Two-qubit controlled-NOT Gate Research Articles

Speed limits for quantum gates in multiqubit systems

We use analytical and numerical calculations to obtain speed limits for various unitary quantum operations in multiqubit systems under typical experimental conditions. The operations that we consider include single-, two-, and three-qubit gates, as well as quantum-state transfer in a chain of qubits. We find in particular that simple methods for implementing two-qubit gates generally provide the fastest possible implementations of these gates. We also find that the three-qubit Toffoli gate time varies greatly depending on the type of interactions and the system's geometry, taking only slightly longer than a two-qubit controlled-not (cnot) gate for a triangle geometry. The speed limit for quantum-state transfer across a qubit chain is set by the maximum spin-wave speed in the chain.

Universal quantum computation with ordered spin-chain networks

It is shown that anisotropic spin chains with gapped bulk excitations and magnetically ordered ground states offer a promising platform for quantum computation, which bridges the conventional single-spin-based qubit concept with recently developed topological Majorana-based proposals. We show how to realize the single-qubit Hadamard, phase, and $\ensuremath{\pi}/8$ gates as well as the two-qubit controlled-not (cnot) gate, which together form a fault-tolerant universal set of quantum gates. The gates are implemented by judiciously controlling Ising exchange and magnetic fields along a network of spin chains, with each individual qubit furnished by a spin-chain segment. A subset of single-qubit operations is geometric in nature, relying on control of anisotropy of spin interactions rather than their strength. We contrast topological aspects of the anisotropic spin-chain networks to those of $p$-wave superconducting wires discussed in the literature.

CONSTRUCTION AND APPLICATION OF FOUR-QUBIT SWAP LOGIC GATE IN NMR QUANTUM COMPUTING

In NMR quantum computing, spin states of spin-1/2 nuclei are called qubits. Quantum logic gates are represented by unitary matrices. As a universal gate, controlled-NOT (CNOT) is a two-qubit gate. For the IS (I = 1/2 and S = 1/2) spin system, two-qubit CNOT gate is represented by a 4 × 4 matrix. SWAP logic gate, which exchanges two quantum states, is constructed by CNOT gates. In this study, first, four-qubit CNOT gates are constructed for the IS (I = 3/2, S = 3/2) spin system. Then, by using these CNOT gates, a four-qubit SWAP logic gate is found. As an application and verification, an obtained SWAP logic gate is applied to the matrix representation of product operators for the IS (I = 3/2, S = 3/2) spin system. SWAP logic gate can also be presented by an NMR pulse sequence. By using the product operator theory, the pulse sequence of the SWAP logic gate is applied to product operators of the IS (I = 3/2, S = 3/2) spin system. The expected exchange results are obtained for both the matrix representation and the pulse sequence of SWAP logic gate.

Quantum gate using qubit states separated by terahertz

A two-qubit quantum gate is realized using electronic excited states in a single ion with an energy separation on the order of a terahertz times the Planck constant as a qubit. Two phase locked lasers are used to excite a stimulated Raman transition between two metastable states $D_{3/2}$ and $D_{5/2}$ separated by 1.82 THz in a single trapped $^{40}$Ca$^+$ ion to construct a qubit, which is used as the target bit for the Cirac-Zoller two-qubit controlled NOT gate. Quantum dynamics conditioned on a motional qubit is clearly observed as a fringe reversal in Ramsey interferometry.

Protocol and quantum circuit for implementing the N-bit discrete quantum Fourier transform in cavity QED

We present a simple protocol and quantum circuit for efficient implementation of the N-bit discrete quantum Fourier transform by using two-qubit controlled-NOT gate and SWCZ gate that is a combination of -SWAP and controlled-Z gates in cavity quantum electrodynamics. In this protocol long-lived electronic states in circular Rydberg atoms are used as quantum bits and the one-bit and two-bit quantum gate operations required for implementing the discrete quantum Fourier transform in the quantum circuit can be easily achieved with atom–microwave resonant interaction and atom–cavity interaction occurring only between two nearest-neighbour atoms. We present the detailed experimental procedure and analyse the experimental feasibility.

