Two-qubit Phase Gate Research Articles

Laser-free trapped ion entangling gates with AESE: adiabatic elimination of spin-motion entanglement

We discuss a laser-free, two-qubit geometric phase gate technique for generating high-fidelity entanglement between two trapped ions. The scheme works by ramping the spin-dependent force on and off slowly relative to the gate detunings, which adiabatically eliminates the spin-motion entanglement (AESE). We show how gates performed with AESE can eliminate spin-motion entanglement with multiple modes simultaneously, without having to specifically tune the control field detunings. This is because the spin-motion entanglement is suppressed by operating the control fields in a certain parametric limit, rather than by engineering an optimized control sequence. We also discuss physical implementations that use either electronic or ferromagnetic magnetic field gradients. In the latter, we show how to ‘AESE’ the system by smoothly turning on the effective spin-dependent force by shelving from a magnetic field insensitive state to a magnetic field sensitive state slowly relative to the gate mode frequencies. We show how to do this with a Rabi or adiabatic rapid passage transition. Finally, we show how gating with AESE significantly decreases the gate’s sensitivity to common sources of motional decoherence, making it easier to perform high-fidelity gates at Doppler temperatures.

Robust two-qubit gates using pulsed dynamical decoupling

We present the experimental implementation of a two-qubit phase gate, using a radio frequency (RF) controlled trapped-ion quantum processor. The RF-driven gate is generated by a pulsed dynamical decoupling sequence applied to the ions’ carrier transitions only. It allows for a tunable phase shift with high-fidelity results. The conditional phase shift is measured using a Ramsey-type measurement with an inferred fringe contrast of up to . We also prepare a Bell state using this laser-free gate. The phase gate is robust against common sources of error. We investigate the effect of the excitation of the center-of-mass (COM) mode, errors in the axial trap frequency, pulse area errors and errors in sequence timing. The contrast of the phase gate is not significantly reduced up to a COM mode excitation 20 phonons, trap frequency errors of +10%, and pulse area errors of −8%. The phase shift is not significantly affected up to 10 phonons and pulse area errors of −2%. Both, contrast and phase shift are robust to timing errors up to −30% and +15%. The gate implementation is resource efficient, since only a single driving field is required per ion. Furthermore, it holds the potential for fast gate speeds (gate times on the order of 100 µs) by using two axial motional modes of a two-ion crystal through improved setups.

Implementation of Photonic Phase Gate and Squeezed States via a Two-Level Atom and Bimodal Cavity

We propose a theoretical model for realizing a photonic two-qubit phase gate in cavity QED using a one-step process. The fidelity and probability of success of the conditional quantum phase gate is very high in the presence of cavity decay. Our scheme only employs one two-level atom, and thus is much simpler than other schemes involving multi-level atoms. This proposal can also be applied to generate two-mode squeezed states; therefore, we give three examples, i.e., the two-mode squeezed vacuum state, two-mode squeezed odd coherent state, and two-mode squeezed even coherent state, to estimate the variance of Duan’s criterion when taking into account cavity decay. It is shown that the variance is smaller than 2 for the three squeezed states in most cases. Furthermore, we utilize logarithmic negativity to measure the entanglement, and find that these squeezed states have very high degrees of entanglement.

Parallel-path implementation of nonadiabatic geometric quantum gates in a decoherence-free subspace with nitrogen-vacancy centers

We propose a scheme for nonadiabatic noncyclic geometric quantum computation in a decoherence-free subspace (DFS). The physical system we used is a cavity quantum electrodynamics system consisting of nitrogen-vacancy (NV) centers in diamond and a whispering-gallery-mode (WGM) microresonator. This scheme not only has the feature of DFSs insensitive to decoherence, but also has the advantage of nonadiabatic noncyclic geometric quantum computation which has the built-in noise-resilience geometric feature and further enhances the robustness due to the ability beyond the limitation of the cyclic condition. An unconventional two-qubit phase gate in DFS has been realized in one step with our parallel protocol, which can largely shorten the computation time and the system error caused by decoherence. In addition, a scheme to realize a parallel process of two evolution paths is put forward to achieve the distribution quantum computation of two WGM microresonators containing a NV center in each. Our scheme may provide a promising way towards the practical realization of high-fidelity geometric quantum computation with the features of a DFS, geometric phase, and parallel implementation process.

Noise-resistant phase gates with amplitude modulation

We propose a simple scheme for implementing fast arbitrary phase gates and employ pulse modulation to improve the gate robustness against different sources of noise. Parametric driving of a cavity is introduced to induce Rabi interactions between the cavity and qutrits, and then a two-qubit arbitrary phase gate is constructed by designing proper logical states. On this basis, we implement amplitude-shaped gates to obtain enhanced resilience to control errors in gate time and frequency detuning. By virtue of specifically designed logical states, the scheme displays intrinsic resistance to the energy relaxations of qutrits. Furthermore, we show that the gate robustness against cavity decay can be enhanced significantly with amplitude modulation.

