High-fidelity laser-free universal control of trapped ion qubits

Universal control of multiple qubits-the ability to entangle qubits and to perform arbitrary individual qubit operations¹-is a fundamental resource for quantum computing², simulation³ and networking⁴. Qubits realized in trapped atomic ions have shown the highest-fidelity two-qubit entangling operations^5-7 and single-qubit rotations⁸ so far. Universal control of trapped ion qubits has been separately demonstrated using tightly focused laser beams^9-12 or by moving ions with respect to laser beams^13-15, but at lower fidelities. Laser-free entangling methods^16-20 may offer improved scalability by harnessing microwave technology developed for wireless communications, but so far their performance has lagged the best reported laser-based approaches. Here we demonstrate high-fidelity laser-free universal control of two trapped-ion qubits by creating both symmetric and antisymmetric maximally entangled states with fidelities of [Formula: see text] and [Formula: see text], respectively (68 per cent confidence level), corrected for initialization error. We use a scheme based on radiofrequency magnetic field gradients combined with microwave magnetic fields that is robust against multiple sources of decoherence and usable with essentially any trapped ion species. The scheme has the potential to perform simultaneous entangling operations on multiple pairs of ions in a large-scale trapped-ion quantum processor without increasing control signal power or complexity. Combining this technology with low-power laser light delivered via trap-integrated photonics^21,22 and trap-integrated photon detectors for qubit readout^23,24 provides an opportunity for scalable, high-fidelity, fully chip-integrated trapped-ion quantum computing.

Quantum-enhanced sensing of a single-ion mechanical oscillator

Special quantum states are used in metrology to achieve sensitivities below the limits established by classically behaving states1,2. In bosonic interferometers, squeezed states3, number states4,5 and 'Schrödinger cat' states5 have been implemented on various platforms and have demonstrated improved measurement precision over interferometers using coherent states6,7. Another metrologically useful state is an equal superposition of two eigenstates with maximally different energies; this state ideally reaches the full interferometric sensitivity allowed by quantum mechanics8,9. Here we demonstrate the enhanced sensitivity of these quantum states in the case of a harmonic oscillator. We extend an existing experimental technique10 to create number states of order up to n = 100 and to generate superpositions of a harmonic oscillator ground state and a number state of the form [Formula: see text] with n up to 18 in the motion of a single trapped ion. Although experimental imperfections prevent us from reaching the ideal Heisenberg limit, we observe enhanced sensitivity to changes in the frequency of the mechanical oscillator. This sensitivity initially increases linearly with n and reaches a maximum at n = 12, where we observe a metrological enhancement of 6.4(4) decibels (the uncertainty is one standard deviation of the mean) compared to an ideal measurement on a coherent state with the same average occupation number. Such measurements should provide improved characterization of motional decoherence, which is an important source of error in quantum information processing with trapped ions11,12. It should also be possible to use the quantum advantage from number-state superpositions to achieve precision measurements in other harmonic oscillator systems.

Versatile laser-free trapped-ion entangling gates

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 eitherσ ^ ϕ ⊗ σ ^ ϕ orσ ^ z ⊗ σ ^ z 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. Theσ ^ z ⊗ σ ^ z gates can be implemented in a novel manner which eases experimental constraints. We present numerical simulations of gate fidelities assuming realistic parameters.

Coupled optical resonance laser locking

We have demonstrated simultaneous laser frequency stabilization of a UV and IR laser, to coupled transitions of ions in the same spectroscopic sample, by detecting only the absorption of the UV laser. Separate signals for locking the different lasers are obtained by modulating each laser at a different frequency and using lock-in detection of a single photodiode signal. Experimentally, we simultaneously lock a 369 nm and a 935 nm laser to the (2)S(1/2) → (2)(P(1/2) and (2)D(3/2) → (3)D([3/2]1/2) transitions, respectively, of Yb(+) ions generated in a hollow cathode discharge lamp. Stabilized lasers at these frequencies are required for cooling and trapping Yb(+) ions, used in quantum information and in high precision metrology experiments. This technique should be readily applicable to other ion and neutral atom systems requiring multiple stabilized lasers.