quantum-viterbi-decoding

name	quantum-viterbi-decoding
description	Quantum Viterbi decoding methodology for hidden quantum Markov models (HQMMs). Extends classical Viterbi algorithm to quantum sequential decision-making with proven advantage over classical diagonal strategies.
version	1.0.0
author	Hermes Agent (Cron Job)
license	MIT
source	arXiv:2605.18912
metadata	{"hermes":{"tags":["Quantum","Viterbi","Hidden-Markov-Model","Sequential-Decision","NISQ"],"related_skills":["quantum-neural-dynamics","hidden-markov-models","quantum-algorithms"]}}

Quantum Viterbi Decoding for HQMMs

Overview

Extends the classical Viterbi algorithm to hidden quantum Markov models (HQMMs), enabling quantum sequential decision-making that provably outperforms any classical diagonal (commuting) strategy.

Paper: "Quantum Viterbi Algorithm" — Accardi, Souissi, Soueidi, Mukhamedov, Rhaima (arXiv:2605.18912, May 2026)

Core Methodology

1. Hidden Quantum Markov Models (HQMMs)

• Classical HMMs: discrete hidden states, probabilistic transitions
• HQMMs: hidden states are pure quantum effects on a continuous manifold
• Observed statistics may be identical, but hidden trajectories differ fundamentally

2. Quantum Viterbi Score

• Classical: max over finite discrete state space
• Quantum: optimization over continuous manifold of pure quantum effects
• Exploits coherent superpositions in hidden memory

3. Strict Quantum Advantage

• Theorem: coherent hidden trajectories achieve strictly higher decoding scores than any classical strategy constrained to diagonal (commuting) effects
• Holds even when both models share the same observed statistics
• Advantage stems from non-commutativity of quantum effects

4. Algorithm Steps

Input: sequence of measurement outcomes O = (o_1, ..., o_T)
       quantum transition operators {E_o}
       initial quantum state |ψ_0⟩

For t = 1 to T:
  For each quantum effect φ:
    δ_t(φ) = max_{φ'} [δ_{t-1}(φ') · ⟨φ|E_{o_t}|φ'⟩²]
    ψ_t(φ) = argmax_{φ'} [·]

Backtrack: find trajectory maximizing joint decoding functional

Applications

• Quantum memories: optimal readout of stored quantum information
• Quantum communication with memory: decoding channels with temporal correlations
• NISQ quantum ML: sequential classification, time-series analysis
• Quantum error correction: syndrome-based trajectory decoding

Implementation Patterns

Pattern 1: Parameterized Quantum Viterbi

# Use parameterized quantum circuits (PQCs) to approximate
# the continuous effect manifold optimization
# Ansatz: U(θ)|0⟩ → measurement → update δ

Pattern 2: Hybrid Classical-Quantum

Classical: maintain δ table, backtracking
Quantum: evaluate ⟨φ|E_o|φ'⟩² via circuit execution
Loop: iterate over discretized effect manifold

Pattern 3: NISQ-Friendly Approximation

• Discretize continuous manifold into finite grid
• Use SWAP test for fidelity estimation
• Apply amplitude amplification for max-finding

Key Insights

1. Non-commutativity as resource: the quantum advantage comes from effects not sharing eigenbasis
2. Continuous vs discrete: quantum Viterbi optimizes over continuous manifold, not discrete set
3. Same observations, different inference: identical observed statistics but different hidden trajectory inference
4. Scalability bottleneck: continuous optimization is harder than discrete; requires PQC approximation

When to Use

• Sequential decision-making under quantum uncertainty
• Quantum systems with memory/temporal correlations
• NISQ-era quantum machine learning tasks
• Any scenario where classical Viterbi is applied to quantum data

Pitfalls

• Continuous manifold optimization is exponentially harder than discrete
• Requires careful discretization for NISQ implementation
• Advantage only manifests when quantum effects are genuinely non-commuting
• Classical baselines with commuting effects may appear competitive on small instances

Activation: quantum viterbi, hidden quantum markov model, HQMM, sequential quantum decoding, quantum advantage decoding, quantum state estimation