Qubit Gates Research Articles

Novel Synthesis Methodology for Fault Tolerant Reversible Circuits by Bounded Model Checking for Linear Temporal Logic

Reversible circuit is of interest due to the characteristics of low energy consumption. This paper proposes a new scheme for synthesizing fault tolerant reversible circuits. A two-step method is put forward to convert an irreversible function into a parity-preserving reversible circuit. By introducing model checking for linear temporal logic, we construct a finite state machine to synthesize small reversible gates from elementary 1-qubit and 2-qubit gates, which is more automatic than the methods proposed previously. Constrains are increased so as to reduce the synthesis time in the two step method. The parity-preserving gate constructed by the two-step method has characteristics of low quantum cost because the quantum representation obtained from the counterexample for a given function in each step has the minimum quantum cost. In order to further reduce the quantum cost and decrease the synthesis time, the semi parity-preserving gates are put forward for the first time. These gates are parity-preserving when the auxiliary input is set to 0 and opposite parity when 1. Maintaining good robustness of the system in performing specific function, semi parity-preserving gate is conducive to detecting the stuck-at fault and partial gate fault in reversible circuits. The innovation of this paper is introducing the formal method to synthesis small fault tolerant gate, so as to construct the circuit with robust (semi) parity-preserving gates.

Parity-gate-based quantum information processing in decoherence-free subspace with nitrogen-vacancy centers

We propose a parity-check gate (PCG) for logical qubits encoded in decoherence-free subspace (DFS) by the coherent optical pulse input–output process with nitrogen-vacancy (NV) centers fixed on the surface of microtoroidal resonators (MTRs) with quantized whispering-gallery modes (WGMs). Using the proposed PCG, we achieve controlled phase flip (CPF) gate, |χ〉 state generation, and multipartite entanglement purification. The present schemes combine the advantages of the robustness of coherent pulse and the immunity to the dephasing noise of the DFS. The performances of these schemes are also analyzed, which shows that all the schemes works well in the low-Q cavity regime and are feasible under the current experimental technology.

Parity-based mirror inversion for efficient quantum state transfer and computation in nearest-neighbor arrays

We introduce an efficient scheme for quantum state transfer that uses a parity-based mirror inversion technique. We design efficient circuits for implementing mirror inversion in Ising ${\mathbit{\ensuremath{\sigma}}}_{\mathbf{X}}{\mathbit{\ensuremath{\sigma}}}_{\mathbf{X}}$ and ${\mathbit{\ensuremath{\sigma}}}_{\mathbf{Y}}{\mathbit{\ensuremath{\sigma}}}_{\mathbf{Y}}$ coupled systems and show how to analytically solve for system parameters to implement the operation in these systems. The key feature of our scheme is a three-qubit parity gate, which we design as a two-control one-target qubit gate. The parity gate operation is implemented by only varying a single control parameter of the system Hamiltonian and the difficulty of implementing this gate is equivalent to that of a controlled-not gate in a two-qubit system. By applying a sequence of $N+1$ parity-based controlled-unitary operations between nearest-neighbor qubits, where all qubits in an $N$-qubit chain function either as controls or targets, we are able to reverse the order of all qubits along the array. These operations are accomplished by varying only a single control parameter per data qubit. The control parameter depends on the physical system under consideration and on the choice of the designer. Since every qubit participates in the mirror-inversion process functioning either as a control or target, all nearest-neighbor couplings are used. Therefore, we do not need additional measures to cancel the effect of any unwanted interactions and the quantum cost of our scheme does not increase in systems that do not have the ability shut off couplings. Moreover, our scheme does not require additional ancillas, nor does it use a pre-engineered mirror-periodic Hamiltonian to govern the evolution of the system. Using our mirror inversion scheme, we also show how to implement a swap gate between two arbitrary remote qubits, move a block of qubits, and implement efficient computing between two remote qubits in nearest-neighbor layouts.

Single-qubit gates for ensemble qubits via off-resonant Raman interaction

In this paper we analyze the fidelity of single-qubit gates based on off-resonant Raman interaction when they are applied to qubits implemented as ensembles of active centers. In particular, we investigate the additional errors induced by the inhomogeneous broadening of the qubit ensemble. We propose a new scheme which can be used to significantly decrease these errors and to realize high-fidelity logic gates for ensemble qubits.

