Session E06: Progress Towards High-Fidelity Quantum Gates

Programmable N-body interactions with trapped ion qubits

The qubit and gate model of a quantum computer employs a universal set of operations, such as single-qubit rotations and two-qubit controlled-NOT gates. While such few-qubit interactions are sufficient for general computation, and can be used to construct many-body entangled states, many-qubit interactions can dramatically simplify quantum circuit structures, speed up their execution, and extend the power of quantum computer systems facing decoherence. We describe a simple protocol for the single-step generation of N-body entangling interactions between trapped atomic ion qubits. We show that qubit state-dependent squeezing operations and displacement forces on the collective atomic motion can generate full N-body interactions. We show how this N-body gate operation allows the single-step implementation of a family of N-bit gate operations such as the powerful N-Toffoli gate, which flips a single qubit if and only if all other N-1 qubits are in a particular state.   

Towards standing-wave Mølmer-Sørensen gates on a quadrupole transition

We present progress towards a laser-driven Mølmer-Sørensen (MS) gate implemented using a novel beam configuration that nulls the carrier coupling, hence allowing for a significant increase in gate speed [1]. 

We couple to the λ=674 nm quadrupole qubit transition, 5S_1/2 → 4D_5/2, in ⁸⁸Sr⁺ with a free-space optical lattice formed by two counter-propagating beams. By controlling the phase of the optical lattice, ions can be placed at the antinodes of the standing wave where the coupling to the carrier is strongly suppressed while the motional coupling is maximised [2]. The two counter-propagating beams form an optical interferometer whose arm length is stabilised by feedback to an AOM. The lattice phase seen by the ion trapped about 50 cm away from the closing point of the interferometer is used to compensate for any changes in the optical path length between this point and the ion position. We demonstrate coherent operations with the lattice for one and two ions and present progress towards implementing the gate interaction on two ions.

[1]  A. M. Steane et al., New J. Phys., 16, p.053049 (2014)

[2]  A. Mundt et al., Phys. Rev. Lett., 89, p.103001 (2002)   

Demonstration of near-infrared light shift gate on optical qubits and investigation of laser noise impact on gate fidelity

The typical native entangling gate for trapped ion systems is the Mølmer Sørensen gate. Here we demonstrate a wavelength insensitive alternative, the light shift gate, on a pair of Ca 40 ions. Instead of driving red and blue tones, we construct a running lattice to impart a time varying state dependent force on the ion pair. This gate has many advantages such as a better interaction strength scaling with power (linear with power instead of electric field), wavelength insensitivity allowing us to work with IR light, which is more ideal for integrated optics applications, and because it is a σz⊗σz interaction, spin echo pulses commute with the gate eliminating σz errors from unwanted stark shifts or drifts in laser frequency. We are working with an optical qubit (729nm transition) and using 845nm light to drive the gate. Because we are driving the gate near a dipole transition and we specifically accumulate phase on the D state making for simpler gate dynamics. We study how it performs under various parameters such as speed, ion spacing, and motional heating. Additionally, we investigate how laser noise reduces fidelity. We attempt to quantify what range constitute "medium" noise which is too slow to be averaged out, but too fast relative to the gate time to act as a constant offset.   

A laser-driven σzσz gate using a bichromatic quadrupole field

Two-qubit entangling gates are essential for quantum computing. We demonstrate a promising approach combining the advantages of two well-known laser-based trapped-ion gate mechanisms, the light-shift gate and the Mølmer–Sørensen gate, which produce a σ_zσ_z and a σ_φσ_φ interaction, respectively. Each scheme has unique advantages. The former acts on the computational basis and can therefore be combined with spin-echo sequences to yield high resilience against a large class of gate errors, while the latter can be trivially implemented on clock-qubits and the laser used to drive gates can be employed for single-qubit rotations as well.

We demonstrate a laser-based two-qubit entangling gate, on the optical quadrupole transition of ⁸⁸Sr⁺, inspired by the idea first proposed in [1], and subsequently demonstrated in the context of laser-free gates [2]. Using a bichromatic laser field, which can conventionally only drive a σ_φσ_φ interaction, we realise a σ_zσ_z gate with the same beam configuration but by a particular choice of detuning and Rabi frequency. Further we discuss the features, including the clock-qubit compatibility, and limitations of this new gate scheme.

