Transducer-based linear combination of unitaries: theory and applications

arXiv:2609.40073 · quant-ph · Submitted 2026-09-30 · Read on arXiv

quant-ph

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Query Complexity — 30× in this paper · explained in 2 episodes
• Sparsity — 14× in this paper · explained in 4 episodes
• Accuracy — 7× in this paper · explained in 1 episode
• Block Encoding — 4× in this paper · explained in 4 episodes
• Ancilla Qubits — 3× in this paper · explained in 1 episode
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Quantum Singular Value Transformation (QSVT) — 2× in this paper · explained in 4 episodes
• Algorithmic Primitives — 1× in this paper · explained in 1 episode
• Core — 1× in this paper · explained in 2 episodes
• Large Language Model (LLM) — 1× in this paper · explained in 3 episodes
• Post-Selection — 1× in this paper · explained in 2 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• Unitary Dynamics — 1× in this paper · explained in 2 episodes

Sources

• Optimal quantum simulation of linear non-unitary dynamics
• Quantum Algorithms for Ground-State Preparation and Green's Function Calculation
• Quantum singular value transformation without block encodings: Near-optimal complexity with minimal ancilla
• Laplace transform based quantum eigenvalue transformation via linear combination of Hamiltonian simulation
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• A Near-Optimal Joint Lower Bound for Sparse Quantum Linear System Solvers
• Elfs, transducers and quantum walks
• Time-Dependent Hamiltonian Simulation with Optimal Query Complexity
• Query-optimal quantum simulation of Lindblad evolution
• The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation
• A shortcut to an optimal quantum linear system solver
• A New Quantum Linear System Algorithm Beyond the Condition Number and Its Application to Solving Multivariate Polynomial Systems
• Faster quantum linear system solver beyond the condition number
• An Optimal Quantum Linear Systems Algorithm
• Well-conditioned multiproduct Hamiltonian simulation
• Multi-product Hamiltonian simulation with explicit commutator scaling
• Circuit Depth Reduction of One-Ancilla Quantum Differential Equation Solver via Extrapolation

Related papers

• 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