应用核磁共振实验实现量子计算的注记

从量子力学的基本原理出发,阐述了利用核磁共振进行量子计算的实验方法,澄清了有关文献中若干容易混淆而又十分重要的概念,并进一步报道CNOT门操作的实验方法和结果.实验结果与理论的预言一致.     

Controlled exchange interaction between pairs of neutral atoms in an optical lattice

Ultracold atoms trapped by light offer robust quantum coherence and controllability, providing an attractive system for quantum information processing and for the simulation of complex problems in condensed matter physics. Many quantum information processing schemes require the manipulation and deterministic entanglement of individual qubits; this would typically be accomplished using controlled, state-dependent, coherent interactions among qubits. Recent experiments have made progress towards this goal by demonstrating entanglement among an ensemble of atoms confined in an optical lattice. Until now, however, there has been no demonstration of a key operation: controlled entanglement between atoms in isolated pairs. Here we use an optical lattice of double-well potentials to isolate and manipulate arrays of paired (87)Rb atoms, inducing controlled entangling interactions within each pair. Our experiment realizes proposals to use controlled exchange coupling in a system of neutral atoms. Although 87Rb atoms have nearly state-independent interactions, when we force two atoms into the same physical location, the wavefunction exchange symmetry of these identical bosons leads to state-dependent dynamics. We observe repeated interchange of spin between atoms occupying different vibrational levels, with a coherence time of more than ten milliseconds. This observation demonstrates the essential component of a neutral atom quantum SWAP gate (which interchanges the state of two qubits). Its 'half-implementation', the root SWAP gate, is entangling, and together with single-qubit rotations it forms a set of universal gates for quantum computation.     

一种量子神经计算网络模型

量子计算以其独特的计算性能引起广泛瞩目,人们越来越多地探讨它与传统计算模式的结合．研究以通用量子逻辑门组(即相移门和受控非门)作为计算基函数,构造新的量子神经计算网络模型．仿真结果显示,就算例而言,该量子神经计算网络的性能优于传统的神经网络．     

Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer

Determining classically whether a coin is fair (head on one side, tail on the other) or fake (heads or tails on both sides) requires an examination of each side. However, the analogous quantum procedure (the Deutsch-Jozsa algorithm) requires just one examination step. The Deutsch-Jozsa algorithm has been realized experimentally using bulk nuclear magnetic resonance techniques, employing nuclear spins as quantum bits (qubits). In contrast, the ion trap processor utilises motional and electronic quantum states of individual atoms as qubits, and in principle is easier to scale to many qubits. Experimental advances in the latter area include the realization of a two-qubit quantum gate, the entanglement of four ions, quantum state engineering and entanglement-enhanced phase estimation. Here we exploit techniques developed for nuclear magnetic resonance to implement the Deutsch-Jozsa algorithm on an ion-trap quantum processor, using as qubits the electronic and motional states of a single calcium ion. Our ion-based implementation of a full quantum algorithm serves to demonstrate experimental procedures with the quality and precision required for complex computations, confirming the potential of trapped ions for quantum computation.     

二粒子未知态的受控量子通信

提出了一个利用七粒子态传送一个二粒子未知态的多方受控量子通信方案。该方案中发送者指定一名控制者,它不能接收二粒子未知态,但是它可以和发送者一起协助接收者重构二粒子未知态。发送者对自己拥有的4个粒子做一次von-Neumann联合测量,控制者在计算基下对它的粒子做测量。接收者根据两次测量结果对自己拥有的粒子做相应的幺正操作,就可以构造出发送者所发送的未知态。可以设置多名接收者,使它们都受到控制者的约束,从而实现多方受控量子通信。     

Realization of the Cirac-Zoller controlled-NOT quantum gate

Quantum computers have the potential to perform certain computational tasks more efficiently than their classical counterparts. The Cirac-Zoller proposal for a scalable quantum computer is based on a string of trapped ions whose electronic states represent the quantum bits of information (or qubits). In this scheme, quantum logical gates involving any subset of ions are realized by coupling the ions through their collective quantized motion. The main experimental step towards realizing the scheme is to implement the controlled-NOT (CNOT) gate operation between two individual ions. The CNOT quantum logical gate corresponds to the XOR gate operation of classical logic that flips the state of a target bit conditioned on the state of a control bit. Here we implement a CNOT quantum gate according to the Cirac-Zoller proposal. In our experiment, two 40Ca+ ions are held in a linear Paul trap and are individually addressed using focused laser beams; the qubits are represented by superpositions of two long-lived electronic states. Our work relies on recently developed precise control of atomic phases and the application of composite pulse sequences adapted from nuclear magnetic resonance techniques.     

Experimental realization of the quantum universal NOT gate

In classical computation, a 'bit' of information can be flipped (that is, changed in value from zero to one and vice versa) using a logical NOT gate; but the quantum analogue of this process is much more complicated. A quantum bit (qubit) can exist simultaneously in a superposition of two logical states with complex amplitudes, and it is impossible to find a universal transformation that would flip the original superposed state into a perpendicular state for all values of the amplitudes. But although perfect flipping of a qubit prepared in an arbitrary state (a universal NOT operation) is prohibited by the rules of quantum mechanics, there exists an optimal approximation to this procedure. Here we report the experimental realization of a universal quantum machine that performs the best possible approximation to the universal NOT transformation. The system adopted was an optical parametric amplifier of entangled photon states, which also enabled us to investigate universal quantum cloning.     

