Toffoli gate made from a single resonant interaction with a trapped ion system

We propose a simple but practical scheme to implement a three-qubit Toffoli gate by a single resonant interaction in a trapped ion system. The scheme does not require two-qubit controlled-NOT gates but uses a three-qubit phase gate and two Hadamard gates, where the phase gate can be implemented by only a single resonant interaction of the trapped ions with the first lower vibrational sideband mode. Both the situations, with and without spontaneous ionic emission, are investigated. Discussions are made for the advantages and the experimental feasibility of our scheme.     

Approximate Toffoli Gate Originated from a Single Resonant Interaction of Cavity Dissipation and Atomic Spontaneous Emission

We propose a potentially practical scheme to implement an approximate three-qubit Toffoli gate by a single resonant interaction in dissipative cavity QED in which the cavity mode decay and atomic spontaneous emission are considered. The scheme does not require two-qubit controlled-NOT gates but uses a three-qubit phase gate and two Hadamard gates, where the approximate phase gate can be implemented by only a single dissipative resonant interaction of atoms with the cavity mode. Discussions are made for the advantages and the experimental feasibility of our scheme.     

Experimental realization of linear-optical partial swap gates

We present a linear-optical implementation of a class of two-qubit partial SWAP gates for polarization states of photons. Different gate operations, including the SWAP and entangling sqrt[SWAP], can be obtained by changing a classical control parameter, namely, the path difference in the interferometer. Reconstruction of output states, full quantum process tomography, and an evaluation of entanglement of formation prove very good performance of the gates.     

Time optimal quantum control of two-qubit systems

We study the optimal quantum control of heteronuclear two-qubit systems described by a Hamiltonian containing both nonlocal internal drift and local control terms.We derive an explicit formula to compute the minimum time required to steer the system from an initial state to a specified final state.As applications the minimal time to implement Controlled-NOT gate,SWAP gate and Controlled-U gate is calculated in detail.The experimental realizations of these quantum gates are explicitly presented.     

A scheme for realizing a distant two-qubit controlled-U gate with nearest qubit-qubit interaction

We propose a new scheme for realizing a distant two-qubit controlled-U gate with nearest qubit-qubit interaction. The present scheme does not need measurement. Furthermore, it is noted that the two-qubit CNOT gates required by the scheme are greatly reduced when compared with the conventional method based on SWAP operations. The scheme is useful in quantum computing with solid-state systems where only interaction between nearest systems is available.     

Generation of Perfectly Entangled Two and Three Qubits States by Classical Random Interaction

This study examines the possibility of finding perfect entanglers for a Hamiltonian which corresponds to several quantum information platforms of interest at the present time. However, in this study, a superconducting circuit is used that stands out from other quantum-computing devices, especially because transmon qubits can be coupled via capacitors or microwave cavities, which enables to combine high coherence, fast gates, and high flexibility in its design parameters. There are currently two factors limiting the performance of superconducting processors: timing mismatch and the limitation of entangling gates to two qubits. In this work, a two-qubit SWAP and a three-qubit Fredkin gate is presented, additionally, a perfect adiabatic entanglement generation between two and three programmable superconducting qubits is also demonstrated. Furthermore, the impact of random dephasing, emission, and absorption noises on the quantum gates and entanglement is also demonstrated in this study. It is demonstrated by numerical simulation that CSWAP gate and W-state generation can be achieved perfectly in one step with high reliability under weak coupling conditions. Hence, this scheme could contribute to quantum teleportation, quantum communication, and some other areas of quantum information processing.     

Virtual qubits: Multilevels instead of multiparticles

The possibility of using multilevel quantum systems with a discrete nonequidistant spectrum for the physical implementation of a universal collection of quantum gates, which is required for constructing an arbitrary algorithm for a quantum computer, is studied on the basis of the proposed virtual-spin formalism. It is shown that such a set of gates, including two-qubit gates, can be constructed on a single spin-3/2 nucleus. The assertion that three-qubit gates can also be realized on a single spin-7/2 quantum particle is substantiated.     

飞秒激光直写光量子逻辑门

量子比特在同一时刻可处于所有可能状态上的叠加特性使得量子计算机具有天然的并行计算能力,在处理某些特定问题时具有超越经典计算机的明显优势.飞秒激光直写技术因其具有单步骤高效加工真三维光波导回路的能力,在制备通用型集成光量子计算机的基本单元—量子逻辑门中发挥着越来越重要的作用.本文综述了飞秒激光直写由定向耦合器构成的光量子比特逻辑门的进展.主要包括定向耦合器的功能、构成、直写和性能表征,集成波片、哈达玛门和泡利交换门等单量子比特逻辑门、受控非门和受控相位门等两量子比特逻辑门的直写加工,并对飞秒激光加工三量子比特逻辑门进行了展望.     

