Hamiltonian Simulation and Linear Combination of Unitary Decomposition of Structured Matrices

arXiv:2603.17816 · quant-ph · Submitted 2026-03-18 · Read on arXiv

quant-ph

Submitted: 2026-03-18

Updated: 2026-09-21

Terminology

• Hamiltonian Simulation — 16× in this paper
• Special Tripotent Hamiltonian — 10× in this paper
• Adjacency Matrix — 9× in this paper · explained in 1 episode
• Quantum Circuits — 8× in this paper · explained in 2 episodes
• Block Encoding — 4× in this paper · explained in 4 episodes
• Partial Differential Equations — 4× in this paper
• Quantization — 4× in this paper · explained in 12 episodes
• Quantum Signal Processing — 3× in this paper
• Single Component Basis — 3× in this paper
• Variationnal Quantum Algorithm — 3× in this paper
• Ancilla Qubits — 2× in this paper · explained in 1 episode
• Linear Combination of Unitary — 2× in this paper
• Quantum Fourier Transform — 2× in this paper
• Quantum Processing Unit — 2× in this paper
• Query Complexity — 2× in this paper · explained in 2 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Adiabatic Evolution — 1× in this paper · explained in 2 episodes
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Linear Combination of Hermitian — 1× in this paper
• Projective Valued Measurement — 1× in this paper
• Quantum Annealing — 1× in this paper
• Quantum Singular Value Transformation (QSVT) — 1× in this paper · explained in 4 episodes

Sources

• Quantum measurements and the Abelian Stabilizer Problem
• Quantum algorithm for solving linear systems of equations
• Quantum Computation by Adiabatic Evolution
• A variational eigenvalue solver on a quantum processor
• A Theory of Trotter Error
• Quantum Algorithms Revisited
• Quantum Arithmetic-based on Quantum Signal Processing
• A tree-approach Pauli decomposition algorithm with application to quantum computing
• Tensorized Pauli decomposition algorithm
• Circuit optimization of Hamiltonian simulation by simultaneous diagonalization of Pauli clusters
• Assessment of various Hamiltonian partitionings for the electronic structure problem on a quantum computer using the Trotter approximation
• Efficient Quantum Circuits for Non-Unitary and Unitary Diagonal Operators with Space-Time-Accuracy trade-offs
• Explicit Quantum Circuits for Block Encodings of Certain Sparse Matrices
• Block-encoding structured matrices for data input in quantum computing
• Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian
• Explicit block encodings of boundary value problems for many-body elliptic operators
• Block encoding of sparse matrices with a periodic diagonal structure
• Quantum circuits for partial differential equations in Fourier space
• Enhancing the Quantum Linear Systems Algorithm using Richardson Extrapolation
• Efficient Variational Quantum Linear Solver for Structured Sparse Matrices

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