Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate*
Dietrich G. Leibfried, Brian DeMarco, Volker Meyer, David Lucas, M. D. Barrett, J. Britton, Wayne M. Itano, Branislav M. Jelenkovic, Chris Langer, Till Rosenband, David J. Wineland
Abstract Universal logic gates for two quantum bits (qubits) form an essential ingredient of quantum computation. Dynamical gates have been proposed1, 2 in the context of trapped ions; however, geometric phase gates (which change only the phase of the physical qubits) offer potential practical advantages because they have higher intrinsic resistance to certain small errors and might enable faster gate implementation. Here we demonstrate a universal geometric π-phase gate between two beryllium ion-qubits, based on coherent displacements induced by an optical dipole force. The displacements depend on the internal atomic states; the motional state of the ions is unimportant provided that they remain in the regime in which the force can be considered constant over the extent of each ion's wave packet. By combining the gate with single-qubit rotations, we have prepared ions in an entangled Bell state with 97% fidelity—about six times better than in a previous experiment3 demonstrating a universal gate between two ion-qubits. The particular properties of the gate make it attractive for a multiplexed trap architecture4, 5 that would enable scaling to large numbers of ion-qubits.
Abstract Universal logic gates for two quantum bits (qubits) form an essential ingredient of quantum computation. Dynamical gates have been proposed1, 2 in the context of trapped ions; however, geometric phase gates (which change only the phase of the physical qubits) offer potential practical advantages because they have higher intrinsic resistance to certain small errors and might enable faster gate implementation. Here we demonstrate a universal geometric π-phase gate between two beryllium ion-qubits, based on coherent displacements induced by an optical dipole force. The displacements depend on the internal atomic states; the motional state of the ions is unimportant provided that they remain in the regime in which the force can be considered constant over the extent of each ion's wave packet. By combining the gate with single-qubit rotations, we have prepared ions in an entangled Bell state with 97% fidelity—about six times better than in a previous experiment3 demonstrating a universal gate between two ion-qubits. The particular properties of the gate make it attractive for a multiplexed trap architecture4, 5 that would enable scaling to large numbers of ion-qubits.
Quantum entangling logic gates are key ingredients for the implementation of a quantum information processing device. In this thesis, we focus on experimental implementations of three types of entangling geometric-phase gates with trapped ions, which rely on the effective spin-spin interactions generated with state-dependent forces. First, a mixed-species entangling gate is demonstrated using a 9Be+ and a 25Mg+ ion to create a Bell state with a fidelity of 0.979(1). Combined with single-qubit gates, we use this mixed-species gate to implement controlled-NOT and SWAP gates. Second, we implement a high-fidelity universal gate set with 9Be+ ions. Single-qubit gates with error per gate of 3.8(1)x10-5 are achieved. By creating a Bell state with a deterministic two-qubit entangling gate, we deduce a gate error as low as 8(4)x10-4. Third, a novel two-qubit entangling gate with dynamical decoupling built-in is demonstrated with a fidelity of 0.974(4). This gate is robust against qubit dephasing errors and offers simplifications in experimental implementation compared to some other gates with trapped ions. Errors in the above implementations are evaluated and methods to further reduce imperfections are discussed. In a separate experiment, correlated measurements made on pairs of ions violate a "chained" Bell inequality obeyed by any local-realistic theory. The lowest chained Bell inequality parameter determined from our measurements is 0.296(12), this value is significantly lower than 0.586, the minimum value derived from a perfect Clauser-Horne-Shimony-Horne (CHSH) Bell inequality experiment. Furthermore, our CHSH Bell inequality results provide a device-independent certification of the deterministically created Bell states.
A novel two-qubit entangling gate for trapped-ion quantum processors is proposed theoretically and demonstrated experimentally. During the gate, double-dressed quantum states are created by applying a phase-modulated continuous driving field. The speed of this quantum gate is an order of magnitude higher than that of previously demonstrated rf controlled two-qubit entangling gates in static magnetic field gradients. At the same time, the field driving the gate dynamically decouples the qubits from amplitude and frequency noise, increasing the qubits’ coherence time by 3 orders of magnitude. The gate requires only a single continuous rf field per qubit, making it well suited for scaling a quantum processor to large numbers of qubits. Implementing this entangling gate, we generate the Bell states | Φ + ⟩ and | Ψ + ⟩ in less than or equal to 313 μ s with fidelities up to 98 − 3 + 2 % in a static magnetic gradient of only 19.09 T / m . At higher magnetic field gradients, the entangling gate speed can be further improved to match that of laser-based counterparts.
Trapped ions are among the most promising candidates for performing quantum information processing tasks. Recently, it was demonstrated how the properties of geometric phases can be used to implement an entangling two-qubit phase gate with significantly reduced operation time while having a built-in resistance against certain types of errors [M. Palmero et al., Phys. Rev. A 95, 022328 (2017)]. We investigate the influence of both quantum and thermal fluctuations on the geometric phase in the Markov regime. We show that additional environmentally induced phases as well as a loss of coherence result from the nonunitary evolution, even at zero temperature. We connect these effects to the associated dynamical and geometrical phases. This suggests a strategy to compensate for the detrimental environmental influences and restore some of the properties of the ideal implementation. Our main result is a strategy for zero temperature to construct forces for the geometric phase gate which compensate for the dissipative effects and leave the produced phase as well as the final motional state identical to the isolated case. We show that the same strategy also helps at finite temperatures. Furthermore, we examine the effects of dissipation on the fidelity and the robustness of a two-qubit phase gate against certain error types.
Practical and robust control of the complex phases of qubit superposition states is necessary for high-fidelity quantum gates. Here we experimentally demonstrate such control in a trapped ultracold 40 Ca + ion, where the phase of qubit ground state is modified by optical driving to an excited state. Using a third spectator quantum level as reference, we experimentally measure the phases generated on the ground state amplitude by different driving schemes. While geometric phases exhibit intrinsic robustness to systematic control errors due to their dependence on global geometric properties (e.g., Berry curvature) rather than dynamical details, their resilience to decoherence remains a topic requiring critical clarification. In this work, we show that geometric phases are not in general immune to environment-induced decoherence, and their practical robustness, including to decoherence, depends on active error-suppression strategies. We implement different driving schemes and find that minimizing excited state decay is more decisive for their robustness on decoherence than whether the phase is of a geometric or dynamical character. This work established and demonstrated a new control strategy that mitigates decoherence effects in geometric/complex phase systems, compensating for their susceptibility to decoherence. We experimentally benchmark four phase-imprinting protocols under a tunable engineered dissipation channel and controlled systematic errors in a single trapped-ion qubit. Our central quantitative finding is that the sensitivity to decoherence is governed by the time-integrated excited-state population, rather than by whether the accumulated phase is labeled geometric or dynamical.
We suggest a fast two-qubit quantum logic gates for trapped ions in thermal motion via geometric phase shifts. In the scheme, several vibrational modes are simultaneously displaced by driving the ions with a single off-resonant standing-wave laser. Under certain conditions, all the vibrational modes simultaneously return to the original points in the phase spaces along corresponding closed paths depending on the electronic states, producing a geometric phase gate. During the gate operation, the ions undergo no electronic transitions and the gate time might be shorter than the period of the center-of-mass vibration.
Abstract 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 99 − 2 + 1 % . 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 µ s) by using two axial motional modes of a two-ion crystal through improved setups.