Space Complexity of Streaming Algorithms on Universal Quantum Computers
Yanglin Hu, Darya Melnyk, Yuyi Wang, Roger Wattenhofer
发表信息：
In: Chen J., Feng Q., Xu J. (eds) Theory and Applications of Models of Computation. TAMC 2020. Lecture Notes in Computer Science, vol 12337. Springer, Cham (2020)
Universal quantum computers are the only general purpose quantum computers known that can be implemented as of today. These computers consist of a classical memory component which controls the quantum memory. In this paper, the space complexity of some data stream problems, such as PartialMOD and Equality, is investigated on universal quantum computers. The quantum algorithms for these problems are believed to outperform their classical counterparts. Universal quantum computers, however, need classical bits for controlling quantum gates in addition to qubits. Our analysis shows that the number of classical bits used in quantum algorithms is equal to or even larger than that of classical bits used in corresponding classical algorithms. These results suggest that there is no advantage of implementing certain data stream problems on universal quantum computers instead of classical computers when space complexity is considered.
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A Single Atom in Front of a Mirror is a Universal Reservoir Computer
Wyant College of Optical Sciences, University of Arizona（亚利桑那大学怀恩特光学科学学院）；Department of Physics, University of Arizona（亚利桑那大学物理系）；School of Electrical Engineering and Telecommunications, University of New South Wales（新南威尔士大学电气工程与电信学院）
Quantum cooling, a deterministic process that drives any state to the lowest eigenstate, has been widely used from studying ground state properties of chemistry and condensed matter quantum physics, to general optimization problems. However, the cooling procedure is generally non-unitary, hence its realization on a quantum computer either requires deep circuits or assumes specific input states with variational circuits. Here, we propose universal quantum cooling algorithms that overcome these limitations. By utilizing a dual phase representation of decaying functions, we show how to universall…
Chern-Simons topological quantum computer is a device that can be effectively described by the Chern-Simons topological quantum field theory and used for quantum computations. Quantum qudit gates of this quantum computer are represented by sequences of quantum $\mathcal{R}$-matrices. Its dimension and explicit form depend on the parameters of the Chern-Simons theory -- level $k$, gauge group $SU(N)$, and representation, which is chosen to be symmetric representation $[r]$. In this paper, we examine the universality of such a quantum computer. We prove that for sufficiently large $k$ it is univ…