Universal quantum computation using all-optical hybrid encoding**Project supported by the National Natural Science Foundation of China (Grant Nos. 61465013, 11465020, and 11264042).

By employing displacement operations, single-photon subtractions, and weak cross-Kerr nonlinearity, we propose an alternative way of implementing several universal quantum logical gates for all-optical hybrid qubits encoded in both single-photon polarization state and coherent state. Since these schemes can be straightforwardly implemented only using local operations without teleportation procedure, therefore, less physical resources and simpler operations are required than the existing schemes. With the help of displacement operations, a large phase shift of the coherent state can be obtained via currently available tiny cross-Kerr nonlinearity. Thus, all of these schemes are nearly deterministic and feasible under current technology conditions, which makes them suitable for large-scale quantum computing.

Quantum phase gate for optical qubits with cavity quantum optomechanics.

We show that a cavity optomechanical system formed by a mechanical resonator simultaneously coupled to two modes of an optical cavity can be used for the implementation of a deterministic quantum phase gate between optical qubits associated with the two intracavity modes. The scheme is realizable for sufficiently strong single-photon optomechanical coupling in the resolved sideband regime, and is robust against cavity losses.

Z-Gate Operation on a Superconducting Flux Qubit via its Readout SQUID

In quantum information processing, fast qubit gates rely on strong coupling to control fields, but unfortunately a qubit generally cannot distinguish actual control fields from environmental noise. One of the desired logic elements, the so-called $Z$-gate, switches the sign of a ``1'' but leaves a ``0'' unchanged. This study presents a $Z$-gate with a tunable coupling element that is strong only when needed, which keeps noise low yet speed high.

High-contrast qubit interactions using multimode cavity QED.

We introduce a new multimode cavity QED architecture for superconducting circuits that can be used to implement photonic memories, more efficient Purcell filters, and quantum simulations of photonic materials. We show that qubit interactions mediated by multimode cavities can have exponentially improved contrast for two qubit gates without sacrificing gate speed. Using two qubits coupled via a three-mode cavity system we spectroscopically observe multimode strong couplings up to 102MHz and demonstrate suppressed interactions off resonance of 10kHz when the qubits are ≈600 MHz detuned from the cavity resonance. We study Landau-Zener transitions in our multimode systems and demonstrate quasiadiabatic loading of single photons into the multimode cavity in 25ns. We introduce an adiabatic gate protocol to realize a controlled-Z gate between the qubits in 95ns and create a Bell state with 94.7% fidelity. This corresponds to an on/off ratio (gate contrast) of 1000.

English

Reversible Logic is an emerging technology; it has hellocious applications in various fields. Reversible logic implementation reduces loss of entropy because of bit manipulations. Conservative reversible logic gate obeys reversible logic rules and also satisfies the property that there is equal number of 1s in the outputs as in the inputs. In this work, modified design of SCRL (Super Conservative Reversible Logic) gate for the design of reversible quantum circuit is presented. The proposed SCRL Integrated Qubit gate has 1 control input which swaps n-1 depending on control input. Barrel shifter forms an integral component of many computing systems. As an example of using the proposed SCRL gate to design efficient reversible quantum circuits, the design of reversible barrel shifter with zero ancilla inputs and zero garbage outputs is illustrated.

Valence tautomeric dinuclear adducts of Co(II) diketonates with redox-active diquinones for the design of spin qubits: computational modeling.

The possibility of employing the mechanism of intramolecular electron transfer between metal and ligand centers in the valence tautomeric complexes formed as electrically neutral 2 : 1 adducts of Co(II) diketonates and redox-active tetradentate di-o-quinones, for quantum information processing, has been computationally studied using the DFT B3LYP*/6-311++G(d,p) method. It has been shown that by the proper choice of a linker group bridging the quinone rings and substituents in the diketonate fragments, complexes with the properties required in 2-qubit quantum gates (sufficiently narrow energy gaps between the spin states and weakly coupled paramagnetic centers) can be designed, in order to realize the mechanism of thermally driven migration of paramagnetic centers between the o-quinone fragments and metal atoms. These are exemplified by the adduct of bis-(hexafluoroacetylacetonate)Co(ii) with a diquinone containing dimethylene linker. Valence tautomerism is considered as a new, promising mechanistic paradigm for the molecular design of 2-qubit molecular systems.

