Quantum AI Architecture Design Guidelines

 Quantum AI Architecture Design Guidelines

A Superselection-Rule–Centered Approach

1. Design Premise: Operability Before Expressibility

Guiding principle:

If a quantum state cannot be operationally accessed, it must not be treated as a computational resource.

In Quantum AI, many proposed advantages originate from mathematically admissible states that are not physically operable due to superselection rules (SSR).

Architecture design must therefore prioritize operational feasibility over formal generality.

2. SSR as a First-Class Architectural Constraint

2.1 What SSR Imposes

Superselection rules enforce that:

• Hilbert space decomposes into mutually isolated sectors
• No physical operator can:
  
• Create coherence between sectors
• Measure relative phases across sectors
• Cross-sector “entanglement” collapses into classical mixtures

Architectural implication:

Cross-sector coherence must be treated as nonexistent, not merely costly.

2.2 SSR vs. Noise Models

Aspect	Noise / Decoherence	Superselection Rule
Nature	Dynamical	Structural
Can error correction fix it?	Sometimes	No
Can more precision help?	Yes	No
Can it be bypassed?	Possibly

Design rule:

Do not model SSR violations as noise or imperfect control.

They are undefined operations, not failed ones.

3. Sector-Aware State Representation

3.1 Sector-Consistent Encoding

Quantum data representations must satisfy:

• All basis states belong to the same superselection sector
• All superpositions are sector-internal
• Labels such as charge, particle number, parity, or reference-frame phase are fixed

Anti-pattern:

Encoding information across particle-number sectors and assuming relative phase is accessible.

3.2 Sector Indexing as Metadata

Each quantum register should explicitly carry:

• Sector label(s)
• Conserved quantities
• Allowed operator algebra

This enables:

• Compile-time rejection of invalid circuits
• Sector-safe optimization
• Hardware–algorithm compatibility checks

4. Entanglement as a Valid Resource: Strict Criteria

Only entanglement that satisfies all three conditions is a usable AI resource:

1. Controllable — can be generated via allowed operators
2. Measurable — observable correlations exist
3. Actionable — convertible into algorithmic advantage

SSR filter:

If entanglement fails any criterion due to sector separation, it is not entanglement for computation, regardless of formal appearance.

5. Algorithm Design Under SSR Constraints

5.1 Allowed Algorithmic Structures

Algorithms should be built from:

• Sector-preserving unitaries
• Symmetry-respecting variational ansätze
• Invariant subspace exploration
• Relational encodings (instead of absolute phases)

Examples:

• Symmetry-adapted VQE
• Number-conserving quantum circuits
• Gauge-invariant quantum models

5.2 Forbidden Assumptions

Avoid algorithms that assume:

• Global phase access across sectors
• Arbitrary basis change between conserved quantities
• “Free” reference frames
• Implicit lifting of SSR via classical post-processing

6. SSR as Inductive Bias in Quantum AI

SSR plays the same role as inductive bias in classical AI:

Classical AI	Quantum AI
Regularization	Superselection constraints
Architectural bias	Sector-preserving structure
Feature invariance	Symmetry & conservation
Overfitting prevention	Elimination of fantasy states

Key insight:

SSR does not reduce expressive power; it removes unphysical degrees of freedom.

7. Reference Frames: Explicit or Absent

If an architecture claims to “bypass” SSR, it must explicitly model:

• Additional quantum systems
• External reference frames
• Their preparation cost
• Their decoherence and trust assumptions

Otherwise, the claim is invalid by definition.

8. Verification Checklist (Design-Time)

Before accepting a Quantum AI architecture, verify:

• Are all states sector-consistent?
• Are all operators sector-preserving?
• Is every claimed entanglement measurable?
• Is any reference frame explicitly modeled?
• Would the algorithm still work if cross-sector phases are erased?

If any answer is “no” → architectural violation of SSR.

9. Strategic Implication

Many failed or exaggerated quantum AI claims are not due to poor hardware, but due to illegal architecture assumptions.

SSR-aware design yields:

• Fewer but real advantages
• Slower but scalable progress
• Architectures that survive experimental reality

10. Bottom Line

Quantum AI does not gain power by ignoring constraints.

It gains power by aligning computation with the structure of reality.

Superselection rules are not obstacles to overcome,

but maps that prevent us from computing in imaginary spaces.