Duality quantum computer and the efficient quantum simulations

Abstract

In this paper, we firstly briefly review the duality quantum computer. Distinctly, the generalized quantum gates, the basic evolution operators in a duality quantum computer are no longer unitary, and they can be expressed in terms of linear combinations of unitary operators. All linear bounded operators can be realized in a duality quantum computer, and unitary operators are just the extreme points of the set of generalized quantum gates. A d-slits duality quantum computer can be realized in an ordinary quantum computer with an additional qudit using the duality quantum computing mode. Duality quantum computer provides flexibility and clear physical picture in designing quantum algorithms, serving as a useful bridge between quantum and classical algorithms. In this review, we will show that duality quantum computer can simulate quantum systems more efficiently than ordinary quantum computers by providing descriptions of the recent efficient quantum simulation algorithms of Childs et al [Quantum Information & Computation, 12(11-12): 901-924 (2012)] for the fast simulation of quantum systems with a sparse Hamiltonian, and the quantum simulation algorithm by Berry et al [Phys. Rev. Lett. 114, 090502 (2015)], which provides exponential improvement in precision for simulating systems with a sparse Hamiltonian.

Quantifiable Simulation of Quantum Computation beyond Stochastic Ensemble Computation

“…Here, it is worth noting that there is a novel QC model, called duality QC, which is originally proposed to exploit the wave–particle duality so that it can also use the linear combinations of 's . The duality QC appears to be more general than the typical QC model and offers more flexibility in quantum algorithm design . However, it will be sufficient for our purpose to consider the (typical) QTM that runs the products of 's as in Equation ; that is, the superiority of the QTM over its classical counterparts, if any , is directly generalized to that of the duality QC model.…”

Quantum Computing

“…求解线性方程组的量子算法可以指数加快方程组的解 法 [28,29] , 封闭量子体系的新量子模拟算法 [30∼32] 改善了量子模拟的精度, 开放量子系统的对偶量子 模拟算法 [33] 不仅加快了计算速度, 而且提高了计算精度, 量子算法又开始了新的发展阶段. 而这些新 量子算法就是利用了非酉演化, 即采用了酉算子的线性组合的对偶量子算法 [29,32,33] .…”

Distribution of standard deviation of an observable among superposed states

“…In fact, quantum coherence is also the essence of interference phenomena, which shows that no interference could be revealed by the observable if the observable commutes with the density matrix [31]. Here we would like to say that the quantum interference has also been extensively studied in [34], and resulted in the new concept of duality quantum computers, which has found striking advantage in the scaling of precision in quantum simulation [35]. Based on the commutation property, an interesting coherence measure, K -coherence, employing the skew information has been raised [36].…”