Detecting and tracking drift in quantum information processors.

If quantum information processors are to fulfill their potential, the diverse errors that affect them must be understood and suppressed. But errors typically fluctuate over time, and the most widely used tools for characterizing them assume static error modes and rates. This mismatch can cause unheralded failures, misidentified error modes, and wasted experimental effort. Here, we demonstrate a spectral analysis technique for resolving time dependence in quantum processors. Our method is fast, simple, and statistically sound. It can be applied to time-series data from any quantum processor experiment. We use data from simulations and trapped-ion qubit experiments to show how our method can resolve time dependence when applied to popular characterization protocols, including randomized benchmarking, gate set tomography, and Ramsey spectroscopy. In the experiments, we detect instability and localize its source, implement drift control techniques to compensate for this instability, and then demonstrate that the instability has been suppressed.

Publisher Correction: Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography.

This corrects the article DOI: 10.1038/ncomms14485.

Experimental Demonstration of a Cheap and Accurate Phase Estimation.

We demonstrate an experimental implementation of robust phase estimation (RPE) to learn the phase of a single-qubit rotation on a trapped Yb^{+} ion qubit. We show this phase can be estimated with an uncertainty below 4×10^{-4} rad using as few as 176 total experimental samples, and our estimates exhibit Heisenberg scaling. Unlike standard phase estimation protocols, RPE neither assumes perfect state preparation and measurement, nor requires access to ancillae. We crossvalidate the results of RPE with the more resource-intensive protocol of gate set tomography.

Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography.

Quantum information processors promise fast algorithms for problems inaccessible to classical computers. But since qubits are noisy and error-prone, they will depend on fault-tolerant quantum error correction (FTQEC) to compute reliably. Quantum error correction can protect against general noise if-and only if-the error in each physical qubit operation is smaller than a certain threshold. The threshold for general errors is quantified by their diamond norm. Until now, qubits have been assessed primarily by randomized benchmarking, which reports a different error rate that is not sensitive to all errors, and cannot be compared directly to diamond norm thresholds. Here we use gate set tomography to completely characterize operations on a trapped-Yb+-ion qubit and demonstrate with greater than 95% confidence that they satisfy a rigorous threshold for FTQEC (diamond norm ≤6.7 × 10-4).

Arrays of individually controlled ions suitable for two-dimensional quantum simulations.

A precisely controlled quantum system may reveal a fundamental understanding of another, less accessible system of interest. A universal quantum computer is currently out of reach, but an analogue quantum simulator that makes relevant observables, interactions and states of a quantum model accessible could permit insight into complex dynamics. Several platforms have been suggested and proof-of-principle experiments have been conducted. Here, we operate two-dimensional arrays of three trapped ions in individually controlled harmonic wells forming equilateral triangles with side lengths 40 and 80 µm. In our approach, which is scalable to arbitrary two-dimensional lattices, we demonstrate individual control of the electronic and motional degrees of freedom, preparation of a fiducial initial state with ion motion close to the ground state, as well as a tuning of couplings between ions within experimental sequences. Our work paves the way towards a quantum simulator of two-dimensional systems designed at will.

Precision alignment of integrated optics in hybrid microsystems.

We achieve submicrometer precision in the integration of micro-optics with surface electrode ion traps. The high-precision alignment is accomplished using off-axis linear Fresnel zone plates (FZPs). Four pairs of FZPs are fabricated on the optics chip that contains the high numerical aperture microlens, a diffractive optical element (DOE). The four pairs of FZPs enable alignment in six translational and rotational degrees of freedom. Four corresponding alignment rulers are etched in the top metal layer of the ion trap, enabling quantification of misalignment. The integration of optics for efficient light delivery and the collection of fluorescence from trapped ions are key to achieving scalability in quantum information processing. An accurate and precise approach to the integration of DOEs advances the scalability of surface electrode ion traps and many other hybrid microsystems.

High speed, high fidelity detection of an atomic hyperfine qubit.

Fast and efficient detection of the qubit state in trapped ion systems is critical for implementing quantum error correction and performing fundamental tests such as a loophole-free Bell test. In this work we present a simple qubit state detection protocol for a (171)Yb+ hyperfine atomic qubit trapped in a microfabricated surface trap, enabled by high collection efficiency of the scattered photons and low background photon count rate. We demonstrate average detection times of 10.5, 28.1, and 99.8 µs, corresponding to state detection fidelities of 99%, 99.856(8)%, and 99.915(7)%, respectively.

Stable optical phase modulation with micromirrors.

We measure the motional fluctuations of a micromechanical mirror using a Michelson interferometer, and demonstrate its interferometric stability. The position stability of the micromirror is dominated by the thermal mechanical noise of the structure. With this level of stability, we utilize the micromirror to realize an optical phase modulator by simply reflecting light off the mirror and modulating its position. The resonant frequency of the modulator can be tuned by applying a voltage between the mirror and an underlying electrode. Full modulation depth of ±π is achieved when the mirror resonantly excited with a sinusoidal voltage at an amplitude of 11 V.

Multiscale optics for enhanced light collection from a point source.

High-efficiency collection of photons emitted by a point source over a wide field of view (FoV) is crucial for many applications. Multiscale optics offer improved light collection by utilizing small optical components placed close to the optical source, while maintaining a wide FoV provided by conventional imaging optics. In this work, we demonstrate collection efficiency of 26% of photons emitted by a pointlike source using a micromirror fabricated in silicon with no significant decrease in collection efficiency over a 10 mm object space.