Quantum Simulation of Dissipative Non-Markovian Coupled Classical Oscillators

arXiv:2609.20721 · quant-ph · Submitted 2026-09-17 · Read on arXiv

quant-ph

Submitted: 2026-09-17

Updated: 2026-09-17

Terminology

• Block Encoding — 51× in this paper · explained in 4 episodes
• BQP — 27× in this paper · explained in 2 episodes
• BQP-Completeness — 14× in this paper · explained in 2 episodes
• Ancilla Qubits — 13× in this paper · explained in 1 episode
• Hilbert Space — 10× in this paper · explained in 2 episodes
• Accuracy — 9× in this paper · explained in 1 episode
• Sparsity — 9× in this paper · explained in 4 episodes
• BQP-complete — 8× in this paper · explained in 2 episodes
• Grounding — 5× in this paper · explained in 3 episodes
• Hamiltonian Simulation — 5× in this paper
• Query Complexity — 5× in this paper · explained in 2 episodes
• Unitary Dynamics — 4× in this paper · explained in 2 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Linear Combination of Hamiltonian Simulation — 2× in this paper
• Non-Markovian Dynamics — 2× in this paper · explained in 5 episodes
• Quantum Circuits — 2× in this paper · explained in 2 episodes
• Alignment — 1× in this paper · explained in 1 episode
• Ancillary Qubits — 1× in this paper · explained in 1 episode
• Decoupling — 1× in this paper · explained in 2 episodes
• Gauge Freedom — 1× in this paper · explained in 2 episodes
• Markovian Ordinary Differential Equation — 1× in this paper
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters
• Optimal quantum simulation of linear non-unitary dynamics
• Quantum algorithms to simulate quadratic classical Hamiltonians and optimal control
• Quantum algorithm for partial differential equations of non-conservative systems with spatially varying parameters
• Exponential Quantum Advantage for Simulating Open Classical Systems
• Ancilla-train quantum algorithm for simulating non-Markovian open quantum systems
• Quantum simulation of non-Markovian dynamical systems
• Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
• On the quantum computational complexity of classical linear dynamics with geometrically local interactions: Dequantization and universality
• Quantum Wave Simulation with Sources and Loss Functions
• Hamiltonian Simulation in the Interaction Picture
• Quantum Addition Circuits and Unbounded Fan-Out
• Quantum state preparation for multivariate functions
• Quantum framework for parameterizing partial differential equations via diagonal block-encoding
• Quantum differential equation solvers: limitations and fast-forwarding
• Exponential improvement in precision for simulating sparse Hamiltonians
• Hamiltonian Simulation Using Linear Combinations of Unitary Operations
• Amplified Amplitude Estimation: Exploiting Prior Knowledge to Improve Estimates of Expectation Values
• An efficient quantum algorithm for preparation of uniform quantum superposition states
• Hamiltonian Simulation by Uniform Spectral Amplification

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