Presents LCU block-encodings for SLAC derivative operators, applies Shannon wavelets and preconditioning, and obtains O(d n^3 α^(k) log(1/ε)) gate complexity for d-dimensional PDEs via QLSA.
Black-box quantum state preparation without arith- metic
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abstract
Black-box quantum state preparation is an important subroutine in many quantum algorithms. The standard approach requires the quantum computer to do arithmetic, which is a key contributor to the complexity. Here we present a new algorithm that avoids arithmetic. We thereby reduce the number of gates by a factor of 286-374 over the best prior work for realistic precision; the improvement factor increases with the precision. As quantum state preparation is a crucial subroutine in many approaches to simulating physics on a quantum computer, our new method brings useful quantum simulation closer to reality.
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Quantum algorithm for solving differential equations using SLAC derivatives
Presents LCU block-encodings for SLAC derivative operators, applies Shannon wavelets and preconditioning, and obtains O(d n^3 α^(k) log(1/ε)) gate complexity for d-dimensional PDEs via QLSA.