Peter J. Love

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.

To enhance the variational quantum eigensolver (VQE), the CAFQA method can utilize classical computational capabilities to identify a better initial state than the Hartree-Fock method. Previous research has demonstrated that the initial state provided by CAFQA recovers more correlation energy than that of the Hartree-Fock method and results in faster convergence. In the present study, we advance the investigation of CAFQA by demonstrating its advantages on a high-fidelity trapped-ion quantum computer located at the Duke Quantum Center -- this is the first experimental demonstration of CAFQA-bootstrapped VQE on a TI device and on any academic quantum device. In our VQE experiment, we use LiH and BeH$_2$ as test cases to show that CAFQA achieves faster convergence and obtains lower energy values within the specified computational budget limits. To ensure the seamless execution of VQE on this academic device, we develop a novel hardware-software interface framework that supports independent software environments for both the circuit and hardware end. This mechanism facilitates the automation of VQE-type job executions as well as mitigates the impact of random hardware interruptions. This framework is versatile and can be applied to a variety of academic quantum devices beyond the trapped-ion quantum computer platform, with support for integration with customized packages.

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.