Quantum controlled-NOT Gate Research Articles

Realization of a photonic controlled-NOT gate sufficient for quantum computation.

We report the first experimental demonstration of a quantum controlled-NOT gate for different photons, which is classically feed forwardable. In the experiment, we achieved this goal with only the use of linear optics, an entangled ancillary pair of photons, and postselection. The techniques developed in our experiment are of significant importance for quantum information processing with linear optics.

Stochastic Liouville equation approach for the effect of noise in quantum computations

We propose a model based on a generalized effective Hamiltonian for studying the effect of noise in quantum computations. The system-environment interactions are taken into account by including stochastic fluctuating terms in the system Hamiltonian. Treating these fluctuations as Gaussian Markov processes with zero mean and $\ensuremath{\delta}$-function correlation times, we derive an exact equation of motion describing the dissipative dynamics for a system of n qubits. We then apply this model to study the effect of noise on the quantum teleportation and a generic quantum controlled-NOT (CNOT) gate. For quantum teleportation, the effect of noise in the quantum channels is found to be additive, and the teleportation fidelity depends on the state of the teleported qubit. The effect of collective decoherence is also studied for the two-qubit entangled states. For the quantum CNOT gate, we study the effect of noise on a set of one- and two-qubit quantum gates, and show that the results can be assembled together to investigate the quality of a quantum CNOT gate operation. We compute the averaged gate fidelity and gate purity for the quantum CNOT gate and investigate phase, bit-flip, and flip-flop errors during the CNOT gate operation. The effects of direct interqubit coupling and fluctuations on the control fields are also studied. We find that the quality of the CNOT gate operation is sensitive to the strengths of the control fields and the strengths of the noise, and the effect of noise is additive regardless of its origin. We discuss the limitations and possible extensions of this model. In sum, we demonstrate a simple model that enables us to investigate the effect of noise in arbitrary quantum circuits under realistic device conditions.

Controlling qubit transitions during non-adiabatic rapid passage through quantum interference

In adiabatic rapid passage, the Bloch vector of a qubit is inverted by slowly inverting an external field to which it is coupled, and along which it is initially aligned. In non-adiabatic twisted rapid passage, the external field is allowed to twist around its initial direction with azimuthal angle φ(t) at the same time that it is non-adiabatically inverted. For polynomial twist, φ(t) ∼ Bt n . We show that, for n ≥ 3, multiple qubit resonances can occur during a single inversion of the external field, producing strong interference effects in the qubit transition probability. The character of the interference is controllable through variation of the twist strength B. Both constructive and destructive interference are possible, allowing qubit transitions to be greatly enhanced or suppressed. Experimental confirmation of these controllable interference effects has already occurred. Application of this interference mechanism to the construction of fast fault-tolerant quantum controlled-NOT and NOT gates is discussed.

Temporal interferometry: A mechanism for controlling qubit transitions during twisted rapid passage with possible application to quantum computing

In an adiabatic rapid passage experiment, the Bloch vector of a two-level system (qubit) is inverted by slowly inverting an external field to which it is coupled, and along which it is initially aligned. In twisted rapid passage, the external field is allowed to twist around its initial direction with azimuthal angle $\ensuremath{\varphi}(t)$ at the same time that it is inverted. For polynomial twist, $\ensuremath{\varphi}(t)\ensuremath{\sim}{\mathrm{Bt}}^{n}.$ We show that for $n>~3,$ multiple avoided crossings can occur during the inversion of the external field, and that these crossings give rise to strong interference effects in the qubit transition probability. The transition probability is found to be a function of the twist strength B, which can be used to control the time separation of the avoided crossings, and hence the character of the interference. Constructive and destructive interference are possible. The interference effects are a consequence of the temporal phase coherence of the wave function. The ability to vary this coherence by varying the temporal separation of the avoided crossings renders twisted rapid passage with adjustable twist strength into a temporal interferometer through which qubit transitions can be greatly enhanced or suppressed. Possible application of this interference mechanism to construction of fast fault-tolerant quantum controlled-NOT and NOT gates is discussed.

Demonstration of an all-optical quantum controlled-NOT gate.

