Low rank approximation in simulations of quantum algorithms
Simulating quantum algorithms on classical computers is challenging when the system size, i.e., the number of qubits used in the quantum algorithm, is moderately large. However, some quantum algorithms and the corresponding quantum circuits can be simulated efficiently on a classical computer if the input quantum state is a low rank tensor and all intermediate states of the quantum algorithm can be represented or approximated by low rank tensors. Here, in this paper, we examine the possibility of simulating a few quantum algorithms by using low-rank canonical polyadic (CP) decomposition to represent the input and all intermediate states of these algorithms. Two rank reduction algorithms are used to enable efficient simulation. We show that some of the algorithms preserve the low rank structure of the input state and can thus be efficiently simulated on a classical computer. However, the rank of the intermediate states in other quantum algorithms can increase rapidly, making efficient simulation more difficult. To some extent, such difficulty reflects the advantage or superiority of a quantum computer over a classical computer. As a result, understanding the low rank structure of a quantum algorithm allows us to identify algorithms that can benefit significantly from quantum computers.
- Research Organization:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- Grant/Contract Number:
- AC02-05CH11231
- OSTI ID:
- 1924648
- Journal Information:
- Journal of Computational Science, Journal Name: Journal of Computational Science Vol. 59; ISSN 1877-7503
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Similar Records
Fully quantum algorithm for mesoscale fluid simulations with application to partial differential equations
Parameter Sensitivity Analysis of the SparTen High Performance Sparse Tensor Decomposition Software (Extended Analysis)