Rovibrational controlled-NOT gates using optimized stimulated Raman adiabatic passage techniques and optimal control theory

Implementation of quantum controlled-NOT (CNOT) gates in realistic molecular systems is studied using stimulated Raman adiabatic passage (STIRAP) techniques optimized in the time domain by genetic algorithms or coupled with optimal control theory. In the first case, with an adiabatic solution (a series of STIRAP processes) as starting point, we optimize in the time domain different parameters of the pulses to obtain a high fidelity in two realistic cases under consideration. A two-qubit CNOT gate constructed from different assignments in rovibrational states is considered in diatomic (NaCs) or polyatomic $({\text{SCCl}}_{2})$ molecules. The difficulty of encoding logical states in pure rotational states with STIRAP processes is illustrated. In such circumstances, the gate can be implemented by optimal control theory and the STIRAP sequence can then be used as an interesting trial field. We discuss the relative merits of the two methods for rovibrational computing (structure of the control field, duration of the control, and efficiency of the optimization).

Ultracold mechanical resonators coupled to atoms in an optical lattice

We propose an experiment utilizing an array of cooled micro-cantilevers coupled to a sample of ultra-cold atoms trapped near a micro-fabricated surface. The cantilevers allow individual lattice site addressing for atomic state control and readout, and potentially may be useful in optical lattice quantum computation schemes. Assuming resonators can be cooled to their vibrational ground state, the implementation of a two-qubit controlled-NOT gate with atomic internal states and the motional states of the resonator is described. We also consider a protocol for entangling two or more cantilevers on the atom chip with different resonance frequencies, using the trapped atoms as an intermediary. Although similar experiments could be carried out with magnetic microchip traps, the optical confinement scheme we consider may exhibit reduced near-field magnetic noise and decoherence. Prospects for using this novel system for tests of quantum mechanics at macroscopic scales or quantum information processing are discussed.

Quantum computation in a decoherence-free subspace with superconducting devices

We propose a scheme to implement quantum computation in decoherence-free subspace with superconducting devices inside a cavity by unconventional geometric manipulation. Universal single-qubit gates in encoded qubit can be achieved with cavity assisted interaction. A measurement-based two-qubit Controlled-Not gate is produced with parity measurements assisted by an auxiliary superconducting device and followed by prescribed single-qubit gates. The measurement of currents on two parallel devices can realize a projective measurement, which is equivalent to the parity measurement on the involved devices.

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.

Learning algorithm and application of quantum BP neural networks based on universal quantum gates

A quantum BP neural networks model with learning algorithm is proposed. First, based on the universality of single qubit rotation gate and two-qubit controlled-NOT gate, a quantum neuron model is constructed, which is composed of input, phase rotation, aggregation, reversal rotation and output. In this model, the input is described by qubits, and the output is given by the probability of the state in which |1〉 is observed. The phase rotation and the reversal rotation are performed by the universal quantum gates. Secondly, the quantum BP neural networks model is constructed, in which the output layer and the hide layer are quantum neurons. With the application of the gradient descent algorithm, a learning algorithm of the model is proposed, and the continuity of the model is proved. It is shown that this model and algorithm are superior to the conventional BP networks in three aspects: convergence speed, convergence rate and robustness, by two application examples of pattern recognition and function approximation.

Loss-tolerant operations in parity-code linear optics quantum computing

A heavy focus for optical quantum computing is the introduction of error correction, and the minimization of resource requirements. We detail a complete encoding and manipulation scheme designed for circuit-model linear optics quantum computing, incorporating scalable operations and loss-tolerant architecture. We also calculate loss thresholds for the gate systems described, with an efficiency of $83%$ required for the single-qubit operations, and $90%$ for the two-qubit controlled-NOT gate.

Towards a universal set of topologically protected gates for quantum computation with Pfaffian qubits

We review the topological quantum computation scheme of Das Sarma et al. from the perspective of the conformal field theory for the two-dimensional critical Ising model. This scheme originally used the monodromy properties of the non-Abelian excitations in the Pfaffian quantum Hall state to construct elementary qubits and execute logical NOT on them. We extend the scheme of Das Sarma et al. by exploiting the explicit braiding transformations for the Pfaffian wave functions containing 4 and 6 quasiholes to implement, for the first time in this context, the single-qubit Hadamard and phase gates and the two-qubit Controlled-NOT gate over Pfaffian qubits in a topologically protected way. In more detail, we explicitly construct the unitary representations of the braid groups B 4 , B 6 and B 8 and use the elementary braid matrices to implement one-, two- and three-qubit gates. We also propose to construct a topologically protected Toffoli gate, in terms of a braid-group based Controlled–Controlled-Z gate precursor. Finally we discuss some difficulties arising in the embedding of the Clifford gates and address several important questions about topological quantum computation in general.