The promise of tremendous computational power, coupled with the development of robust error-correcting schemes, has fuelled extensive efforts to build a quantum computer. The requirements for realizing such a device are confounding: scalable quantum bits (two-level quantum systems, or qubits) that can be well isolated from the environment, but also initialized, measured and made to undergo controllable interactions to implement a universal set of quantum logic gates. The usual set consists of single qubit rotations and a controlled-NOT (CNOT) gate, which flips the state of a target qubit conditional on the control qubit being in the state 1. Here we report an unambiguous experimental demonstration and comprehensive characterization of quantum CNOT operation in an optical system. We produce all four entangled Bell states as a function of only the input qubits' logical values, for a single operating condition of the gate. The gate is probabilistic (the qubits are destroyed upon failure), but with the addition of linear optical quantum non-demolition measurements, it is equivalent to the CNOT gate required for scalable all-optical quantum computation.

Teleportation of an atomic momentum state

In this paper, we propose a scheme for teleportating a superposition of atomic center-of-mass momentum states to a superposition of the cavity field using quantum controlled-NOT gate via atomic scattering in the Bragg regime and cavity quantum electrodynamics.

Numerical simulation of a quantum controlled-not gate implemented on four-spin molecules at room temperature

We study numerically the non-resonant effects on four-spin molecules at room temperature with the implemented quantum controlled-not gate and using the 2πk method. The four nuclear spins in each molecule represent a four-qubit register. The qubits interact with each other through Ising-type interaction which is characterized by the coupling constant Ja,b. We study the errors on the reduced density matrix as a function of the Rabi frequency, Ω, using the 2πk method and when all the coupling constants are equal or when one of them is different from the others.

Realization of the Cirac–Zoller controlled-NOT quantum gate

Quantum computers have the potential to perform certain computational tasks more efficiently than their classical counterparts. The Cirac-Zoller proposal for a scalable quantum computer is based on a string of trapped ions whose electronic states represent the quantum bits of information (or qubits). In this scheme, quantum logical gates involving any subset of ions are realized by coupling the ions through their collective quantized motion. The main experimental step towards realizing the scheme is to implement the controlled-NOT (CNOT) gate operation between two individual ions. The CNOT quantum logical gate corresponds to the XOR gate operation of classical logic that flips the state of a target bit conditioned on the state of a control bit. Here we implement a CNOT quantum gate according to the Cirac-Zoller proposal. In our experiment, two 40Ca+ ions are held in a linear Paul trap and are individually addressed using focused laser beams; the qubits are represented by superpositions of two long-lived electronic states. Our work relies on recently developed precise control of atomic phases and the application of composite pulse sequences adapted from nuclear magnetic resonance techniques.

Linear optical controlled-NOT gate in the coincidence basis

We describe the operation and tolerances of a non-deterministic, coincidence basis, quantum CNOT gate for photonic qubits. It is constructed solely from linear optical elements and requires only a two-photon source for its demonstration.

Qubitless Quantum Logic

We discuss the implementation of quantum logic in a system of strongly interacting particles. The implementation is qubitless since “logical qubits” do not correspond to any well-defined physical substates. As an illustration, we present the results of simulations of the quantum controlled-NOT gate and Shor’s algorithm for a chain of spin-1/2 particles with Heisenberg coupling. Our proposal extends quantum information processing theory to systems with permanent strong coupling between the two-state subsystems. PACS: 03.67.Lx; 03.65.Ta

Magnetically switched quantum waveguide qubit

Recently, quantum computing has gained notoriety as a computational method that has the possibility to greatly increase the speed of calculations compared with traditional, binary computing. To this end, simulations of a quantum controlled-not gate implemented by a quantum waveguide are examined. The waveguide is composed of two quantum wires and a tuned coupling region and the simulations consist of a solution to Schrödinger’s equation via the Usuki method of mode matching. The use of Gaussian wave packets in previous work on this topic is questioned and various methods of tuning the coupling region in order to guide the quantum wave are investigated. Simulations are shown for a tuned waveguide in which the wave can be switched by the application of an external magnetic field.

