Quantum algorithms for systems of linear equations inspired by adiabatic quantum computing
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. Innsbruck (Austria). Dept. of Theoretical Physics
We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state |x⟩ that is proportional to the solution of the system of linear equations $$A\overrightarrow{x} = \overrightarrow{b}$$. The time complexities of our algorithms are O(κ2log(κ)/ε) and O(κ log(κ)/ε), where κ is the condition number of A and ε is the precision. Both algorithms are constructed using families of Hamiltonians that are linear combinations of products of A, the projector onto the initial state |b⟩, and single-qubit Pauli operators. The algorithms are conceptually simple and easy to implement. They are not obtained from equivalences between the gate model and adiabatic quantum computing. They do not use phase estimation or variable-time amplitude amplification, and do not require large ancillary systems. We discuss a gate-based implementation via Hamiltonian simulation and prove that our second algorithm is almost optimal in terms of κ. Like previous methods, our techniques yield an exponential quantum speed-up under some assumptions. Our results emphasize the role of Hamiltonian-based models of quantum computing for the discovery of important algorithms.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE Laboratory Directed Research and Development (LDRD) Program
- Grant/Contract Number:
- 89233218CNA000001
- OSTI ID:
- 1781370
- Report Number(s):
- LA-UR--17-20510
- Journal Information:
- Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 6 Vol. 122; ISSN 0031-9007
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
Quantum annealing for systems of polynomial equations
|
journal | July 2019 |
Hybrid classical-quantum linear solver using Noisy Intermediate-Scale Quantum machines
|
journal | November 2019 |
| Hybrid classical-quantum linear solver using Noisy Intermediate-Scale Quantum machines | text | January 2019 |
Similar Records
Exact solutions for universal holonomic quantum gates