Adiabatic passage for one-step generation of <Emphasis Type="Italic">n</Emphasis>-qubit Greenberger–Horne–Zeilinger states of superconducting qubits via quantum Zeno dynamics

An efficient scheme is proposed for generating n-qubit Greenberger–Horne–Zeilinger states of n superconducting qubits separated by (\(n-1\)) coplanar waveguide resonators capacitively via adiabatic passage with the help of quantum Zeno dynamics in one step. In the scheme, it is not necessary to precisely control the time of the whole operation and the Rabi frequencies of classical fields because of the introduction of adiabatic passage. The numerical simulations for three-qubit Greenberger–Horne–Zeilinger state show that the scheme is insensitive to the dissipation of the resonators and the energy relaxation of the superconducting qubits. The three-qubit Greenberger–Horne–Zeilinger state can be deterministically generated with comparatively high fidelity in the current experimental conditions, though the scheme is somewhat sensitive to the dephasing of superconducting qubits.     

Fast synthesis of the Fredkin gate via quantum Zeno dynamics

We propose a scheme for fast synthesizing the Fredkin gate with rf SQUID qubits. This scheme utilizes the quantum Zeno dynamics induced by continuous couplings and the non-identical couplings between SQUIDs and superconducting cavity. The effects of decoherence on the performance for the gate are analyzed in virtue of master equation and non-unitary evolution with full Hamiltonian. The strictly numerical simulation shows that the fidelity of this Fredkin gate is relatively high corresponding to current typical experimental parameters. Furthermore, an equivalent physical model is also constructed in an array of coupled cavities.     

On implementing nondestructive triplet Toffoli gate with entanglement swapping operations via the GHZ state analysis

We investigate an novel implementation of a Toffoli gate using multiple independent auxiliary photons prepared beforehand in single-qubit states. This gate can be performed nondestructively with entanglement swapping via the Greenberger–Horne–Zeilinger state analysis. We evaluate the performance of the proposed Toffoli gate with the fidelity based on different computation bases. The multi-qubit-entanglement gate is no longer theoretical since it can be implemented in principle with single-qubit photons.     

Implementing gate operations between uncoupled qubits in linear nearest neighbor arrays using a learning algorithm

We propose a new scheme to implement gate operations in a one dimensional linear nearest neighbor array, by using dynamic learning algorithm. This is accomplished by training quantum system using a back propagation technique, to find the system parameters that implement gate operations directly. The key feature of our scheme is that, we can reduce the computational overhead of a quantum circuit by finding the parameters to implement the desired gate operation directly, without decomposing them into a sequence of elementary gate operations. We show how the training algorithm can be used as a tool for finding the parameters for implementing controlled-NOT (CNOT) and Toffoli gates between next-to-nearest neighbor qubits in an Ising-coupled linear nearest neighbor system. We then show how the scheme can be used to find parameters for realizing swap gates first, between two adjacent qubits and then, between two next-to-nearest-neighbor qubits, in each case without decomposing it into 3 CNOT gates. Finally, we show how the scheme can be extended to systems with non-diagonal interactions. To demonstrate, we train a quantum system with Heisenberg interactions to find the parameters to realize a swap operation.     

Upper bounds for reversible circuits based on Young subgroups

We present tighter upper bounds on the number of Toffoli gates needed in reversible circuits. Both multiple controlled Toffoli gates and mixed polarity Toffoli gates have been considered for this purpose. The calculation of the bounds is based on a synthesis approach based on Young subgroups that results in circuits using a more generalized gate library. Starting from an upper bound for this library we derive new bounds which improve the existing bound by around 77%.     

Using non-ideal gates to implement universal quantum computing between uncoupled qubits

In many physical systems, when implementing quantum gate operations unavoidable global and relative phases occur as by-products due to the internal structure of the governing Hamiltonian. To correct, additional phase rotation gates are used, which increases the computational overhead. Here, we show how these phase by-products can actually be used to our advantage by using them to implement universal quantum computing between qubits not directly coupled to each other. The gate operations, CNOT, Toffoli, and swap gates, require much less computational overhead than present schemes, and are achieved with fidelity greater than 99%. We then present a linear nearest-neighbor architecture that takes full advantage of the phase by-products, and we show how to implement gates from a universal set efficiently in this layout. In this scheme gate operations are realized by only varying a single control parameter per data qubit, and the ability to tune couplings is not required.     

Improved quantum ripple-carry addition circuit

A serious obstacle to large-scale quantum algorithms is the large number of elementary gates, such as the controlled-NOT gate or Toffoli gate. Herein, we present an improved linear-depth ripple-carry quantum addition circuit, which is an elementary circuit used for quantum computations. Compared with previous addition circuits costing at least two Toffoli gates for each bit of output, the proposed adder uses only a single Toffoli gate. Moreover, our circuit may be used to construct reversible circuits for modular multiplication, Cx mod M with x < M, arising as components of Shor’s algorithm. Our modular-multiplication circuits are simpler than previous constructions, and may be used as primitive circuits for quantum computations.     

扩展Toffoli门及其在多输出电路设计中的应用

用量子计算电路实现布尔逻辑运算是发展量子计算的一个重要目标。提出了量子扩展Toffoli门,及其在实现多输出逻辑电路中的转换算法。该算法将传统PLA文件的SOP积项转换到实现等价逻辑功能的量子Toffoli积项,能够用量子扩展Toffoli门实现。通过MCNC基准电路的测试结果表明,与经典PLA描述相比,用扩展Toffoli门能够更有效地描述多输出逻辑函数。     

Toffoli gate and quantum correlations: a geometrical approach

By using a geometrical approach, we investigate the behavior of the quantum Toffoli gate in connection to quantum correlations. Special attention is paid to states with maximally mixed marginals. Finally and in the same vein, we scrutinize the Hadamard gate.     

Toffoli门及相位估计的分解

给出了Toffoli门和量子相位估计第一阶段运算P这两个受控运算的分解及相应的图示说明,使得人们可以更好地从矩阵论和算子论的角度理解与应用Toffoli门和量子相位估计。     

One-step implementation of a multi-target-qubit controlled phase gate in a multi-resonator circuit QED system

Circuit quantum electrodynamics system composed of many qubits and resonators may provide an excellent way to realize large-scale quantum information processing (QIP). Because of key role for large-scale QIP and quantum computation, multi-qubit gates have drawn intensive attention recently. Here, we present a one-step method to achieve a multi-target-qubit controlled phase gate in a multi-resonator system, which possesses a common control qubit and multiple different target qubits distributed in their respective resonators. Noteworthily, the implementation of this multi-qubit phase gate does not require classical pulses, and the gate operation time is independent of the number of qubits. Besides, the proposed scheme can in principle be adapted to a general type of qubits like natural atoms, quantum dots, and solid-state qubits (e.g., superconducting qubits and NV centers).     

Quantum state transfer with a two-dimensional Cooper-pair box qubit array

A theoretical scheme is proposed to transfer quantum state with a two-dimensional Cooper-pair box qubit array in circuit QED devices, in which coplanar transmission line resonators play the role of a quantum data bus. Based on the Raman transitions, the resonator-assisted quantum state transfer between any selected pair of qubits can be performed by addressing the local gate pulses. Thus the scheme may offer an effective route towards scalable quantum state transfer with superconducting qubits.     

Efficient experimental design of high-fidelity three-qubit quantum gates via genetic programming

We have designed efficient quantum circuits for the three-qubit Toffoli (controlled–controlled-NOT) and the Fredkin (controlled-SWAP) gate, optimized via genetic programming methods. The gates thus obtained were experimentally implemented on a three-qubit NMR quantum information processor, with a high fidelity. Toffoli and Fredkin gates in conjunction with the single-qubit Hadamard gates form a universal gate set for quantum computing and are an essential component of several quantum algorithms. Genetic algorithms are stochastic search algorithms based on the logic of natural selection and biological genetics and have been widely used for quantum information processing applications. We devised a new selection mechanism within the genetic algorithm framework to select individuals from a population. We call this mechanism the “Luck-Choose” mechanism and were able to achieve faster convergence to a solution using this mechanism, as compared to existing selection mechanisms. The optimization was performed under the constraint that the experimentally implemented pulses are of short duration and can be implemented with high fidelity. We demonstrate the advantage of our pulse sequences by comparing our results with existing experimental schemes and other numerical optimization methods.     

Efficient processing of enumerative set-based queries

Many applications often require finding sets of entities of interest that meet certain constraints. Such set-based queries (SQs) can be broadly classified into two types: optimization SQs that involve some optimization constraint and enumerative SQs that do not have any optimization constraint. While there has been much research on the evaluation of optimization SQs, there is very little work on the evaluation of enumerative SQs, which represent the most fundamental fragment of set-based queries. In this paper, we address the problem of evaluating enumerative SQs using RDBMS. While enumerative SQs can be expressed using SQL, existing relational engines, unfortunately, are not able to efficiently evaluate such queries due to their complexity. In this paper, we propose a novel evaluation approach for enumerative SQs. Our experimental results on PostgreSQL demonstrate that our proposed approach outperforms the conventional approach by up to three orders of magnitude.     

Generation and swapping of multi-qubit entangled state in a coupled superconducting resonator array

An efficient method is proposed for the generation and swapping of multi-qubit entangled state in an array of linearly coupled superconducting resonators, each of which is coupled to N superconducting qubits. With the external driving fields to adjust the desired qubit–resonator interaction, we firstly show that the multipartite entangled state of superconducting qubits hosted in two nearest-neighbor interacting resonators can be deterministically realized. Furthermore, by utilizing the produced entangled state, we put forward a protocol for the swapping of quantum entangled state in the coupled resonator array based on measurement, i.e., the multi-particle entangled state can be achieved for the qubits in long-distance separated resonators. The numerical simulation suggests that our scheme is feasible with current circuit QED technology.     

Synthesis of reversible circuits with minimal costs

We present fast algorithms to synthesize exact minimal reversible circuits for various types of gate and cost. By reducing reversible logic synthesis problems to permutation group problems, we use the powerful algebraic software GAP to solve such problems. Our approach can minimize for arbitrary cost functions of gates. In addition, we show that Peres gates are a better choice than the standard Toffoli gates in libraries of universal reversible gates. This work was supported by the NNSF of China under Grant 60773205 and the Fund of Cultivating Leading Scholars in UESTC.     

基于正反控制门的可逆逻辑综合

提出一种基于正反控制(PNC)门可逆网络的级联算法,为3位输入/输出函数设计相应的模板,给出级联网络的约简算法。实验结果表明,与Toffoli门级联成的网络相比,使用PNC门的可逆网络中门的数量较少,在降低网络代价方面具有一定优势。     

Efficiency of open quantum walk implementation of dissipative quantum computing algorithms

An open quantum walk formalism for dissipative quantum computing is presented. The approach is illustrated with the examples of the Toffoli gate and the Quantum Fourier Transform for 3 and 4 qubits. It is shown that the algorithms based on the open quantum walk formalism are more efficient than the canonical dissipative quantum computing approach. In particular, the open quantum walks can be designed to converge faster to the desired steady state and to increase the probability of detection of the outcome of the computation.     

基于正反控制模型的可逆逻辑综合

对一般Toffoli门进行了衍变和推广,给出了一个正反控制可逆级联模型(PNCRC),该模型拥有五种基本线型,并能正反控制目标位的输出.基于该模型给出了相应的可逆综合算法.对输入数不大于16的NCMCBench-mark函数进行测试并与已有的可逆综合方法比较,结果表明,利用该模型进行的可逆综合,垃圾信息数和可逆门数的优化效果都具有一定程度的改善.     

Quantum computation and entangled state generation via long-range off-resonant Raman coupling

A scheme is proposed to implement two-qubit controlled quantum phase gate and SWAP gate and generate two-qubit entangled state via long-range off-resonant Raman coupling between two spatially separated superconducting quantum-interference devices (SQUIDs). In the scheme each SQUID is coupled with a single-mode cavity individually and the two distant cavities are connected by an optical fiber. The two lowest levels of each SQUID are used to represent the two logical states of a qubit while the two intermediate levels of each SQUID are used to facilitate coherent coupling of quantum states of the qubits during the virtual excitation process of photon. The scheme is robust against fiber loss, cavity decay, and the effect of spontaneous decay from the higher levels and it would be an important step toward distributed quantum computation and long-distance entanglement distribution.