Interaction cost of nonlocal gates

We introduce the interaction cost of a nonlocal gate as the minimal time of interaction required to perform the gate when assisting the process with fast local unitaries. This cost, of interest both in the areas of quantum control and quantum information, depends on the specific interaction, and allows one to compare in an operationally meaningful manner any two nonlocal gates. In the case of a two-qubit system, an analytical expression for the interaction cost of any unitary operation given any coupling Hamiltonian is obtained. One gate may be more time consuming than another for any possible interaction. This defines a partial order structure in the set of nonlocal gates, that compares their degree of nonlocality. We analytically characterize this partial order in a region of the set of two-qubit gates.     

Modified Khaneja--Glaser Decomposition and Realization of Three-Qubit Quantum Gate

Optimal implementation of quantum gates is crucial for realization of quantum computation. We slightly modify the Khaneja-Glaser decomposition （KGD） for n-qubits and give a new Cartan subalgbra in the second step of the decomposition. Based on this modified KGD, we investigate the realization of three-qubit logic gate and obtain the result that a general three-qubit quantum logic gate can be implemented using at most 73 one-qubit gates rotations with respect to the y and z axes and 26 CNOT gates.     

One-Step Realization of SWAP Gate with Superconducting Quantum-Interference Devices and Atoms in Cavity QED

We put forward a simple scheme for one-step realization of a two-qubit SWAP gate with SQUIDs (superconducting quantum-interference devices) in cavity QED via Raman transition. In this scheme, the cavity field is only virtually excited and thus the cavity decay is suppressed. The SWAP gate is realized by using only two lower flux states of the SQUID system and the excited state would not be excited. Therefore, the effect of decoherence caused from the levels of the SQUID system is possibly minimized. The scheme can also be used to implement the SWAP gate with atoms.     

三量子比特纠缠Greenberger-Horne-Zeilinger态和W态的量子线路实现

两个简单的量子线路被提出分别用来制备三量子比特Greenberger-Horne-Zeilinger(GHZ)态和W态。众所周知,任意的多量子比特门都可以由受控非门和单量子比特门复合而成。同样,我们发现三量子比特GHZ态和W态也可以由受控非门和单量子比特门来制备。因此,从量子计算的角度来看我们的方案十分重要。由于在整个过程只用到了单量子比特操作和双量子比特操作,所以我们的方案在实验中很容易实现。     

Efficient Nonlocal <Emphasis Type="Italic">M</Emphasis>-Control and <Emphasis Type="Italic">N</Emphasis>-Target Controlled Unitary Gate Using Non-symmetric GHZ States

Efficient local implementation of a nonlocal M-control and N-target controlled unitary gate is considered. We first show that with the assistance of two non-symmetric qubit⁽¹⁾-qutrit^(N) Greenberger-Horne-Zeilinger (GHZ) states, a nonlocal 2-control and N-target controlled unitary gate can be constructed from 2 local two-qubit CNOT gates, 2N local two-qutrit conditional SWAP gates, N local qutrit-qubit controlled unitary gates, and 2N single-qutrit gates. At each target node, the two third levels of the two GHZ target qutrits are used to expose one and only one initial computational state to the local qutrit-qubit controlled unitary gate, instead of being used to hide certain states from the conditional dynamics. This scheme can be generalized straightforwardly to implement a higher-order nonlocal M-control and N-target controlled unitary gate by using M non-symmetric qubit⁽¹⁾-qutrit^(N) GHZ states as quantum channels. Neither the number of the additional levels of each GHZ target particle nor that of single-qutrit gates needs to increase with M. For certain realistic physical systems, the total gate time may be reduced compared with that required in previous schemes.     

高维辅助的普适量子线路优化

受到Lanyon等(Lanyon B P et al 2008 Nature Physics. 5 134)利用高维Hilbert空间成功简化Toffoli门的启发, 本文将辅助维度应用到普适量子线路中, 结合Cosine-Sine Decomposition(CSD), Quantum Shannon Decomposition(QSD)等矩阵分解方法, 优化了两比特和三比特普适幺正量子线路, 给出了计算n比特普适量子线路复杂度的公式, 并利用线性光学和腔QED系统设计了实验方案. 结果表明, 两比特和三比特量子线路的复杂度已分别接近和优于目前最优结果, 且随着比特数的增加, 本方案的优势愈加明显.     

