From Simple Sources to Quantum Advantage: Homomorphic Polynomial Transduction via Relative Decoding

arXiv:2609.35101 · quant-ph · Submitted 2026-09-28 · Read on arXiv

quant-ph

Submitted: 2026-09-28

Updated: 2026-09-28

Code: https://github.com/dsfranca/RDQINumerics

Terminology

• Trace — 54× in this paper · explained in 2 episodes
• Gibbs State — 10× in this paper · explained in 2 episodes
• Trace Distance — 8× in this paper · explained in 3 episodes
• Accuracy — 7× in this paper · explained in 1 episode
• Benchmark — 5× in this paper · explained in 2 episodes
• Decoded Quantum Interferometry (DQI) — 5× in this paper · explained in 2 episodes
• Embeddings — 3× in this paper · explained in 2 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Hubbard Model — 3× in this paper · explained in 3 episodes
• Adam — 2× in this paper · explained in 2 episodes
• Stabilizer States — 2× in this paper · explained in 2 episodes
• Antiferromagnetic Correlation — 1× in this paper · explained in 1 episode
• Axioms — 1× in this paper · explained in 2 episodes
• Combinatorial Optimization — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Decode — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Objective Function — 1× in this paper · explained in 2 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Unitary Dynamics — 1× in this paper · explained in 2 episodes

Sources

• Optimization by Decoded Quantum Interferometry
• Hamiltonian Decoded Quantum Interferometry
• Verifiable Quantum Advantage via Optimized DQI Circuits
• Multivariate Decoded Quantum Interferometry for Weighted Optimization
• Decoded Quantum Interferometry Beyond Hamming: Rank-Metric and Translation Association Schemes
• Hamiltonian Decoded Quantum Interferometry for General Pauli Hamiltonians
• On the Complexity of Decoded Quantum Interferometry
• Spin Glass Transitions Obstruct Decoded Quantum Interferometry
• Stabilizer Formalism for Operator Quantum Error Correction
• Hardness of decoding quantum stabilizer codes
• A Factorization Identity for Twisted Multinomial Coefficients with Application to Pilot States in Hamiltonian Decoded Quantum Interferometry
• Sequential generation of entangled multi-qubit states
• The density-matrix renormalization group in the age of matrix product states
• Efficient thermalization and universal quantum computing with quantum Gibbs samplers
• The Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
• Near-optimal ground state preparation
• Sampling from the thermal quantum Gibbs state and evaluating partition functions with a quantum computer
• Quantum algorithms for Gibbs sampling and hitting-time estimation
• Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics

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• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
• Polynomial-time classical and quantum simulation of quantum impurity models
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity