Topological and subsystem codes on low-degree graphs with flag qubits

In this work we introduce two code families, which we call the heavy hexagon code and heavy square code. Both code families are implemented by assigning physical data and ancilla qubits to both vertices and edges of low degree graphs. Such a layout is particularly suitable for superconducting qubit architectures to minimize frequency collisions and crosstalk. In some cases, frequency collisions can be reduced by several orders of magnitude. The heavy hexagon code is a hybrid surface/Bacon-Shor code mapped onto a (heavy) hexagonal lattice whereas the heavy square code is the surface code mapped onto a (heavy) square lattice. In both cases, the lattice includes all the ancilla qubits required for fault-tolerant error-correction. Naively, the limited qubit connectivity might be thought to limit the error-correcting capability of the code to less than its full distance. Therefore, essential to our construction is the use of flag qubits. We modify minimum weight perfect matching decoding to efficiently and scalably incorporate information from measurements of the flag qubits and correct up to the full code distance while respecting the limited connectivity. Simulations show that high threshold values for both codes can be obtained using our decoding protocol. Further, our decoding scheme can be adapted to other topological code families.Comment: 20 pages, 21 figures, Comments welcome! V2 conforms to journal specification

Suppression of Unwanted ZZZZ Interactions in a Hybrid Two-Qubit System

Mitigating crosstalk errors, whether classical or quantum mechanical, is critically important for achieving high-fidelity entangling gates in multi-qubit circuits. For weakly anharmonic superconducting qubits, unwanted $ZZ$ interactions can be suppressed by combining qubits with opposite anharmonicity. We present experimental measurements and theoretical modeling of two-qubit gate error for gates based on the cross resonance interaction between a capacitively shunted flux qubit and a transmon and demonstrate the elimination of the $ZZ$ interaction.Comment: 5+16 pages, 5+13 figures, corrected typos, hyperlinking fixed, modified sections in supplemen

Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity

Preparing and manipulating quantum states of mechanical resonators is a highly interdisciplinary undertaking that now receives enormous interest for its far-reaching potential in fundamental and applied science. Up to now, only nanoscale mechanical devices achieved operation close to the quantum regime. We report a new micro-optomechanical resonator that is laser cooled to a level of 30 thermal quanta. This is equivalent to the best nanomechanical devices, however, with a mass more than four orders of magnitude larger (43 ng versus 1 pg) and at more than two orders of magnitude higher environment temperature (5 K versus 30 mK). Despite the large laser-added cooling factor of 4,000 and the cryogenic environment, our cooling performance is not limited by residual absorption effects. These results pave the way for the preparation of 100-m scale objects in the quantum regime. Possible applications range from quantum-limited optomechanical sensing devices to macroscopic tests of quantum physics

Laser-annealing Josephson junctions for yielding scaled-up superconducting quantum processors

As superconducting quantum circuits scale to larger sizes, the problem of frequency crowding proves a formidable task. Here we present a solution for this problem in fixed-frequency qubit architectures. By systematically adjusting qubit frequencies post-fabrication, we show a nearly ten-fold improvement in the precision of setting qubit frequencies. To assess scalability, we identify the types of 'frequency collisions' that will impair a transmon qubit and cross-resonance gate architecture. Using statistical modeling, we compute the probability of evading all such conditions, as a function of qubit frequency precision. We find that without post-fabrication tuning, the probability of finding a workable lattice quickly approaches 0. However with the demonstrated precisions it is possible to find collision-free lattices with favorable yield. These techniques and models are currently employed in available quantum systems and will be indispensable as systems continue to scale to larger sizes.Comment: 9 pages, 6 figures, Supplementary Information. Update to correct typo in author name and in text. Updated acknowledgements and corrected typo in acknowledgement

Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity

Preparing and manipulating quantum states of mechanical resonators is a highly interdisciplinary undertaking that now receives enormous interest for its far-reaching potential in fundamental and applied science. Up to now, only nanoscale mechanical devices achieved operation close to the quantum regime. We report a new micro-optomechanical resonator that is laser cooled to a level of 30 thermal quanta. This is equivalent to the best nanomechanical devices, however, with a mass more than four orders of magnitude larger (43 ng versus 1 pg) and at more than two orders of magnitude higher environment temperature (5 K versus 30 mK). Despite the large laser-added cooling factor of 4,000 and the cryogenic environment, our cooling performance is not limited by residual absorption effects. These results pave the way for the preparation of 100-um scale objects in the quantum regime. Possible applications range from quantum-limited optomechanical sensing devices to macroscopic tests of quantum physics.Comment: Published versio

Efficient and Sensitive Capacitive Readout of Nanomechanical Resonator Arrays NANO LETTERS

Here we describe all-electronic broadband motion detection in radio frequency nanomechanical resonators. Our technique relies upon the measurement of small motional capacitance changes using an LC impedance transformation network. We first demonstrate the technique on a single doubly clamped beam resonator with a side gate over a wide range of temperatures from 20 mK to 300 K. We then apply the technique to accomplish multiplexed readout of an array of individually addressable resonators, all embedded in a single high-frequency circuit. This technique may find use in a variety of applications ranging from ultrasensitive mass and force sensing to quantum information processing. Introduction. Nanotechnology derives its power from the unique and useful properties of devices engineered at tiny length scales. Among the most promising of these nanodevices are nanoelectromechanical systems (NEMS). 1 Because of their very small masses, high frequencies, lo

Direct Measurements of Surface Scattering in Si Nanosheets Using a Microscale Phonon Spectrometer: Implications for Casimir-Limit Predicted by Ziman Theory

Thermal transport in nanostructures is strongly affected by phonon-surface interactions, which are expected to depend on the phonon’s wavelength and the surface roughness. Here we fabricate silicon nanosheets, measure their surface roughness (∼1 nm) using atomic force microscopy (AFM), and assess the phonon scattering rate in the sheets with a novel technique: a microscale phonon spectrometer. The spectrometer employs superconducting tunnel junctions (STJs) to produce and detect controllable nonthermal distributions of phonons from ∼90 to ∼870 GHz. This technique offers spectral resolution nearly 10 times better than a thermal conductance measurement. We compare measured phonon transmission rates to rates predicted by a Monte Carlo model of phonon trajectories, assuming that these trajectories are dominated by phonon-surface interactions and using the Ziman theory to predict phonon-surface scattering rates based on surface topology. Whereas theory predicts a diffuse surface scattering probability of less than 40%, our measurements are consistent with a 100% probability. Our nanosheets therefore exhibit the so-called “Casimir limit” at a much lower frequency than expected if the phonon scattering rates follow the Ziman theory for a 1 nm surface roughness. Such a result holds implications for thermal management in nanoscale electronics and the design of nanostructured thermoelectrics