Speeding up transmissions of unknown quantum information along Ising-type quantum channels

Quantum teleportation with entanglement channels and a series of two-qubit SWAP gates between the nearestneighbor qubits are usually utilized to achieve the transfers of unknown quantum state from the sender to the distant receiver. In this paper, by simplifying the usual SWAP gates we propose an approach to speed up the transmissions of unknown quantum information, specifically including the single-qubit unknown state and two-qubit unknown entangled ones,by a series of entangling and disentangling operations between the remote qubits with distant interactions. The generic proposal is demonstrated specifically with experimentally-existing Ising-type quantum channels without transverse interaction; liquid NMR-molecules driven by global radio frequency electromagnetic pulses and capacitively-coupled Josephson circuits driven by local microwave pulses. The proposal should be particularly useful to set up the connections between the distant qubits in a chip of quantum computing.     

Quantum computing through electron propagation in edge states of quantum spin Hall systems

We propose to implement quantum computing by the on-demand control of the wave packets propagation in helical edge channels of the quantum spin Hall systems (QSHs). Two non-commutative single-qubit gates are realized by the gate voltages applied on the edge channels. The two-qubit controlled phase gate is implemented by the capacitive Coulomb interaction between two adjacent edge channels from two parallel QSHs. A universal set of quantum gates thus can be realized in an all-electrical way. It is also shown that the fidelity and the purity of the controlled phase gate can reach a high value, with both the time delay and the finite width of the wave packets taken into account.     

Quantum logic via the exchange blockade in ultracold collisions

A nuclear spin can act as a quantum switch that turns on or off ultracold collisions between atoms even when there is neither interaction between nuclear spins nor between the nuclear and electron spins. This "exchange blockade" is a new mechanism for implementing quantum logic gates that arises from the symmetry of composite identical particles, rather than direct coupling between qubits. We study the implementation of the entangling sqrt SWAP gate based on this mechanism for a model system of two atoms, each with ground electronic configuration 1S0, spin 1/2 nuclei, and trapped in optical tweezers. We evaluate a proof-of-principle protocol based on adiabatic evolution of a one-dimensional double Gaussian well, calculating fidelities of operation as a function of interaction strength, gate time, and temperature.     

Unselective ground-state blockade of Rydberg atoms for implementing quantum gates

A dynamics regime of Rydberg atoms, unselective ground-state blockade (UGSB), is proposed in the context of Rydberg antiblockade (RAB), where the evolution of two atoms is suppressed when they populate in an identical ground state. UGSB is used to implement a SWAP gate in one step without individual addressing of atoms. Aiming at circumventing common issues in RAB-based gates including atomic decay, Doppler dephasing, and fluctuations in the interatomic coupling strength, we modify the RAB condition to achieve a dynamical SWAP gate whose robustness is much greater than that of the nonadiabatic holonomic one in the conventional RAB regime. In addition, on the basis of the proposed SWAP gates, we further investigate the implementation of a three-atom Fredkin gate by combining Rydberg blockade and RAB. The present work may facilitate to implement the RAB-based gates of strongly coupled atoms in experiment.     

Exact two-qubit universal quantum circuit

We provide an analytic way to implement any arbitrary two-qubit unitary operation, given an entangling two-qubit gate together with local gates. This is shown to provide explicit construction of a universal quantum circuit that exactly simulates arbitrary two-qubit operations in SU(4). Each block in this circuit is given in a closed form solution. We also provide a uniform upper bound of the applications of the given entangling gates, and find that exactly half of all the controlled-unitary gates satisfy the same upper bound as the CNOT gate. These results allow for the efficient implementation of operations in SU(4) required for both quantum computation and quantum simulation.     

Quantum logic gates operation using SQUID qubits in bimodal cavity

We present a scheme to realize the basic two-qubit logic gates such as the quantum phase gate and SWAP gate using a detuned microwave cavity interacting with three-level superconducting-quantum-interference-device (SQUID) qubit(s), by placing SQUID(s) in a two-mode microwave cavity and using adiabatic passage methods. In this scheme, the two logical states of the qubit are represented by the two lowest levels of the SQUID, and the cavity fields are treated as quantized. Compared with the previous method, the complex procedures of adjusting the level spacing of the SQUID and applying the resonant microwave pulse to the SQUID to create transformation are not required. Based on superconducting device with relatively long decoherence time and simplified operation procedure, the gates operate at a high speed, which is important in view of decoherence.