Query-Optimal and Gate-Efficient Lindbladian Simulation

arXiv:2609.18757 · quant-ph, cs.DS · Submitted 2026-09-16 · Read on arXiv

quant-ph, cs.DS

Submitted: 2026-09-16

Updated: 2026-09-16

Comments: 62 pages, 5 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Query Complexity — 18× in this paper · explained in 2 episodes
• Block Encoding — 15× in this paper · explained in 4 episodes
• Trace — 8× in this paper · explained in 2 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Approximation Bound — 2× in this paper · explained in 1 episode
• Gibbs State — 2× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Lindblad master equation — 1× in this paper · explained in 2 episodes
• Unitary Dynamics — 1× in this paper · explained in 2 episodes

Sources

• A quantum algorithm to simulate Lindblad master equations
• A new quantum ripple-carry addition circuit
• Time-Dependent Hamiltonian Simulation with Optimal Query Complexity
• Local minima in quantum systems
• Quantum Langevin Dynamics for Optimization
• Efficient Quantum Algorithms for Simulating Lindblad Evolution
• Faster Quantum Simulation Of Markovian Open Quantum Systems Via Randomisation
• L'evy-Khintchine Structure Enables Fast-Forwardable Lindbladian Simulation
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• Efficient Optimal Control of Open Quantum Systems
• Exponentially accurate open quantum simulation via randomized dissipation with minimal ancilla
• Transformation of quantum states using uniformly controlled rotations
• Exponential Lindbladian fast forwarding and exponential amplification of certain Gibbs state properties
• Query-optimal quantum simulation of Lindblad evolution

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