Phase Gate Research Articles

Robust teleportation and multipartite entanglement analyzers via quantum-dot spins in weak-coupling cavity quantum electrodynamics regime

We propose a special conditional phase gate (CPG) U^(π/2) between the photon and the electron spin confined in a quantum dot (QD) embedded in a microcavity operating in the weak-coupling regime. This CPG U^(π/2) provides an optical method to manipulate the QDs with photon parity. By using it, we present a scheme for implementing a state teleportation between two remote QD cavities and a scheme for constructing a photonic Bell-state analyzer. Furthermore, a multipartite Greenberger–Horne–Zeilinger state analyzer is also proposed. This multipartite entanglement analyzer can also be used as a multipartite entanglement generator. All these schemes are operated in the weak-coupling regime, so the high fidelities and efficiencies can be maintained even in the case of a bad cavity, and the schemes are accessible with current technologies.

An Aharonov—Anandan phase gate in the sub-Hilbert space of a coupling flux qubits system

We study two flux qubits with a parameter coupling scenario. Under the rotating wave approximation, we truncate the 4-dimensional Hilbert space of a coupling flux qubits system to a 2-dimensional subspace spanned by two dressed states |01〉 and |10〉. In this subspace, we illustrate how to generate an Aharnov—Anandan phase, based on which, we can construct a NOT gate (as effective as a C-NOT gate) in this coupling flux qubits system. Finally, the fidelity of the NOT gate is also calculated in the presence of the simulated classical noise.

Observation of Quantum Interference as a Function of Berry’s Phase in a Complex Hadamard Optical Network

Emerging models of quantum computation driven by multiphoton quantum interference, while not universal, may offer an exponential advantage over classical computers for certain problems. Implementing these circuits via geometric phase gates could mitigate requirements for error correction to achieve fault tolerance while retaining their relative physical simplicity. We report an experiment in which a geometric phase is embedded in an optical network with no closed loops, enabling quantum interference between two photons as a function of the phase.

Randomized Benchmarking of Multiqubit Gates

We describe an extension of single-qubit gate randomized benchmarking that measures the error of multiqubit gates in a quantum information processor. This platform-independent protocol evaluates the performance of Clifford unitaries, which form a basis of fault-tolerant quantum computing. We implemented the benchmarking protocol with trapped ions and found an error per random two-qubit Clifford unitary of 0.162±0.008, thus setting the first benchmark for such unitaries. By implementing a second set of sequences with an extra two-qubit phase gate inserted after each step, we extracted an error per phase gate of 0.069±0.017. We conducted these experiments with transported, sympathetically cooled ions in a multizone Paul trap-a system that can in principle be scaled to larger numbers of ions.

Two-qubit geometric phase gate for quantum dot spins using cavity polariton resonance

We describe a design to implement a two-qubit geometric phase gate, by which a pair of electrons confined in adjacent quantum dots are entangled. The entanglement is a result of the Coulomb exchange interaction between the optically excited exciton-polaritons and the localized spins. This optical coupling, resembling the electron-electron Ruderman-Kittel-Kasuya-Yosida (RKKY) inter- actions, offers high speed, high fidelity two-qubit gate operation with moderate cavity quality factor Q. The errors due to the finite lifetime of the polaritons can be minimized by optimizing the optical pulse parameters (duration and energy). The proposed design, using electrostatic quantum dots, maximizes entanglement and ensures scalability.

High-fidelity quantum gates via analytically solvable pulses

It is shown that a family of analytically solvable pulses can be used to obtain high fidelity quantum phase gates with surprising robustness against imperfections in the system or pulse parameters. Phase gates are important because they can implement the necessary operations for universal quantum computing. They are particularly suited for systems such as self-assembled quantum dots, trapped ions, and defects in solids, as these are typically manipulated by the transient excitation of a state outside the qubit subspace.

Qutrit magic state distillation

Magic state distillation (MSD) is a purification protocol that plays an important role in fault-tolerant quantum computation. Repeated iteration of the steps of an MSD protocol generates pure single non-stabilizer states, or magic states, from multiple copies of a mixed resource state using stabilizer operations only. Thus mixed resource states promote the stabilizer operations to full universality. MSD was introduced for qubit-based quantum computation, but little has been known concerning MSD in higher-dimensional qudit-based computation. Here, we describe a general approach for studying MSD in higher dimensions. We use it to investigate the features of a qutrit MSD protocol based on the five-qutrit stabilizer code. We show that this protocol distils non-stabilizer magic states, and identify two types of states that are attractors of this iteration map. Finally, we show how these states may be converted, via stabilizer circuits alone, into a state suitable for state-injected implementation of a non-Clifford phase gate, enabling non-Clifford unitary computation.

ONE-STEP IMPLEMENTATION OF CONTROLLED PHASE GATES FOR THREE ATOMS TRAPPED IN SEPARATED CAVITIES

A scheme is proposed for implementing the controlled phase gate for three atoms trapped in separated cavities coupled by optical fibers. The energy-level distances of the qubit system become unequal as a consequence of the virtual photon exchange between the atomic qubits, which allows the selective excitation of the qubit system in the symmetric Dicke subspace. The conditional phase shift is produced after a single selective Rabi oscillation and the operation is insensitive to cavity loss and fiber decay.