Implementing two-qubit phase gates by exchanging non-Abelian quasiparticles

We study how to implement two-qubit phase gates by exchanging non-Abelian quasiparticles. We firstly investigate quantum dynamics of a single trapped ion with two stable electronic ground states and with a larger energy gap from the rest of the spectrum, which is held in the Lamb–Dicke regime of a driven optical lattice. A set of degenerate Schrodinger’s cat states with the same expected energy is found, and wavepackets of the probability densities occupying different spin states are identical to the quasiparticles obeying the proposed non-Abelian interchange. The controlled transitions between different instantaneous degenerate ground states are illustrated for an array of $$\delta $$-shaped laser pulses. Making use of the mathematical equivalence between the single-ion system and the center-of-mass system of two trapped ions, the two-qubit phase gates are implemented by exchanging the non-Abelian quasiparticles of the center-of-mass motion via the periodic state-dependent forces. Such phase gates depend on geometric and topological properties of the system, which makes them resistant to certain errors. The results can be justified with the current experimental capability and may be extended to an array of weakly coupled trapped-ion pairs for demonstrating the non-Abelian statistics of the quasiparticles and for encoding the topological qubits.

Dephasing-Insensitive Quantum Information Storage and Processing with Superconducting Qubits.

A central task towards building a practical quantum computer is to protect individual qubits from decoherence while retaining the ability to perform high-fidelity entangling gates involving arbitrary two qubits. Here we propose and demonstrate a dephasing-insensitive procedure for storing and processing quantum information in an all-to-all connected superconducting circuit involving multiple frequency-tunable qubits, each of which can be controllably coupled to any other through a central bus resonator. Although it is generally believed that the extra frequency tunability enhances the control freedom but induces more dephasing impact for superconducting qubits, our results show that any individual qubit can be dynamically decoupled from dephasing noise by applying a weak continuous and resonant driving field whose phase is reversed in the middle of the pulse. More importantly, we demonstrate a new method for realizing a two-qubit phase gate with inherent dynamical decoupling via the combination of continuous driving and qubit-qubit swapping coupling. We find that the weak continuous driving fields not only enable the conditional dynamics essential for quantum information processing, but also protect both qubits from dephasing during the gate operation.

Implementation of quantum phase gate between two atoms via Rydberg antiblockade and adiabatic passage**Project supported by the National Natural Science Foundation of China (Grant No. 11464046).

Combining adiabatic passage and Rydberg antiblockade, we propose a scheme to implement a two-qubit phase gate between two Rydberg atoms. Detuning parameters between frequencies of atomic transitions and those of the corresponding driving lasers are carefully chosen to offset the blockade effect of two Rydberg atoms, so that an effective Hamiltonian, representing a single-photon detuning Λ-type three-level system and concluding the quantum state of two Rydberg atoms excited simultaneously, is obtained. The adiabatic-passage technique, based on the effective Hamiltonian, is adopted to implement a two-atom phase gate by using two time-dependent Rabi frequencies. Numerical simulations indicate that a high-fidelity two-qubit π-phase gate is constructed and its operation time does not have to be controlled accurately. Besides, owing to the long coherence time of the Rydberg state, the phase gate is robust against atomic spontaneous emission.

Resonant dipole – dipole interaction of Rydberg atoms for realisation of quantum computations

We report the application of the resonant dipole – dipole interaction of Rydberg atoms for the realisation of quantum computations with ultracold neutral atoms. Coherent population oscillations between the collective states of systems consisting of two interacting atoms make it possible to implement two-qubit phase gates, which are necessary for universal quantum computations. The schemes studied are alternatives to two-qubit gates based on the Rydberg dipole blockade effect. In contrast, the schemes we propose do not require large dipole – dipole interaction energies and can be realised for atoms that are at a considerable distance from each other.The bibliography includes 27 references.

One-step quantum phase gate in the ultrastrong coupling regime of circuit QED

In a previous publication (Phys Rev Lett 108: 120501, 2012), Romero et al. proposed an ultrastrong coupling circuit QED system that can implement a two-qubit quantum phase gate with four controlling pulses. Based on this architecture, we demonstrate that an ultrafast two-qubit phase gate can also be realized with only one oscillation and lower coupling strengths. In our operation scheme, two identical qubits evolve synchronously under a single pulse with a duration determined by a specific coupling strength. The phase gate can also be obtained periodically. The influences of parameter fluctuations are estimated. We demonstrate that the fidelities can be greater than 99% if the parameter fluctuations are controlled within 5%.

