Three-qubit Gate Research Articles

Note on Implementation of Three-Qubit SWAP Gate

In this paper, the synthesis and implementation of three-quhit SWAP gate is discussed. The three-quhit SWAP gate can be decomposed into product of 2 two-qubit SWAP gates, and it can be realized by 6 CNOT gates. Research illustrated that although the result is very simple, the current methods of matrix decomposition for multi-qubit gate can not get that. Then the implementation of three-qubit SWAP gate in the three spin system with Ising interaction is investigated and the sequence of control pulse and drift process to implement the gate is given. It needs 23 control pulses and 12 drift processes. Since the interaction can not be switched on and off at will, the realization of three-qubit SWAP gate in specific quantum system also can not simply come down to 2 two-qubit SWAP gates.

Phase Entanglers for Multi-Qubit States

The emerging and innovative field of quantum computation and quantum information could bring new insight to our understanding of nature with many applications such as quantum cryptography, quantum secret sharing, quantum teleportation, and quantum computer. In conventional scheme, a quantum computer could be design by quantum gates and circuits. In this paper, we construct geometrical controlled phase quantum gate entanglers for multi-qubit states based on the complex projective Grassmann variety which is defined by the Plucker embedding of Grassmann space. We explicitly give an expression for a geometrical three-qubit quantum gate entangler. We also discuss in detail the construction of the gate entangler for four-qubit states. Moreover, We give illustrative examples of physical implementations of our quantum gate entangler for two- and multi-qubit systems.

One-step implementing three-qubit phase gate via manipulating rf SQUID qubits in the decoherence-free subspace with respect to cavity decay

We present a scheme for implementing a three-qubit phase gate via manipulating rf superconducting quantum interference device (SQUID) qubits in the decoherence-free subspace with respect to cavity decay. Through appropriate changes of the coupling constants between rf SQUIDs and cavity, the scheme can be realized only in one step. A high fidelity is obtained even in the presence of decoherence.

Three-qubit phase gate on three modes of a cavity

We show that a three-qubit phase gate on three modes of a cavity can be realized via resonant atom–cavity interaction. By introducing two strong classical fields and modulating the amplitudes, we obtain the effective form of nonlinear interaction between photons in the three-mode cavity. The availability is testified via numerical analysis. We also consider both the situations with and without effect of decoherence.

Three-qubit PHASE gate in lateral quantum dots: Influence of the acoustic phonon and quantum-dot configuration

Three-qubit PHASE gate in lateral quantum dots: Influence of the acoustic phonon and quantum-dot configuration

Three-qubit Fredkin gate based on cavity quantum electrodynamics

This paper presents a scheme for implementing a Fredkin gate on three modes of a cavity. The scheme is based on the dispersive atom-cavity interaction. By modulating the cavity frequency and the atomic transition frequency appropriately, it obtains the effective form of nonlinear interaction between photons in the three-mode cavity. This availability is testified via numerical analysis. It also considers both the situations with and without dissipation.

Implementation of quantum gates via optimal control

Starting with the basic control system model often employed in nuclear magnetic resonance pulse design, we derive more realistic control system models taking into account effects such as off-resonant excitation for systems with fixed inter-qubit coupling controlled by globally applied electromagnetic fields, as well as for systems controlled by a combination of a global fields and local control electrodes. For both models optimal control is used to find controls that implement a set of two- and three-qubit gates with fidelity of at least 99.99%.

Realization of Three-Qubit Controlled-Phase Gate Operation with Atoms in Cavity QED System

We propose a scheme for realization of three-qubit controlled-phase gate via passing two three-level atoms through a high-Q optical cavity in a cavity QED system. In the presented protocol, the two stable ground states of the atoms act as the two controlling qubits and the zero- and one-photon Fock states of the cavity-field form the target qubit, and no auxiliary state or any measurement is required. The numerical simulation shows that the gate fidelities remain at a high level under the influence of the atomic spontaneous emission, the decay of the cavity mode and deviation of the coupling strength. The experimental feasibility of our proposal is also discussed.

Two simple schemes for implementing Toffoli gate via atom–cavity field interaction in cavity quantum electrodynamics

This paper proposes two schemes for implementing three-qubit Toffoli gate with an atom (as target qubit) sent through a two-mode cavity (as control qubits). The first scheme is based on the large-detuning atom–cavity field interaction and the second scheme is based on the resonant atom-field interaction. Both the situations with and without cavity decay and atomic spontaneous emission are considered. The advantages and the experimental feasibility of these two schemes are discussed.