Micromotion in trapped atom-ion systems

We examine the validity of the harmonic approximation, where the radio-frequency ion trap is treated as a harmonic trap, in the problem regarding the controlled collision of a trapped atom and a single trapped ion. This is equivalent to studying the effect of the micromotion since this motion must be neglected for the trapped ion to be considered as a harmonic oscillator. By applying the transformation of Cook and Shankland we find that the micromotion can be represented by two periodically oscillating operators. In order to investigate the effect of the micromotion on the dynamics of a trapped atom-ion system, we calculate (i) the coupling strengths of the micromotion operators by numerical integration and (ii) the quasienergies of the system by applying the Floquet formalism, a useful framework for studying periodic systems. It turns out that the micromotion is not negligible when the distance between the atom and the ion traps is shorter than a characteristic distance. Within this range the energy diagram of the system changes remarkably when the micromotion is taken into account, which leads to undesirable consequences for applications that are based on an adiabatic process of the trapped atom-ion system. We suggest a simple scheme for bypassing the micromotion effect in order to successfully implement a quantum controlled phase gate proposed previously and create an atom-ion macromolecule. The methods presented here are not restricted to trapped atom-ion systems and can be readily applied to studying the micromotion effect in any system involving a single trapped ion.

1→N quantum controlled phase gate realized in a circuit QED system

We propose an effective method to realize the quantum phase gate of one qubit simultaneously controlling N qubits. We use the system in which the transmon qubits are capacitively coupled to a superconducting transmission line resonator driven by a strong microwave field. In our scheme, the phase gate can be realized in a time (nanosecond-scale) much shorter than decoherence time (microsecond-scale), and it is more immune to the 1/f charge noise and has longer dephasing time due to the favorable properties of the transmon qubits in the system.

Fidelity of a Rydberg-blockade quantum gate from simulated quantum process tomography

We present a detailed error analysis of a Rydberg blockade mediated controlled-NOT quantum gate between two neutral atoms as demonstrated recently in Phys. Rev. Lett. 104, 010503 (2010) and Phys. Rev. A 82, 030306 (2010). Numerical solutions of a master equation for the gate dynamics, including all known sources of technical error, are shown to be in good agreement with experiments. The primary sources of gate error are identified and suggestions given for future improvements. We also present numerical simulations of quantum process tomography to find the intrinsic fidelity, neglecting technical errors, of a Rydberg blockade controlled phase gate. The gate fidelity is characterized using trace overlap and trace distance measures. We show that the trace distance is linearly sensitive to errors arising from the finite Rydberg blockade shift and introduce a modified pulse sequence which corrects the linear errors. Our analysis shows that the intrinsic gate error extracted from simulated quantum process tomography can be under 0.002 for specific states of $^{87}$Rb or Cs atoms. The relation between the process fidelity and the gate error probability used in calculations of fault tolerance thresholds is discussed.

Fast Quantum Gate with Superconducting Flux Qubits Coupled to a Cavity

We present a way for fast implementation of a two-qubit controlled phase gate with superconducting flux qubits coupled to a cavity. A distinct feature of this proposal is that since only qubit-cavity resonant interaction and qubit-pulse resonant interaction are used, the gate can be performed much faster when compared with the previous proposals. This proposal does not require adjustment of the qubit level spacings during the gate operation. In addition, neither uniformity in the qubit parameters nor exact placement of qubits in the cavity is needed by this proposal.

Synthesis of arbitrary SU(3) transformations of atomic qutrits

Several scenarios are proposed and analyzed for engineering of arbitrary preselected SU(3) transformations of laser-driven atomic qutrits. Two of the most natural implementations of qutrits are considered, in which the three qutrit states are coupled to each other via two-photon transitions through either (i) a common state in a tripod linkage pattern or (ii) two upper states in an M-shaped linkage chain. The SU(3) transformation for the tripod qutrit can be realized by 3 Givens SU(2) rotations, which require 9 consecutive interaction steps. Alternatively, because under certain conditions the propagator of the tripod system reduces to the Householder reflection operator, any SU(3) transformation can be constructed physically by 3 Householder reflections, each of which is implemented in a single interaction step. As an example, the discrete Fourier transform can be synthesized by 7 consecutive interaction steps with Givens rotations or, alternatively, by only a single Householder reflection and a phase gate. For the M-qutrit, the propagator is given by coupled Householder reflections and it cannot be reduced to Givens rotations or independent Householder reflections. By using these coupled Householder reflections it is shown that an arbitrary SU(3) transformation of the M qutrit can be realized with just two fields in at most 3 interaction steps; the discrete Fourier transform, in particular, requires only 2 interaction steps.

