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HDQMF: Holographic Feature Decomposition Using Quantum Algorithms
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Proposes HDQMF, a modified Grover's algorithm with phase-based approximate oracle that decomposes bundled-then-bound hypervectors (HDC memorized-factorization), claiming quadratic speedup over resonator networks.
Problem
Decomposing composite holographic hypervectors built by bind-then-bundle in HDC/VSA is combinatorially expensive classically; existing resonator networks scale poorly and fail to converge at low dimension.
Approach
Extends Grover's search with a similarity-dependent phase oracle (phase e^{iπδ}) and alternating inverse oracle applications, enabling approximate search over factorizations of bundled bound hypervectors with quadratic speedup, using MXOR gates for binding.
Key results
- On simulated factorization vs. resonator network (D=50, K=10), HDQMF reaches Ps=0.025 with NS=72 effective steps versus resonator network Ps=0.06 with NS=338 (Table 1).
- At D=50 in the scene memorization case, the resonator network fails to converge while the quantum algorithm correctly identifies the marked state (Fig. 6).
- Analytical optimal iteration count derived as Nitr = (π/4)·sqrt(NF/(kM)), claimed quadratic speedup.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HDQMF instead of the Resonator Network | Factorization · (D=50, K=10) | NS: 338 -> 72 | Helped |
| Use HDQMF instead of the Resonator Network | Factorization · (D=50, K=20) | NS: 368 -> 91 | Helped |
| Use HDQMF instead of the Resonator Network | Factorization · (D=500, K=10) | NS: 338 -> 44 | Helped |
| Use HDQMF instead of the Resonator Network | Factorization · (D=500, K=20) | NS: 195 -> 47 | Helped |
| Increase hypervector dimension (ablation) | HDQMF · Factorization | peak probability of finding a marked state | Helped |
| Increase the number of bundled vectors M (ablation) | HDQMF · Memorized factorization | iterations to peak probability | Helped |
Surprising findings
- Resonator network reaches higher success probability at some settings (e.g., D=500, K=10: Ps 0.10 vs HDQMF 0.064), though HDQMF needs fewer effective steps in most reported cases.
Limitations
- Practicality depends on quantum hardware with limited qubits, stability and reliability.
- Results are simulated; no execution on real quantum devices reported.
- Algorithm is expected to be used alongside classical solutions.
Experimental setup
Benchmarks: simulated factorization with random codebooks (N=100, F=3) scene memorization case study (numbers, colors, locations)
Metrics: probability of correct factorization number of iterations effective number of steps
Baselines: Resonator Network
Builds on: Grover's algorithm resonator network Multiply-Add-Permute (MAP)
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