Three-qubit quantum gates and filters for linear optical quantum-information processing

We present a linear optical scheme for the implementation of a three-qubit quantum gate that can be considered as a generalization of the two-qubit partial-SWAP gate. The gate leaves unchanged all fully symmetric states of three qubits, and all states antisymmetric with respect to the transposition of some pair of qubits acquire a phase shift $\ensuremath{\phi}$. The gate operates in the coincidence basis and requires one auxiliary pair of photons prepared in the maximally entangled Bell state. By altering parameters of the proposed interferometric scheme, we can also obtain a quantum filter that attenuates amplitudes of the three-qubit states according to their permutation symmetry properties.

Realization of Toffoli gate operation using four-level atoms in cavity QED system

This paper proposes a scheme for realization of a three-qubit Toffoli gate operation using three four-level atoms by a selective atom-field interaction in a cavity quantum electrodynamics system. In the proposed protocol, the quantum information is encoded on the stable ground states of atoms, and atomic spontaneous emission is negligible as the large atom-cavity detuning effectively suppresses the spontaneous decay of the atoms. The influence of the dissipation on fidelity and success probability of the three-qubit Toffoli gate is also discussed. The scheme can also be applied to realize an N-qubit Toffoli gate and the interaction time required does not rise with increasing the number of qubits.

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.

Implementing a Fredkin Gate via Atomic-Ensemble Resonant Interactions with Two-Mode Cavity Quantum Electrodynamics

We present a scheme to implement the three-qubit Fredkin gate. The scheme uses an atomic ensemble consisting of four-level atoms interacting resonantly with a two-mode eld. Both the situations with and without cavity decay are considered. We discuss 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.

Vibrational computing: Simulation of a full adder by optimal control

Within the context of vibrational molecular quantum computing, we investigate the implementation of a full addition of two binary digits and a carry that provides the sum and the carry out. Four qubits are necessary and they are encoded into four different normal vibrational modes of a molecule. We choose the bromoacetyl chloride molecule because it possesses four bright infrared active modes. The ground and first excited states of each mode form the one-qubit computational basis set. Two approaches are proposed for the realization of the full addition. In the first one, we optimize a pulse that implements directly the entire addition by a single unitary transformation. In the second one, we decompose the full addition in elementary quantum gates, following a scheme proposed by Vedral et al. [Phys. Rev. A 54, 147 (1996)]. Four elementary quantum gates are necessary, two two-qubit CNOT gates (controlled NOT) and two three-qubit TOFFOLI gates (controlled-controlled NOT). All the logic operations consist in one-qubit flip. The logic implementation is therefore quasiclassical and the readout is based on a population analysis of the vibrational modes that does not take the phases into account. The fields are optimized by the multitarget extension of the optimal control theory involving all the transformations among the 2(4) qubit states. A single cycle of addition without considering the preparation or the measure or copy of the result can be carried out in a very competitive time, on a picosecond time scale.

One-Step Implementation of Mulitqubit Quantum Phase Gate in a Cavity QED System

An alternative protocol is proposed to implement three-qubit phase gate between photon and atoms in a high-Q bimodel optical cavity The idea can be extended to directly implement N-qubit phase gate, and the gating time that is required to implement the protocol does not rise with increasing number of qubits. The influence of cavity decay and atomic spontaneous emission on the gate fidelity is also discussed.

Three-qubit phase gate based on cavity quantum electrodynamics

We describe a three-qubit quantum phase gate which is implemented by passing a four-level atom in a cascade configuration initially in its ground state through a three-mode optical cavity. The three qubits are represented by the photons in the three modes of the cavity. Under appropriate detunings, coupling coefficients, and interaction times, this system exhibits like a three-qubit quantum phase gate. Such a quantum phase gate has potential applications in quantum search.

Implementation of three-qubit Grover search in cavity quantum electrodynamics

Using resonant interaction of three Rydberg atoms with a single-mode microwave cavity, we consider a realization of the three-qubit Grover search algorithm in the presence of weak cavity decay, based on a previous idea for a three-qubit quantum gate [Chen et al., Phys. Rev. A 73, 064304 (2006)]. We simulate the searching process under the influence of the cavity decay and show that our scheme could be achieved efficiently to find a marked state with high fidelity. The required operations are very close to the capabilities of current cavity QED techniques.

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.

Efficient scheme for implementing anN-qubit Toffoli gate by a single resonant interaction with cavity quantum electrodynamics

A scheme for implementing a three-qubit Toffoli gate with atoms sent through a microwave cavity is proposed by choosing nonidentical coupling constants between the atoms and cavity. The scheme can be generalized to implement an $N$-qubit Toffoli gate and the gating time does not change with an increase of the number of qubits.