Andrew J. Landahl

We analyze the use of the Solovay Kitaev (SK) algorithm to generate an ensemble of one qubit rotations over which to perform randomized compilation. We perform simulations to compare the trace distance between the quantum state resulting from an ideal one qubit $R_{Z}$ rotation and discrete SK decompositions. We find that this simple randomized gate synthesis algorithm can reduce the approximation error of these rotations in the absence of gate errors in simulation by at least a factor of two compared to a naive gate synthesis algorithm. We test the technique under the effects of a simple coherent noise model and find that it can mitigate coherent noise. We also run our algorithm on Sandia National Laboratories' QSCOUT trapped-ion device and find that randomization is able to help in the presence of realistic noise sources.

Current noisy intermediate-scale quantum (NISQ) trapped-ion devices are subject to errors which can significantly impact the accuracy of calculations if left unchecked. A form of error mitigation called zero noise extrapolation (ZNE) can decrease an algorithm's sensitivity to these errors without increasing the number of required qubits. Here, we explore different methods for integrating this error mitigation technique into the Variational Quantum Eigensolver (VQE) algorithm for calculating the ground state of the HeH+ molecule at 0.8 Angstrom in the presence of realistic noise. Using the Quantum Scientific Computing Open User Testbed (QSCOUT) trapped-ion device, we test three methods of scaling noise for extrapolation: time-stretching the two-qubit gates, scaling the sideband amplitude parameter, and inserting two-qubit gate identity operations into the ansatz circuit. We find time-stretching and sideband amplitude scaling fail to scale the noise on our particular hardware in a way that can be directly extrapolated to zero noise. Scaling our noise with global gate identity insertions and extrapolating after variational optimization, we achieve an estimate of the ground state energy within -0.004 +- 0.04 Hartree; outside chemical accuracy, but greatly improved over our non-error-mitigated estimate with error 0.127 +- 0.008 Hartree. Our results show that the efficacy of this error mitigation technique depends on choosing the correct implementation for a given device architecture.

The Quantum Scientific Computing Open User Testbed (QSCOUT) is a trapped-ion quantum computer testbed realized at Sandia National Laboratories on behalf of the Department of Energy's Office of Science and its Advanced Scientific Computing (ASCR) program. Here we describe Jaqal, for Just another quantum assembly language, the programming language we invented to specify programs executed on QSCOUT. Jaqal is useful beyond QSCOUT---it can support mutliple hardware targets because it offloads gate names and their pulse-sequence definitions to external files. We describe the capabilities of the Jaqal language, our approach in designing it, and the reasons for its creation. To learn more about QSCOUT, Jaqal, or JaqalPaq, the metaprogramming Python package we developed for Jaqal, please visit https://qscout.sandia.gov, https://gitlab.com/jaqal, or send an e-mail to qscout@sandia.gov.

QSCOUT is the Quantum Scientific Computing Open User Testbed, a trapped-ion quantum computer testbed realized at Sandia National Laboratories on behalf of the Department of Energy's Office of Science and its Advanced Scientific Computing (ASCR) program. Jaqal, for Just Another Quantum Assembly Language, is the programming language used to specify programs executed on QSCOUT. This document contains a specification of Jaqal along with a summary of QSCOUT 1.0 capabilities, example Jaqal programs, and plans for possible future extensions. To learn more about QSCOUT and the Jaqal language developed for it, please visit qscout.sandia.gov or send an e-mail to qscout@sandia.gov.