Ultrafast quantum computation in ultrastrongly coupled circuit QED systems

The latest technological progress of achieving the ultrastrong-coupling regime in circuit quantum electrodynamics (QED) systems has greatly promoted the developments of quantum physics, where novel quantum optics phenomena and potential computational benefits have been predicted. Here, we propose a scheme to accelerate the nontrivial two-qubit phase gate in a circuit QED system, where superconducting flux qubits are ultrastrongly coupled to a transmission line resonator (TLR), and two more TLRs are coupled to the ultrastrongly-coupled system for assistant. The nontrivial unconventional geometric phase gate between the two flux qubits is achieved based on close-loop displacements of the three-mode intracavity fields. Moreover, as there are three resonators contributing to the phase accumulation, the requirement of the coupling strength to realize the two-qubit gate can be reduced. Further reduction in the coupling strength to achieve a specific controlled-phase gate can be realized by adding more auxiliary resonators to the ultrastrongly-coupled system through superconducting quantum interference devices. We also present a study of our scheme with realistic parameters considering imperfect controls and noisy environment. Our scheme possesses the merits of ultrafastness and noise-tolerance due to the advantages of geometric phases.

Fast phase gates with trapped ions

We implement faster-than-adiabatic two-qubit phase gates using smooth state-dependent forces. The forces are designed to leave no final motional excitation, independently of the initial motional state in the harmonic, small-oscillations limit. They are simple, explicit functions of time and the desired logical phase of the gate, and are based on quadratic invariants of motion and Lewis-Riesenfeld phases of the normal modes.

Optimal control for Rydberg quantum technology building blocks

We consider a platform for quantum technology based on Rydberg atoms in optical lattices where each atom encodes one qubit of information and external lasers can manipulate their state. We demonstrate how optimal control theory enables the functioning of two specific building blocks on this platform: We engineer an optimal protocol to perform a two-qubit phase gate and to transfer the information within the lattice among specific sites. These two elementary operations allow to design very general operations like storage of atoms and entanglement purification as, for example, needed for quantum repeaters.

Unconventional geometric phase gates for two distant atoms trapped in spatially separate cavities

In this paper, we propose a scheme for implementing an unconventional two-qubit geometric phase gate for two distant atoms trapped in cavities connected by an optical fiber. During the gate operation, the atoms are still in the ground states, while the cavity modes and fiber mode are displaced along a circle in the phase space. In this way, the system can acquire different geometric phases conditional upon the atomic states. We find that the operation of the geometric phase gate can be speeded up as the detuning between the cavity field and light fields decreases. Moreover, it is observed that the fidelity for the geometric phase gate is remarkably insensitive to the fluctuation of the detuning parameter. The effects of cavity decay and fiber loss on the gate have also been checked.

Multi-qubit quantum phase gates based on surface plasmons of a nanosphere

The Dicke subradiance and superradiance resulting from the interaction between surface plasmons of a nanosphere and an ensemble of quantum emitters have been investigated using a Green’s function approach. Based on such an investigation, we propose a scheme for a deterministic multi-qubit quantum phase gate. As an example, two-qubit, three-qubit, and four-qubit quantum phase gates have been designed and analyzed in detail. Phenomena due to the losses in the metal are discussed. Potential applications of these phenomena to quantum-information processing are anticipated.

Low-error measurement-free phase gates for qubus computation

We discuss the desired criteria for a two-qubit phase gate and present a method for realizing such a gate for quantum computation that is measurement free and low error. The gate is implemented between qubits via an intermediate bus mode. We take a coherent state as the bus and use cross-Kerr-type interactions between the bus and the qubits. This new method is robust against parameter variations and is thus low error. It fundamentally improves on previous methods due to its deterministic nature and the lack of approximations used in the geometry of the phase rotations. This interaction is applicable both to solid-state and photonic qubit systems.

Effect of Multiphoton Processes on Geometric Quantum Computation in Superconducting Circuit QED

We study the influence of multi-photon processes on the geometric quantum computation in the systems of superconducting qubits based on the displacement-like and the general squeezed operator methods. As an example, we focus on the question about how to implement a two-qubit geometric phase gate using superconducting circuit quantum electrodynamics with both single- and two-photon interaction between the qubits and the cavity modes. We find that the multiphoton processes are not only controllable but also improve the gating speed. The comparison with other physical systems and experimental feasibility are discussed in detail.

On the entanglement and engineering phase gates without dynamical phases for a two-qubit system with Dzyaloshinski-Moriya interaction in magnetic field

We calculate Berry phases and entanglement of adiabatic states for a two spin-1/2 system described by the Heisenberg model with Dzyaloshinski-Moriya (DM) interaction; one of the spins is driven by a time-varing rotating magnetic field and the other is coupled with a static magnetic field. This static magnetic field can be used for controlling as well as vanishing the Berry phases and entanglement of the system state. Besides, we show that the Berry phase and entanglement are not always exact but useful to detect energy levels approach. Additionally, we find that a nontrivial two-spin unitary transformation, purely based on Berry phases, can be obtained by using two consecutive cycles with the opposite direction of the static magnetic field, opposite signs of the exchange constant as well as DM interaction, and a phase shift of the rotating magnetic field. This unitary transformation presents a two-qubit geometric phase gate.

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.