Lyapunov control on quantum systems

We review the scheme of quantum Lyapunov control and its applications into quantum systems. After a brief review on the general method of quantum Lyapunov control in closed and open quantum systems, we apply it into controlling quantum states and quantum operations. The control of a spin-1/2 quantum system, driving an open quantum system into its decoherence free subspace (DFS), constructing single qubit and two-qubit logic gates are taken to illustrate the scheme. The optimalization of the Lyapunov control is also reviewed in this article.

A quantum backpropagation multilayer perceptron (QBMLP) for predicting iron adsorption capacity of calcareous soil from aqueous solution

Removal of miscible hazardous materials from aqueous solutions is an alarming problem for the environmental scientists. Several linear and nonlinear regression models like Langmuir, Freundlich, D–R, Tempkin isotherm models are in vogue for determining the adsorbing capacity of standard adsorbents used for this purpose.In this article, we propose a novel quantum inspired backpropagation multilayer perceptron (QBMLP) based on quantum gates (single qubit rotation gates and two qubit controlled-not gates) for the prediction of this adsorption behavior exhibited by calcareous soil oftentimes used in adsorbing miscible iron from aqueous solutions. The backpropagation learning formulae for the proposed QBMLP architecture has also been generalized for multiple number of layers in both field homogeneous and field heterogeneous configurations characterized by three standard activations, viz., sigmoid, tanh and tan1.5h functions.Applications of the efficiency of the proposed QBMLP over the regression models are demonstrated with regards to the prediction behavior of the adsorption of iron by calcareous soil from an aqueous solution with effect to various characteristic adsorbent parameters. The adsorption process is considered to be a physical one since the activation energy (EA) of ferrous ion adsorption is 9.469kJmol−1 due to Arrhenius. Moreover, the thermodynamic parameters of Gibb's free energy (G0), enthalpy (H0) and entropy (S0) values indicate it be spontaneous.Results indicate that QBMLP predicts the adsorption behavior of calcareous soil to a very closer extent thereby obviating the need for further regression/experimental analysis. Comparison with the performance of a similar classical multilayer perceptron (MLP) architecture also reveals the prediction and time efficiency of the proposed QBMLP architecture.

Two dimensional kicked quantum Ising model: dynamical phase transitions

Using an efficient one and two qubit gate simulator operating on graphical processing units, we investigate ergodic properties of a quantum Ising spin model on a two-dimensional lattice, which is periodically driven by a δ-pulsed transverse magnetic field. We consider three different dynamical properties: (i) level density, (ii) level spacing distribution of the Floquet quasienergy spectrum, and (iii) time-averaged autocorrelation function of magnetization components. Varying the parameters of the model, we found transitions between ordered (non-ergodic) and quantum chaotic (ergodic) phases, but the transitions between flat and non-flat spectral density do not correspond to transitions between ergodic and non-ergodic local observables. Even more surprisingly, we found good agreement of level spacing distribution with the Wigner surmise of random matrix theory for almost all values of parameters except where the model is essentially non-interacting, even in regions where local observables are not ergodic or where spectral density is non-flat. These findings question the versatility of the interpretation of level spacing distribution in many-body systems and stress the importance of the concept of locality.

Individual addressing of trapped 171Yb+ ion qubits using a microelectromechanical systems-based beam steering system

The ability to individually manipulate the increasing number of qubits is one of the many challenges towards scalable quantum information processing with trapped ions. Using micro-mirrors fabricated with micro-electromechanical systems technology, we focus laser beams on individual ions in a linear chain and steer the focal point in two dimensions. We demonstrate sequential single qubit gates on multiple 171Yb+ qubits and characterize the gate performance using quantum state tomography. Our system features negligible crosstalk to neighboring ions ( <3×10−4), and switching speed comparable to typical single qubit gate times (<2 μs).

