Develops a quantum algorithm for linear matrix differential equations with query complexity O~(ν L t / ε) that is nearly optimal and yields polynomial to exponential speedups for open quantum system simulation.
The discrete adiabatic quantum linear system solver has lower constant factors than the random- ized adiabatic solver
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Probabilistic quantum algorithm prepares mixed states proportional to Lyapunov equation solutions and matrix inverses using oracles for input matrices and a deterministic stopping rule.
The paper gives a QLSS with query complexity (1+O(ε))κ ln(2√2/ε) using one kernel reflection when ||x|| is known, or O(κ log(1/ε)) overall, with explicit bound 56κ + 1.05κ ln(1/ε).
SparQSim is a sparse-state quantum simulator in C++ supporting QRAM that outperforms dense Schrödinger simulators on high-sparsity benchmark circuits and produces consistent results for quantum linear system solvers.
citing papers explorer
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Efficient quantum algorithm for linear matrix differential equations and applications to open quantum systems
Develops a quantum algorithm for linear matrix differential equations with query complexity O~(ν L t / ε) that is nearly optimal and yields polynomial to exponential speedups for open quantum system simulation.
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Probabilistic quantum algorithm for Lyapunov equations and matrix inversion
Probabilistic quantum algorithm prepares mixed states proportional to Lyapunov equation solutions and matrix inverses using oracles for input matrices and a deterministic stopping rule.
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A shortcut to an optimal quantum linear system solver
The paper gives a QLSS with query complexity (1+O(ε))κ ln(2√2/ε) using one kernel reflection when ||x|| is known, or O(κ log(1/ε)) overall, with explicit bound 56κ + 1.05κ ln(1/ε).
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SparQSim: Simulating Scalable Quantum Algorithms via Sparse Quantum State Representations
SparQSim is a sparse-state quantum simulator in C++ supporting QRAM that outperforms dense Schrödinger simulators on high-sparsity benchmark circuits and produces consistent results for quantum linear system solvers.