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.
Universal computation by quantum walk
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Hermitian weighted graphs enable universal exact realization of arbitrary complex QL-bits as real-spectrum eigenstates, with discrete {0, ±1, ±i} couplings dense in the state space.
CE-QAOA with finite layers achieves dimension-free success probability bounds q0 ≥ x/(1+x) via Fejér filtering under a wrapped phase-separation condition.
Quadratic bosonic Hamiltonian simulation is BQP-complete for a broad class that includes classical oscillator networks and continuous-time quantum walks, but becomes PostBQP-hard when extended to more general quadratic interactions.
Quantum walks integrated with variational circuits and CUDA-Q acceleration generate high-fidelity adaptive probability distributions for 1D financial modeling and 2D digit patterns.
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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Universal Complex Quantum-Like Bits from Hermitian Weighted Graphs
Hermitian weighted graphs enable universal exact realization of arbitrary complex QL-bits as real-spectrum eigenstates, with discrete {0, ±1, ±i} couplings dense in the state space.
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Finite-Depth, Finite-Shot Guarantees for Constrained Quantum Optimization via Fej\'er Filtering
CE-QAOA with finite layers achieves dimension-free success probability bounds q0 ≥ x/(1+x) via Fejér filtering under a wrapped phase-separation condition.
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Complexity of Quadratic Bosonic Hamiltonian Simulation: $\mathsf{BQP}$-Completeness and $\mathsf{PostBQP}$-Hardness
Quadratic bosonic Hamiltonian simulation is BQP-complete for a broad class that includes classical oscillator networks and continuous-time quantum walks, but becomes PostBQP-hard when extended to more general quadratic interactions.
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Quantum Walks-Based Adaptive Distribution Generation with Efficient CUDA-Q Acceleration
Quantum walks integrated with variational circuits and CUDA-Q acceleration generate high-fidelity adaptive probability distributions for 1D financial modeling and 2D digit patterns.