Quantum computers promise to solve certain problems more efficiently than their digital counterparts. A major challenge towards practically useful quantum computing is characterizing and reducing the various errors that accumulate during an algorithm running on large-scale processors. Current characterization techniques are unable to adequately account for the exponentially large set of potential errors, including cross-talk and other correlated noise sources. Here we develop cycle benchmarking, a rigorous and practically scalable protocol for characterizing local and global errors across multi-qubit quantum processors. We experimentally demonstrate its practicality by quantifying such errors in non-entangling and entangling operations on an ion-trap quantum computer with up to 10 qubits, and total process fidelities for multi-qubit entangling gates ranging from for 2 qubits to for 10 qubits. Furthermore, cycle benchmarking data validates that the error rate per single-qubit gate and per two-qubit coupling does not increase with increasing system size.
We report on the design of a cryogenic setup for trapped ion quantum computing containing a segmented surface electrode trap. The heat shield of our cryostat is designed to attenuate alternating magnetic field noise, resulting in 120 dB reduction of 50 Hz noise along the magnetic field axis. We combine this efficient magnetic shielding with high optical access required for single ion addressing as well as for efficient state detection by placing two lenses each with numerical aperture 0.23 inside the inner heat shield. The cryostat design incorporates vibration isolation to avoid decoherence of optical qubits due to the motion of the cryostat. We measure vibrations of the cryostat of less than ±20 nm over 2 s. In addition to the cryogenic apparatus, we describe the setup required for an operation with Ca and Sr ions. The instability of the laser manipulating the optical qubits in Ca is characterized by yielding a minimum of its Allan deviation of 2.4 ⋅ 10 at 0.33 s. To evaluate the performance of the apparatus, we trapped Ca ions, obtaining a heating rate of 2.14(16) phonons/s and a Gaussian decay of the Ramsey contrast with a 1/e-time of 18.2(8) ms.
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