Fast Dynamical Decoupling of the Mølmer-Sørensen Entangling Gate

Abstract

Engineering entanglement between quantum systems often involves coupling through a bosonic mediator, which should be disentangled from the systems at the operation's end. The quality of such an operation is generally limited by environmental and control noise. One of the prime techniques for suppressing noise is by dynamical decoupling, where one actively applies pulses at a rate that is faster than the typical time scale of the noise. However, for boson-mediated gates, current dynamical decoupling schemes require executing the pulses only when the boson and the quantum systems are disentangled. This restriction implies an increase of the gate time by a factor of √ N , with N being the number of pulses applied. Here we propose and realize a method that enables dynamical decoupling in a boson mediated system where the pulses can be applied while spin-boson entanglement persists, resulting in an increase in time that is at most a factor of π 2 , independently of the number of pulses applied. We experimentally demonstrate the robustness of our fast dynamically decoupled entangling gate to σz noise with ions in a Paul trap.High quality on-demand generation of entanglement is a necessary condition for quantum information processing and quantum metrology. While for some physical platforms entanglement is generated by an inherent direct interaction between subsystems, various platforms of interest make use of a mediating boson with spindependent coupling. For instance, the interaction between trapped ions is carried via a vibrational phonon [1][2][3][4][5][6][7][8][9][11][12][13]; superconducting qubits are entangled via a microwave photon [16][17][18]; the interaction between distant NVs can be carried via a nanomechanical oscillator's phonon [19,20] and a cavity photon carries the interaction between atoms in cavity QED architectures [21,23,24]. The common Hamiltonian representing these quantum systems is of the formwith σ α,i representing the Pauli matrix in the α direction of the i th spin. In the trapped ion case this Hamiltonian allows one to execute the Mølmer-Sørensen (MS) gate [1]. After times 2πn/ε for an integer n, the boson is disentangled from the spins, leaving the spins entangled via a geometric phase which is proportional to the area of the closed circle traced by the boson trajectory in phase space [2, 3,25].Despite considerable progress in achieving high-fidelity entanglement in recent years, entanglement fidelity remains a primary obstacle for performance of large scale quantum information processing, and more particularly fault-tolerant quantum computation. Attempts to improve the fidelity of entangling gates must overcome the limitations imposed by environmental noise as well as imperfections in the control apparatus. Dynamical decoupling is a common method for fighting the effects of noise. When utilizing dynamical decoupling pulses [26,27] during the entangling gate operation, one is required to consider the affect on the spin dependent coupling to the mediating boson. In many experiments, a sing...

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