prolog meta-predicates for specifically **"how to automatically encode all 120 total orderings of a 5-item cluster into a Max-Plus matrix $${A}$$,"** or shall we further refine this structural proposal in a "sandbox"?