Quantum teleportation in a solid-state system

We propose a practical solid-state system capable of demonstrating quantum teleportation. The set-up exploits recent advances in the optical control of excitons in coupled quantum dots, in order to produce maximally-entangled Bell and Greenberger-Horne-Zeilinger (GHZ) states. Only two unitary transformations are then required: a quantum Controlled-Not gate and a Hadamard gate. The laser pulses necessary to generate the maximally-entangled states, and the corresponding unitary transformations, are given explicitly.

Bell-state analyzer with channeled atomic particles

Recent advances in cooling and trapping of atomic particles has opened up the possibility of building microscopic networks of tubelike traps. As possible applications, we describe how a quantum controlled-NOT gate and a Bell-state analyzer could be implemented using atomic particles, which propagate through the system of channels and interact with the device potential and each other.

Quantum Computer Using Coupled-Quantum-Dot Molecules

We propose a method for implementing a quantum computer using artificial molecules. The artificial molecule consists of two coupled quantum dots stacked along the z direction and one single electron. One-qubit and two-qubit gates are constructed by one molecule and two coupled molecules, respectively. The ground state and the first excited state of the molecule are used to encode the |0> and |1> states of a qubit. The qubit is manipulated by a resonant electromagnetic wave that is applied directly to the qubit through a microstrip line. The coupling between two qubits in a quantum-controlled NOT gate is switched on (off) by floating (grounding) the metal film electrodes. We study the operations of the gates using a box-shaped quantum dot model and numerically solving a time-dependent Schrödinger equation, and demonstrate that the quantum gates can perform quantum computations. The operating speed of the gates is about one operation per 4 ps. The reading operation of the output of the quantum computer can be performed by detecting the polarization of the qubits.

Simplified quantum logic gates with trapped ions in thermal motion

A simplified scheme is presented for realizing a two-bit quantum logic gate in an ion trap. As the scheme of Sørensen and Mølmer [Phys. Rev. Lett. 82 (1999) 1971], our scheme is insensitive to the interaction with the environment. However, the quantum controlled-not gate between two ions can

Quantum controlled-NOT gate with 'hot' trapped ions

Quantum controlled-NOT gate with 'hot' trapped ions

Quantum controlled-NOT gate with ‘hot’ trapped ions

We present a novel method of performing quantum logic gates in trapped ion quantum computers which does not require the ions to be cooled down to the ground state of their vibrational modes, thereby avoiding one of the principal experimental difficulties encountered in realizing this technology. Our scheme employs adiabatic passages and a phase shift conditional on the phonon number state.

Dynamics of a quantum control-not gate for an ensemble of four-spin molecules at room temperature

We investigate numerically a single-electromagnetic-pulse implementation of a quantum control-not (CN) gate for an ensemble of Ising spin systems at room temperature. For an ensemble of four-spin ``molecules'' we simulate the time evolution of the density matrix for both digital and superpositional initial conditions. Our numerical calculations confirm the feasibility of implementation of a quantum CN gate in this system at finite temperature, using a single electromagnetic \ensuremath{\pi} pulse. We also study the quantum dynamics of creating entangled states in a macroscopic paramagnetic spin system at low temperatures, and compare the related quantum and corresponding classical dynamics. In the quantum case, one can create entangled states using a resonant interaction between the spin system and the electromagnetic \ensuremath{\pi} pulse. In the classical limit, the interaction of the spin system with the same pulse becomes nonresonant and the corresponding classical dynamics differs significantly from the quantum dynamics. This difference in the behavior of the macroscopic magnetization can be used in experiments as an indication of the existence of entangled states.

Dynamics of a Control-Not gate for a quantum system of two weakly interacting spins

We present the results of computer simulations of dynamics of the quantum Control-Not gate for the system of two spins connected by a weak Ising interaction. It is demonstrated that, for both “digital” and “superposition” initial conditions, 3 resonant π-pulse can provide an adequate implementation of the quantum Control-Not gate. We also consider the influence of slightly non-resonant π-pulse and noise on the dynamics of the quantum Control-Not gate.

Quantum controlled-NOT gate based on a single quantum dot

Quantum controlled-NOT gate based on a single quantum dot