In this Letter, we construct the quantum algorithms for the Simon problem and the period-finding problem, which do not require initializing the auxiliary qubits involved in the process of functional evaluation but are as efficient as the original algorithms. In these quantum algorithms, one can use any arbitrarily mixed state as the auxiliary qubits, and furthermore can recover the state of the auxiliary qubits to the original one after completing the computations. Since the recovered state can be employed in any other computations, we obtain that a single preparation of the auxiliary qubits in an arbitrarily mixed state is sufficient to implement the iterative procedure in the Simon algorithm or the period-finding algorithm.
Reducing multi-qubit interactions in adiabatic quantum computation without adding auxiliary qubits. Part 2: The "split-reduc" method and its application to quantum determination of Ramsey numbers
量子退火最近已用于确定3 < m < 9和R（3，3）的拉姆齐数R（m，2）[Bian等人（2013）PRL 111，130505]。这是当时最大的绝热演化算法实验。然而，在该计算中，超过66%的量子位是辅助量子位，因此所使用的拉姆齐数哈密顿量的大小远远小于所使用的设备的全部128量子位容量。需要这些辅助量子位的原因是因为当时（以及现在）最好的量子退火设备无法实现超过2量子位相互作用的多量子位相互作用，并且它们在2量子位相互作用的能力方面也受到限制。我们提出了一种方法，该方法通过减少多量子位和2量子位相互作用，允许使用量子退火设备的全部量子位容量。使用我们的方法，2013年Ramsey数量子计算中使用的设备可以在10分钟内确定R（16，2）和R（4，3）。
Auxiliary-qubit-free quantum approximate optimization algorithm for the minimum dominating set problem
State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications（北京邮电大学网络与交换技术国家重点实验室）；National Key Laboratory of Security Communication, Institute of Southwestern Communication（西南通信研究所信息安全通信国家级重点实验室）
Universal quantum entangling gates are a crucial building block in the large-scale quantum computation and quantum communication, and it is an important task to find simple ways to implement them. Here an effective quantum circuit for the implementation of a controlled-NOT (CNOT) gate is constructed by introducing a non-computational quantum state in the auxiliary space. Furthermore, the method is extended to the construction of a general n-control-qubit Toffoli gate with (2n-1) qubit-qudit gates and (2n-2) single-qudit gates. Based on the presented quantum circuits, the polarization CNOT and …
Transient energy backflow enhanced ergotropy in an open qubit quantum battery assisted by an auxiliary oscillator
Center for Quantum Materials and Computational Condensed Matter Physics, Faculty of Science, Kunming University of Science and Technology（昆明理工大学理学院量子材料与计算凝聚态物理中心）
We introduce a minimal model for realizing a fast-to-slow scrambling transition mediated by an auxiliary central qubit (c-qubit). The c-qubit is coupled to a spin-$1/2$ Ising model with local Ising interactions and tunable c-qubit-spin coupling. Each spin becomes next-nearest neighbor to all others through the c-qubit, which mediates effective all-to-all interactions. As the interaction with the c-spin increases, we find a surprising transition from super-ballistic scrambling and information growth to continuously restricted sub-ballistic entanglement and operator growth. This slow growth occu…
Experimental replication of single-qubit quantum phase gates
我们通过实验证明了最近提出的量子相位门超复制协议的底层物理机制[W. Dür，P. Sekatski，and M. Skotiniotis，Phys. Rev. Lett. 114，120503（2015）]，其允许在大N.我们实现1->2复制的单量子位相位门是基于线性光学和量子位编码成单光子的状态。我们采用量子Toffoli门将输入的两个量子比特态的结构信息压印到辅助量子比特上，对辅助量子比特应用复制操作，然后通过合适的量子测量将辅助量子比特与其他量子比特解纠缠。我们的复制协议的特点，全量子过程层析成像，并观察到良好的协议的实验结果与理论。
Effective quantum information processing is tantamount in part to the minimization the quantum resources needed by quantum logic gates. Here, we propose an optimization of an n-controlled-qubit Fredkin gate with a maximum of 2n+1 two-qubit gates and 2n single-qudit gates by exploiting auxiliary Hilbert spaces. The number of logic gates required improves on earlier results on simulating arbitrary n-qubit Fredkin gates. In particular, the optimal result for one-controlled-qubit Fredkin gate (which requires three qutrit-qubit partial-swap gates) breaks the theoretical nonconstructive lower bound …
Quantum protocols based on adiabatic evolution are remarkably robust against imperfections of control pulses and system uncertainties. While adiabatic protocols have been successfully implemented for quantum operations such as quantum state transfer and single-qubit gates, their use for geometric two-qubit gates remains a challenge. In this paper, we propose a general scheme to realize robust geometric two-qubit gates in multi-level qubit systems where the interaction between the qubits is mediated by an auxiliary system (such as a bus or coupler). While our scheme utilizes Stimulated Raman Ad…
The deterministic quantum computation with one qubit (DQC1) model is a restricted model of quantum computing able to calculate efficiently the normalized trace of a unitary matrix. In this work we analyse the quantum correlations named entanglement, Bell's nonlocality, quantum discord, and coherence generated by the DQC1 circuit considering only two qubits (auxiliary and control). For the standard DQC1 model only quantum discord and coherence appear. By introducing a filter in the circuit we purify the auxiliary qubit taking it out from the totally mixed state and consequently promoting other …
Reducing multi-qubit interactions in adiabatic quantum computation without adding auxiliary qubits. Part 1: The "deduc-reduc" method and its application to quantum factorization of numbers