Quantum gates between capacitively coupled double quantum dot two-spin qubits

We study the two-qubit controlled-not gate operating on qubits encoded in the spin state of a pair of electrons in a double quantum dot. We assume that the electrons can tunnel between the two quantum dots encoding a single qubit, while tunneling between the quantum dots that belong to different qubits is forbidden. Therefore, the two qubits interact exclusively through the direct Coulomb repulsion of the electrons. We find that entangling two-qubit gates can be performed by the electrical biasing of quantum dots and/or tuning of the tunneling matrix elements between the quantum dots within the qubits. The entangling interaction can be controlled by tuning the bias through the resonance between the singly-occupied and doubly-occupied singlet ground states of a double quantum dot.

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.

Toffoli gate originating from a single resonant interaction with cavity QED

We propose a potentially practical scheme to implement a three-qubit Toffoli gate by a single resonant interaction in cavity QED. 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 atoms with the cavity mode. Both the situations with and without cavity decay are considered. We discuss the advantages and the experimental feasibility of our scheme.

General method for realizing the conditional phase-shift gate and a simulation of Grover’s algorithm in an ion-trap system

It is well known that, in order to build the universal quantum circuit, one only needs one-qubit rotation gate and two-qubit controlled-NOT gate and until now quantum networks have been built from these gates. However, the minimum components of quantum networks in real experiments are not these quantum gates, so we develop a general method for realizing the conditional phase-shift gate in multiqubit ion-trap quantum computation which has the scalability to $N$ qubits $(N\ensuremath{\geqslant}3)$. The duration of the laser manipulations for the proposed conditional phase-shift gate is almost the same as that for the controlled-NOT gate in ion-trap quantum computation. Moreover, we simulate Grover's algorithm taking into consideration the real laser fluctuations and analyze the effect of decoherence on the practical search.

Selective pulse implementation of two-qubit gates for spin-32-based fullerene quantum-information processing

We propose two potentially practical schemes to carry out two-qubit quantum gates on endohedral fullerenes $\mathrm{N}@{\mathrm{C}}_{60}$ or $\mathrm{P}@{\mathrm{C}}_{60}$. The qubits are stored in electronic spin degrees of freedom of the doped atom N or P. By means of the magnetic dipolar coupling between two neighboring fullerenes, the two-qubit controlled-NOT gate and the two-qubit conditional phase gate are performed by selective microwave pulses assisted by the refocusing technique. We will discuss the necessary additional steps for the universality of our proposal. We will also show that our proposal is useful for both quantum gating and the readout of quantum information from the spin-based qubit state.

Quantum Logic Networks for Probabilistic and Controlled Teleportation of Unknown Quantum States**The project supported by National Natural Science Foundation of China under Grant No. 10271081 and the Natural Science Foundationof Hebei Province of China under Grant No. A2004000141

We present simplification schemes for probabilistic and controlled teleportation of the unknown quantum states of both one particle and two particles and construct efficient quantum logic networks for implementing the new schemes by means of the primitive operations consisting of single-qubit gates, two-qubit controlled-not gates, Von Neumann measurement, and classically controlled operations. In these schemes the teleportation are not always successful but with certain probability.

Time-domain simulation of a universal quantum gate

This paper describes the simulation of two coupled particles using the finite-difference time-domain method. We include both unrestricted spin and spatial degrees of freedom for the two particles within the Hartree-Fock approximation. Using spin as a basis, a two-qubit controlled-NOT gate as well as several single qubit gates are simulated in GaAs. We find that the double-occupancy problem can be largely circumvented.

Quantum logical networks for probabilistic teleportation of many particle state of general form

The scheme for probabilistic teleportation of an $N$-particle state of general form is proposed. As the special cases we construct efficient quantum logic networks for implementing probabilistic teleportation of a two-particle state, a three-particle state and a four-particle state of general form, built from single qubit gates, two-qubit controlled-not gates, Von Neumann measurement and classically controlled operations.