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arXiv:2403.04730 · Physical Review X

Fast, Robust, and Laser-Free Universal Entangling Gates for Trapped-Ion Quantum Computing

Markus Nünnerich, D. Cohen, Patrick Barthel, Patrick H. Huber, Dorna Niroomand, Alex Retzker, Christof Wunderlich

Published Jun 3, 2025• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevx.15.021079

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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.
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.
We present a general theory for laser-free entangling gates with trapped-ion hyperfine qubits, using either static or oscillating magnetic-field gradients combined with a pair of uniform microwave fields symmetrically detuned about the qubit frequency. By transforming into a 'bichromatic' interaction picture, we show that either or geometric phase gates can be performed. The gate basis is determined by selecting the microwave detuning. The driving parameters can be tuned to provide intrinsic dynamical decoupling from qubit frequency fluctuations. The gates can be implemented in a novel manner which eases experimental constraints. We present numerical simulations of gate fidelities assuming realistic parameters.
Universal control of multiple qubits-the ability to entangle qubits and to perform arbitrary individual qubit operations-is a fundamental resource for quantum computation, simulation, and networking. We implement a new scheme for universal control of trapped ion qubits based on microwave magnetic fields and rf magnetic field gradients instead of laser beams, and create entangled states whose fidelity is statistically indistinguishable from the highest-fidelity laser-beam-generated entangled states reported to date. We describe the rf and microwave electronics used, and discuss avenues for using this scheme in a large-scale trapped ion quantum processor.
This thesis describes experimental work on implementing single and two qubit gates in ¹7¹Yb+ ions using methods suitable for a large scale quantum computer. By combining a magnetic field gradient with microwave and radiofrequency radiation, the spin and motional states of the ions are coupled which allows multi-qubit operations to be performed, as well as providing individual addressing of ions in frequency space. A dressed state qubit is used which exhibits an increase of over two orders of magnitude in the coherence time for a qubit that it is sensitive to the magnetic field gradient. Using this system, single qubit gates are characterised using the technique of randomised benchmarking, resulting in a measured average error per gate of 9(3)x10¯4. A new type of two qubit gate is experimentally demonstrated, which in comparison to a standard two qubit gate shows significantly increased resilience to two major sources of gate infidelity: heating of the motional mode of the ions during gate operations, and incorrectly set gate field frequencies. These types of errors are expected to become increasingly important with the move towards quantum processors with large numbers of qubits. Using this same technique, a two qubit gate is also demonstrated at a higher initial temperature with a significantly improved fidelity compared to standard methods. These gate techniques are used to demonstrate work towards implementing positiondependent quantum logic, a method which could remove the correlation between the number of ions and the number of gate fields required in a large scale quantum computing architecture. A method to move the dressed state qubit through a magnetic field gradient while preserving quantum information is demonstrated, as well as a method to optimise the phase of a two qubit gate of unknown phase in order to implement a CNOT logic gate. This provides a path forwards to demonstrating a CNOT gate using position-dependent quantum logic.
This thesis describes experimental work in which the spin and motional states of one and two trapped atomic ions are manipulated with long-wavelength radiation in the microwave and radio frequency (RF) regime. This allows single- and two-qubit quantum logic gates to be implemented with long-wavelength radiation, in contrast to laser frequency radiation used in the majority of work to date. The two-qubit gate scheme developed represents a significant advance towards a large scale quantum computing architecture in which laser light is not needed for coherent manipulation. An experimental setup is built in which a macroscopic linear Paul trap is fitted with permanent magnets to create a strong axial magnetic field gradient. This addition allows the spin and motional states of the ions to be coupled using long-wavelength radiation. The coherence time of qubits that are sensitive to the magnetic field gradient is increased by nearly three orders of magnitude with the use of dressed states and the lifetime and coherence time are measured to be T1 = 0.63(4) s and T2 = 0.65(5) s, respectively. Using the dressed-state qubit, sideband cooling of a single ion to the motional ground state is demonstrated, and the final mean phonon number after cooling is measured to be \bar{n} = 0.13(4). Finally, a two-qubit gate is demonstrated using the dressed-state qubits in conjunction with the magnetic field gradient, and a Bell state fidelity of F = 0.985(12) is determined. This is a significant increase in fidelity for a two-qubit gate based on long-wavelength radiation compared to previous work. The errors are analysed and it is shown that with the next generation of microfabricated traps being developed in the group, the gate fidelity using this scheme can be pushed far into the fault tolerant regime. This makes this scheme promising as an integral part of a large scale quantum computing architecture.
A proposal for a phase gate and a Mølmer–Sørensen gate in the dressed state basis is presented. In order to perform the multi-qubit interaction, a strong magnetic field gradient is required to couple the phonon-bus to the qubit states. The gate is performed using resonant microwave driving fields together with either a radio-frequency (RF) driving field, or additional detuned microwave driving fields. The gate is robust to ambient magnetic field fluctuations due to an applied resonant microwave driving field. Furthermore, the gate is robust to fluctuations in the microwave Rabi frequency and is decoupled from phonon dephasing due to a resonant RF or a detuned microwave driving field. This makes this new gate an attractive candidate for the implementation of high-fidelity microwave based multi-qubit gates. The proposal can also be realized in laser-based set-ups.