# Improved bounds on the randomized and quantum complexity of initial-value problems

@article{Kacewicz2005ImprovedBO, title={Improved bounds on the randomized and quantum complexity of initial-value problems}, author={Boleslaw Z. Kacewicz}, journal={J. Complex.}, year={2005}, volume={21}, pages={740-756} }

## 3 Citations

### The randomized complexity of initial value problems

- Mathematics, Computer ScienceJ. Complex.
- 2008

### Almost optimal solution of initial-value problems by randomized and quantum algorithms

- Computer Science, MathematicsJ. Complex.
- 2006

### The Quantum Setting with Randomized Queries for Continuous Problems

- Computer Science, MathematicsQuantum Inf. Process.
- 2006

It is proved that for path integration the authors have an exponential improvement for the qubit complexity over the quantum setting with deterministic queries, which limits the power of quantum computation for continuous problems.

### On the Complexity of Searching for a Maximum of a Function on a Quantum Computer

- Computer Science, MathematicsQuantum Inf. Process.
- 2006

It is shown that quantum computation yields a quadratic speed-up over deterministic and randomized algorithms.

### Numerical Analysis on a Quantum Computer

- Computer ScienceLSSC
- 2005

Having matching upper and lower complexity bounds for the quantum setting, this work is in a position to assess the possible speedups quantum computation could provide over classical deterministic or randomized algorithms for these numerical problems.

### Tractability of Multivariate Problems

- Mathematics, Computer Science
- 2008

The main purpose of this book is to study weighted spaces and to obtain conditions on the weights that are necessary and sufficient to achieve various notions of tractability, depending on how to measure the lack of exponential dependence.

### Adaptive Itô-Taylor algorithm can optimally approximate the Itô integrals of singular functions

- Mathematics, Computer ScienceJ. Comput. Appl. Math.
- 2010

### Finding Solutions of the Navier‐Stokes Equations through Quantum Computing—Recent Progress, a Generalization, and Next Steps Forward

- PhysicsAdvanced Quantum Technologies
- 2021

Efficient simulation of a quantum system's dynamics is expected to be an important application area for quantum computers as existing classical computers cannot do this. However, quantum systems are…

### Qubit complexity of continuous problems

- Computer Science, Mathematics
- 2005

It is shown how to obtain the classical query complexity for continuous problems and a simple formula is established for a lower bound on the qubit complexity in terms of the Classical query complexity.

### Finding flows of a Navier–Stokes fluid through quantum computing

- Computer Science, Physics
- 2020

This work presents a quantum algorithm for solving the Navier–Stokes nonlinear partial differential equations, and points to a large new application area for quantum computing with substantial economic impact, including the trillion-dollar aerospace industry, weather-forecasting, and engineered-plasma technologies.

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