Driven coherent oscillations of a single electron spin in a quantum dot

The ability to control the quantum state of a single electron spin in a quantum dot is at the heart of recent developments towards a scalable spin-based quantum computer. In combination with the recently demonstrated controlled exchange gate between two neighbouring spins, driven coherent single spin rotations would permit universal quantum operations. Here, we report the experimental realization of single electron spin rotations in a double quantum dot. First, we apply a continuous-wave oscillating magnetic field, generated on-chip, and observe electron spin resonance in spin-dependent transport measurements through the two dots. Next, we coherently control the quantum state of the electron spin by applying short bursts of the oscillating magnetic field and observe about eight oscillations of the spin state (so-called Rabi oscillations) during a microsecond burst. These results demonstrate the feasibility of operating single-electron spins in a quantum dot as quantum bits.     

Geometric quantum computation using nuclear magnetic resonance

A significant development in computing has been the discovery that the computational power of quantum computers exceeds that of Turing machines. Central to the experimental realization of quantum information processing is the construction of fault-tolerant quantum logic gates. Their operation requires conditional quantum dynamics, in which one sub-system undergoes a coherent evolution that depends on the quantum state of another sub-system; in particular, the evolving sub-system may acquire a conditional phase shift. Although conventionally dynamic in origin, phase shifts can also be geometric. Conditional geometric (or 'Berry') phases depend only on the geometry of the path executed, and are therefore resilient to certain types of errors; this suggests the possibility of an intrinsically fault-tolerant way of performing quantum gate operations. Nuclear magnetic resonance techniques have already been used to demonstrate both simple quantum information processing and geometric phase shifts. Here we combine these ideas by performing a nuclear magnetic resonance experiment in which a conditional Berry phase is implemented, demonstrating a controlled phase shift gate.     

Decoherence-protected quantum gates for a hybrid solid-state spin register

Protecting the dynamics of coupled quantum systems from decoherence by the environment is a key challenge for solid-state quantum information processing. An idle quantum bit (qubit) can be efficiently insulated from the outside world by dynamical decoupling, as has recently been demonstrated for individual solid-state qubits. However, protecting qubit coherence during a multi-qubit gate is a non-trivial problem: in general, the decoupling disrupts the interqubit dynamics and hence conflicts with gate operation. This problem is particularly salient for hybrid systems, in which different types of qubit evolve and decohere at very different rates. Here we present the integration of dynamical decoupling into quantum gates for a standard hybrid system, the electron-nuclear spin register. Our design harnesses the internal resonance in the coupled-spin system to resolve the conflict between gate operation and decoupling. We experimentally demonstrate these gates using a two-qubit register in diamond operating at room temperature. Quantum tomography reveals that the qubits involved in the gate operation are protected as accurately as idle qubits. We also perform Grover's quantum search algorithm, and achieve fidelities of more than 90% even though the algorithm run-time exceeds the electron spin dephasing time by two orders of magnitude. Our results directly allow decoherence-protected interface gates between different types of solid-state qubit. Ultimately, quantum gates with integrated decoupling may reach the accuracy threshold for fault-tolerant quantum information processing with solid-state devices.     

概率门量子进化算法

量子进化算法(QEA)比传统进化算法(EA)有更好的种群多样性和全局寻优能力，但它采用概率操作过程，具有随机性和盲目性．将量子进化算法中的旋转门以概率门代替，在概率分析及实例验证的基础上，说明概率门量子进化算法(PGQEA)能使得对种群选取过程控制在全局优化的方向下，并且能更快地收敛于最优解。     

Preparation of pseudopure state in nuclear spin ensemble using CNOT gates combination

Nuclear magnetic resonance (NMR) is one of the experimental schemes for quantum computation. Most initial state of quantum algorithm in NMR computation is the pseudopure state. Until now, there are several methods to prepare pseudopure state. This note, based on the idea of controlled-not (CNOT) gates combination, has analyzed the characteristics of this method in the odd- and even-qubit system. Also, we have designed the pulse sequence for a 4-qubit sample to obtain pseudopure state, and realized it in the experiment. This method reduces the complexity of experiment and gives a high signal-to-noise (S/N) ratio.     

基于IBM Q平台的量子图像算法研究

为使量子图像处理算法在量子计算机上得到验证与发展,结合IBM量子实验平台(IBM Q)上量子计算操作与量子图像处理理论的研究,设计了一种基于IBM Q平台的量子图像分割方法.提出了一种基于新型强化量子图像表达式(NEQR)的改进型强化量子图像表达式(IEQR),并根据IEQR表达式初始化量子图像分割电路.该电路由量子比较器(QBSC)和受控旋转门(Cswap)构成.最终在IBM Q和本地经典计算机仿真两种平台下实现了2×2和4×4大小的量子图像分割,实验结果表明了该算法的可行性和有效性,并验证了量子计算机的优越性.     