Optically controlled phase gate for two spin qubits in coupled quantum dots

We present a feasible scheme for performing an optically controlled phase gate between two conduction electron spin qubits in adjacent self-assembled quantum dots. Interaction between the dots is mediated by the tunneling of the valence hole state, which is activated only by applying a laser pulse of the right polarization and frequency. Combining the hole tunneling with the Pauli blocking effect, we obtain conditional dynamics for the two quantum dots, which is the essence of our gating operations. Our results are of explicit relevance to the recent generation of vertically stacked self-assembled InAs quantum dots, and show that by a design which avoids unintended dynamics the gate could be implemented in theory in the 10-ps range and with a fidelity over 90%. Our proposal therefore offers an accessible path to the demonstration of ultrafast quantum logic in quantum dots.

Continuous-mode effects and photon-photon phase gate performance

The effects arising from the inherent continuous-mode nature of photonic pulses were poorly understood but significantly influence the performance of quantum devices employing photonic pulse interaction in nonlinear media. Such effects include the entanglement between the continuous wave-vector modes due to pulse interaction as well as the consequence of a finite system bandwidth. We present the first analysis on these effects for interactions between single-photon pulses, demonstrating their impact on the performance of quantum phase gates based on such process. Our study clarifies a realistic picture of this type of quantum devices.

Electromagnetically induced transparency and photon-photon interactions with Rydberg atoms

We discuss electromagnetically induced transparency in a cold ensemble of atoms optically excited to the Rydberg states. Strong dipole-dipole or van der Waals interactions between the atomic Rydberg states translate into large nonlocal nonlinearities for a propagating probe field. In the case of weak quantum fields, this can be used to attain a conditional phase shift of π between pairs of single photons realizing a deterministic photonic phase gate. For stronger fields, long-range interactions between the atoms constrain the medium to behave as a collection of superatoms, each comprising a blockade volume that can accommodate at most one Rydberg excitation. The propagation of a probe field is affected by its two-photon correlations within the blockade distance, which are strongly damped due to low saturation threshold of the superatoms. Our calculations reproduce and interpret the results of recent experiments.

Interaction-Free Quantum Optical Fredkin Gates in $\chi^{(2)}$ Microdisks

We present novel “interaction-free” realizations of quantum optical Fredkin gates that do not rely on direct physical coupling between the target light (signal) and the control light (pump). The interaction-free feature of such gates allow to overcome the fundamental limits of photon loss and quantum-state decoherence imposed by the signal-pump coupling. This advantage, together with the low inherent quantum-noise level in χ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(2)</sup> microdisks, gives rise to substantially improved performance over the existing Fredkin-gate designs. Explicitly using lithium-niobate mircrodisks, we present two kinds of interaction-free Fredkin gates, a phase gate and an optical-path gate, both of which are designed with telecom-band applications in mind. For both gates, the threshold pump peak power to achieve a gate contrast >;100 and a signal loss <;10% is hundreds of microwatts for practical parameters of the devices.

Multiqubit quantum phase gate using four-level superconducting quantum interference devices coupled to superconducting resonator

In this paper, we propose a scheme to realize three-qubit quantum phase gate of one qubit simultaneously controlling two target qubits using four-level superconducting quantum interference devices (SQUIDs) coupled to a superconducting resonator. The two lowest levels ∣0〉 and ∣1〉 of each SQUID are used to represent logical states while the higher energy levels ∣2〉 and ∣3〉 are utilized for gate realization. Our scheme does not require adiabatic passage, second order detuning, and the adjustment of the level spacing during gate operation which reduce the gate time significantly. The scheme is generalized for an arbitrary n-qubit quantum phase gate. We also apply the scheme to implement three-qubit quantum Fourier transform.

Manifestation of a nonclassical Berry phase of an electromagnetic field in atomic Ramsey interference

The Berry phase acquired by an electromagnetic field undergoing an adiabatic and cyclic evolution in phase space is a purely quantum-mechanical effect of the field. However, this phase is usually accompanied by a dynamical contribution and cannot be manifested in any light-beam interference experiment because it is independent of the field state. We here show that such a phase can be produced using an atom coupled to a quantized field and driven by a slowly changing classical field, and it is manifested in atomic Ramsey interference oscillations. We also show how this effect may be applied to one-step implementation of multiqubit geometric phase gates, which is impossible by previous geometric methods. The effects of dissipation and fluctuations in the parameters of the pump field on the Berry phase and visibility of the Ramsey interference fringes are analyzed.

Multiplexing single-beam coherent anti-stokes Raman spectroscopy with heterodyne detection

Multiplex detection of single beam coherent anti-Stokes Raman spectra is achieved by phase shaping of a narrow gate probe. The spectrally resolved signal is amplified via a local oscillator derived from the same single beam and is disentangled via double quadrature spectral interferometry. Spectral resolution and spectral range are defined by the width and position of the phase gate, which can be easily set by a femtosecond pulse shaper. Such phase-only multiplexed single beam coherent anti-Stokes Raman spectroscopy is demonstrated for simple molecules and is combined with Raman line reconstruction methods to obtain dispersion free Raman resonances.