Project Details
Description
Abhishek Singh Rawat 48073636 not available in PURE as of 24/10/2023.
Simulation of quantum systems was Feynman’s original motivation to propose quantum computers. Apart from predicting the behavior of physical systems, Hamiltonian simulation has algorithmic applications, leading to a steady increase in the number of algorithms using Hamiltonian simulation subroutines or methods inspired by them. A key challenge that needs to be addressed is improving scaling to achieve a square root of sparsity without incurring significant overhead in other parameters, which is essential for non-sparse cases but can also be beneficial for sparse cases, particularly in the context of implementing general unitary transformations. Another line of research I would like to explore is in the context of time-dependent sparse Hamiltonians. There are several quantum algorithms in the literature that are intended to simulate the dynamics of time-dependent quantum many-body Hamiltonians, starting from algorithms based on the Lie-Trotter-Suzuki decomposition with complexity scaling polynomially in error. Subsequent developments resulted in logarithmic error scaling, leading to time-dependent Hamiltonian simulation approaches such as approximating the truncated Dyson series of the evolution operator, the interaction-picture simulation. Furthermore, Berry et al. improved the Hamiltonian scaling to L1-norm, by taking into account the dynamic properties of time-dependent Hamiltonians. Despite these advancements, the optimal complexity scaling of time-dependent Hamiltonian simulation remains an open question. It is unclear whether the scaling can be further improved by making the factor of log(1/eps) additive rather than multiplicative, similar to the case of time-independent systems, or whether the current scaling is optimal.
Simulation of quantum systems was Feynman’s original motivation to propose quantum computers. Apart from predicting the behavior of physical systems, Hamiltonian simulation has algorithmic applications, leading to a steady increase in the number of algorithms using Hamiltonian simulation subroutines or methods inspired by them. A key challenge that needs to be addressed is improving scaling to achieve a square root of sparsity without incurring significant overhead in other parameters, which is essential for non-sparse cases but can also be beneficial for sparse cases, particularly in the context of implementing general unitary transformations. Another line of research I would like to explore is in the context of time-dependent sparse Hamiltonians. There are several quantum algorithms in the literature that are intended to simulate the dynamics of time-dependent quantum many-body Hamiltonians, starting from algorithms based on the Lie-Trotter-Suzuki decomposition with complexity scaling polynomially in error. Subsequent developments resulted in logarithmic error scaling, leading to time-dependent Hamiltonian simulation approaches such as approximating the truncated Dyson series of the evolution operator, the interaction-picture simulation. Furthermore, Berry et al. improved the Hamiltonian scaling to L1-norm, by taking into account the dynamic properties of time-dependent Hamiltonians. Despite these advancements, the optimal complexity scaling of time-dependent Hamiltonian simulation remains an open question. It is unclear whether the scaling can be further improved by making the factor of log(1/eps) additive rather than multiplicative, similar to the case of time-independent systems, or whether the current scaling is optimal.
| Acronym | SQA Round 8 |
|---|---|
| Status | Active |
| Effective start/end date | 1/02/24 → 1/02/28 |