NMR experimental implementation of three-parties quantum superdense coding

In this study, we report an experiment realization of quantum superdense coding (QSDC) between three parties using nuclear magnetic resonance (NMR). The experimental results have shown that in terms of the QSDC schemes between multiparties proposed by Liu et al. and Crudka et al., three-qubit QSDC can transmit three bits of classical information by sending two qubits only. Our results experimentally show that quantum superdense coding, as one of the quantum information processing protocols, is superior to classical ones.     

Grover算法的非定域实现

用核磁共振技术目前只能做到对7个量子比特的演示计算。为此有人提出"分布式量子计算机"的方案。该文考察Grover搜索算法非定域实现,分析为实现这种非定域操作所需的Einstein-Podolsky-Rosen(EPR)纠缠对资源。以2个量子比特为例,说明非定域实现Grover搜索的全过程,并推广到N个量子比特情况下非定域实现的资源需求情况。N为要搜索数据库的大小。结果表明,某些情况下,非定域Grover算法耗用比经典Grover算法更多个EPR对,甚至比经典计算机所用的资源还多,此时的非定域量子计算失去了量子计算的优势。     

Implementation of a Toffoli gate with superconducting circuits

The Toffoli gate is a three-quantum-bit (three-qubit) operation that inverts the state of a target qubit conditioned on the state of two control qubits. It makes universal reversible classical computation possible and, together with a Hadamard gate, forms a universal set of gates in quantum computation. It is also a key element in quantum error correction schemes. The Toffoli gate has been implemented in nuclear magnetic resonance, linear optics and ion trap systems. Experiments with superconducting qubits have also shown significant progress recently: two-qubit algorithms and two-qubit process tomography have been implemented, three-qubit entangled states have been prepared, first steps towards quantum teleportation have been taken and work on quantum computing architectures has been done. Implementation of the Toffoli gate with only single- and two-qubit gates requires six controlled-NOT gates and ten single-qubit operations, and has not been realized in any system owing to current limits on coherence. Here we implement a Toffoli gate with three superconducting transmon qubits coupled to a microwave resonator. By exploiting the third energy level of the transmon qubits, we have significantly reduced the number of elementary gates needed for the implementation of the Toffoli gate, relative to that required in theoretical proposals using only two-level systems. Using full process tomography and Monte Carlo process certification, we completely characterize the Toffoli gate acting on three independent qubits, measuring a fidelity of 68.5?±?0.5 per cent. A similar approach to realizing characteristic features of a Toffoli-class gate has been demonstrated with two qubits and a resonator and achieved a limited characterization considering only the phase fidelity. Our results reinforce the potential of macroscopic superconducting qubits for the implementation of complex quantum operations with the possibility of quantum error correction.     

Clifford代数与量子逻辑门

以 Clifford代数为工具 ,讲座量子比特 ( Qubit)与量子逻辑门 (量子非门 ,Hadamard门 ,量子受控非门 ,Toffoli门等 )的有关性质。     

NIQGA改进及基于可变角距离的新型量子进化算法

为了提高量子进化算法的执行效率,在NIQGA算法基础上,通过改进△θi和S(αi,βi)参数表提出了一种改进算法INIQGA.又通过引入量子比特间角距离定义,提出了一种基于可变角距离旋转的量子进化算法QEA-VAR,该算法采用旋转门操作进行种群进化时,依据当前染色体中量子比特|φ〉i与最优解对应基态| 0〉或| 1〉的...     

An algorithmic benchmark for quantum information processing

Quantum information processing offers potentially great advantages over classical information processing, both for efficient algorithms and for secure communication. Therefore, it is important to establish that scalable control of a large number of quantum bits (qubits) can be achieved in practice. There are a rapidly growing number of proposed device technologies for quantum information processing. Of these technologies, those exploiting nuclear magnetic resonance (NMR) have been the first to demonstrate non-trivial quantum algorithms with small numbers of qubits. To compare different physical realizations of quantum information processors, it is necessary to establish benchmark experiments that are independent of the underlying physical system, and that demonstrate reliable and coherent control of a reasonable number of qubits. Here we report an experimental realization of an algorithmic benchmark using an NMR technique that involves coherent manipulation of seven qubits. Moreover, our experimental procedure can be used as a reliable and efficient method for creating a standard pseudopure state, the first step for implementing traditional quantum algorithms in liquid state NMR systems. The benchmark and the techniques can be adapted for use with other proposed quantum devices.     

多光子W态的高效制备

量子纠缠的制备是量子信息科学研究的一个重要课题.利用已有的控制路径门和融合门,给出一类重要的多光子最大纠缠态——W态的制备方案.区别于此前线性光学方案,该方案的实现是确定性的,并且不是基于后验选择的方式,因此可以避免线性光学方案的概率问题以及制备出来的量子态在使用上的局限性.同时方案实现所需的资源仅随光子数的增加而呈线性增长,比之传统线路量子计算模式下的多项式增长有着极大的优化.总之方案的确定性、适用性、高效性等特点,将使得方案更具可行性,也更适用于大规模量子信息过程.