Counterfactual distributed controlled-phase gate for quantum-dot spin qubits in double-sided optical microcavities

The existing distributed quantum gates required physical particles to be transmitted between two distant nodes in the quantum network. We here demonstrate the possibility to implement distributed quantum computation without transmitting any particles. We propose a scheme for a distributed controlled-phase gate between two distant quantum-dot electron-spin qubits in optical microcavities. The two quantum-dot-microcavity systems are linked by a nested Michelson-type interferometer. A single photon acting as ancillary resource is sent in the interferometer to complete the distributed controlled-phase gate, but it never enters the transmission channel between the two nodes. Moreover, we numerically analyze the effect of experimental imperfections and show that the present scheme can be implemented with high fidelity in the ideal asymptotic limit. The scheme provides further evidence of quantum counterfactuality and opens promising possibilities for distributed quantum computation.

Interplay between exchange interaction and magnetic field gradient in a double quantum dot with two individual electron spin qubits

We studied experimentally the coherent exchange interaction between two antiparallel electron spins in a double quantum dot with an increasing magnetic field gradient between the two dots. We observed an increase of the oscillation frequency and a reduction of the oscillation contrast. Both observations are consistent with a simple model of two spins interacting via exchange interaction. The demonstrated control of the two-electron spin states is interesting to produce gates for individual spin qubits.

Exchange-based two-qubit gate for singlet-triplet qubits

We analyze a simple exchange-based two-qubit gate for singlet-triplet qubits in gate-defined semiconductor quantum dots that can be implemented in a single exchange pulse. Excitations from the logical subspace are suppressed by a magnetic field gradient that causes spin-flip transitions to be non-energy-conserving. We show that the use of adiabatic pulses greatly reduces leakage processes comapred to square pulses. We also characterize the effect of charge noise on the entanglement fidelity of the gate both analytically and in simulations; demonstrating high entanglement fidelities for physically realistic experimental parameters. Specifically we find that it is possible to achieve fidelities and gate times that are comparable to single-qubit states using realistic magnetic field gradients.

Nonadiabatic corrections to a quantum dot quantum computer working in adiabatic limit

The time of operation of an adiabatic quantum computer must be less than the decoherence time, otherwise the computer would be nonoperative. So far, the nonadiabatic corrections to an adiabatic quantum computer are merely theoretical considerations. By the above reason, we consider the particular case of a quantum-dot-confined electron spin qubit working adiabatically in the nanoscale regime (e.g., in the MeV range of energies) and include nonadiabatic corrections in it. If the decoherence times of a quantum dot computer are ∼100 ns [J M Kikkawa and D D Awschalom, Phys. Rev. Lett. 80, 4313 (1998)] then the predicted number of one qubit gate (primitive) operations of the Loss–DiVincenzo quantum computer in such an interval of time must be >10 10. However, if the quantum-dot-confined electron spin qubit is very excited (i.e., the semiclassical limit) the number of operations of such a computer would be approximately the same as that of a classical computer. Our results suggest that for an adiabatic quantum computer to operate successfully within the decoherence times, it is necessary to take into account nonadiabatic corrections.

Controllable interdot coupling in a Si-based double quantum dot system for a qubit gate

We have implemented a Si-based coupled double-dot device with five independent gates vertically layered above the active channel, which can provide more effective controllability of interdot coupling without changing the potential shape of an individual dot. We observed a transition from a merged single dot to the coupled double dot by adjusting the interdot coupling strength via a central gate. From the honeycomb charge stability diagram, the capacitance-related critical parameters of the coupled double dot, which will be of impotance in the Si-based two-qubit gate applications, are deduced.

Dynamically corrected gates for qubits with always-on Ising couplings: Error model and fault tolerance with the toric code

We describe how a universal set of dynamically-corrected quantum gates can be implemented using sequences of shaped decoupling pulses on any qubit network forming a sparse bipartite graph with always-on Ising interactions. These interactions are constantly decoupled except when they are needed for two-qubit gates. We analytically study the error operators associated with the constructed gates up to third order in the Magnus expansion, analyze these errors numerically in the unitary time evolution of small qubit clusters, and give a bound on high-order errors for qubits on a large square lattice. We prove that with a large enough toric code the present gate set can be used to implement a fault-tolerant quantum memory.