[1]: Sutherland et al., New Journal of Physics, 21(3):33033, 2019

[2]: Srinivas et al., Nature, 597(7875), 209–213, 2021   

Optical crosstalk mitigation methods for a trapped ion qubit array

We present experimental work performed in a cryogenic apparatus exploiting a segmented ion trap architecture for the implementation of quantum algorithms. The quantum register consists of a linear string of ⁴⁰Ca⁺ ions which are individually controlled by tightly focused laser beams perpendicular to the crystal axis. Light is delivered by a waveguide array allowing to individually feed each ion with a separately controlled laser beam.

Reducing ion spacing allows for faster and higher fidelity entangling gates. It increases the spectral separation of radial motional modes and the resulting stronger axial confinement reduces the detrimental effects from noisy transverse motion. However, the spatial profile of the addressing beams is fundamentally limited by diffraction, therefor leading to significant optical crosstalk for closely spaced ion strings. This will lead to unwanted errors on spectator qubits which can be suppressed at the gate level. 

We implement a novel coherent optical cancellation method by applying parallel compensation pulses on spectator ion(s). We compare this method against known techniques such as composite pulse sequences and noise refocusing methods using randomized benchmarking for one and two-qubit gates.   

Metastable Qubit Operations in 171Yb+

The metastable ("m-type") qubit defined on the zero-field hyperfine clock states in the long-lived ²F^o_7/2 manifold in ¹⁷¹Yb⁺ gives a promising pathway to low cross-talk, high fidelity multi-qubit operations using the same ion species. We describe heralded state preparation, single qubit operations, and state measurement in the m-type qubit. Additionally, we put quantitative limits on the effect of direct illumination by ground state ("g-type")  qubit state preparation and detection laser light on the m-type qubit coherence and operational frequency. We present our work toward coupling the m-type qubit to motion and coherent transfer between g-type and m-type qubits in ¹⁷¹Yb⁺.    

Implementing Real-Time Logical Qubit Error Detection & Correction on a Trapped Ion Quantum Computer

Implementing a full error-corrected logical qubit requires high-fidelity gates, mid-circuit ancilla measurement, and the determination of the appropriate correction operation using the measurement. Our recent results demonstrating the central components of quantum error correction [1] focused on a single cycle of error detection and correction, due to technical control limitations. Here, we discuss some of those limitations and present a heterogeneous approach to addressing this issue with a custom gate waveform generator. Finally, we will present progress towards demonstrating multiple rounds of error correction on a Bacon-Shor-13-encoded logical qubit using trapped 171Yb+ ions.   

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Entangling gates in trapped-ion quantum computing have primarily targeted stationary ions with initial motional distributions that are thermal and close to the ground state. However, future systems will likely incur significant non-thermal excitation due to, e.g., ion transport, longer operational times, and increased spatial extent of the trap array. In this research, we analyze the impact of such coherent motional excitation on entangling-gate error by performing simulations of Mølmer-Sørenson (MS) gates on a pair of trapped-ion qubits with both thermal and coherent excitation present in a shared motional mode at the start of the gate. We discover that a small amount of coherent displacement dramatically erodes gate performance in the presence of experimental noise, and we demonstrate that applying only limited control over the phase of the displacement can suppress this error. We then use experimental data from transported ions to analyze the impact of coherent displacement on MS-gate error under realistic conditions.   

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In this work, we derive analytic formulae that determine the effect of error mechanisms in laser-free one- and two-qubit gates in trapped ions and electrons. First, we analyze, and derive expressions for, the effect of driving field inhomogeneities on one-qubit gate fidelities. Second, we derive expressions for two-qubit gate errors, including static motional frequency shifts, trap anharmonicities, field inhomogeneities, heating, and motional dephasing. We show that, for small errors, each of our expressions for infidelity converges to its respective numerical simulation; this shows that our formulae are sufficient for determining error budgets for high-fidelity gates, obviating numerical simulations in future projects. All of the derivations are general to any internal qubit state, and any \textit{mixed} state of the ion crystal's motion. Finally, we note that, while this manuscript focuses on laser-free systems, static motional frequency shifts, trap anharmonicities, heating, and motional dephasing are also important error mechanisms in laser-based gates, and our expressions apply.   

Photon scattering rates in trapped ion qubits

In trapped-ion qubits, gates are often performed using two-photon stimulated Raman transitions. During such a transition, there is a risk of spontaneous photon scattering, which reduces the gate fidelity. Some past models of these scattering rates are suitable for moderate detunings but lose accuracy the further the laser is tuned from resonance. We present calculations of the scattering rates and show how including certain corrections changes the predictions of the model, in particular, lower scattering rates at large red detuning. Additionally, we discuss recent experimental work from our lab towards measuring the scattering rates in this far-detuned regime.