Quantum computing is entering the mainstream as part of cloud offerings, where it serves as a special-purpose accelerator in larger applications. However, it is still challenging for developers and researchers to design, build and manage the resources for Hybrid Quantum-Classical (HQC) applications that include both classical logic (x86, ARM) and quantum circuit blocks, and run across both traditional and quantum processors. Further, quantum hardware is available on public cloud and even on-premise as private clouds, with varying capabilities, costs and queue times. Further, such quantum circuits also expose optimization methods that offer cost, time, accuracy and parallelism trade-offs. So, there is a compelling for easy composition of HQC applications that can be effortlessly and efficiently deployed on hybrid clouds. In this paper, we propose a framework to intuitively compose and deploy “zero-touch” quantum-classical Function-as-a-Service (FaaS) workflows through various workflow patterns that leverage diverse cloud system (workflow partitioning, adaptive polling) and quantum (circuit cutting, qubit reuse) optimizations. These utilize our XFaaS FaaS workflow framework for hybrid cloud deployments on AWS and Azure, and IBM Qiskit SDK for the quantum circuit toolchain. We also offer detailed experimental profiling of these optimizations for realistic and synthetic HQC applications on real clouds, and on real and simulated quantum hardware, and analyze the benefits of cloud system and quantum circuit optimizations. Our results demonstrate up to 53 % improvement in time and 80 % in cost when quantum circuit optimization on hardware is used in conjunction with dynamic fan-out.

Error syndromes for heavy hexagonal code and other topological codes such as surface code have typically been decoded by using Minimum Weight Perfect Matching– (MWPM) based methods. Recent advances have shown that topological codes can be efficiently decoded by deploying machine learning (ML) techniques, in particular with neural networks. In this work, we first propose an ML-based decoder for heavy hexagonal code and establish its efficiency in terms of the values of threshold and pseudo-threshold for various noise models. We show that the proposed ML-based decoding method achieves ~ 5 × higher values of threshold than that for MWPM. Next, exploiting the property of subsystem codes, we define gauge equivalence for heavy hexagonal code, by which two distinct errors can belong to the same error class. A linear search-based method is proposed for determining the equivalent error classes. This provides a quadratic reduction in the number of error classes to be considered for both bit flip and phase flip errors and thus a further improvement of ~ 14% in the threshold over the basic ML decoder. Last, a novel technique based on rank to determine the equivalent error classes is presented, which is empirically faster than the one based on linear search.

Large-scale quantum computers mandate error correction and fault tolerance. Due to constraints on the number of qubits, fault tolerance is difficult to achieve in near-term quantum systems. Therefore, error correction should require minimal resources. Gates in the near-term devices are also noisy. Quantum error correction code blocks built with these noisy gates can inject further error in the circuit. The goals for error correction in near-term systems are as follows: (i) using a small number of qubits for encoding, and (ii) keeping cost of circuits for encoding and decoding low. In this paper, we propose two techniques to achieve these mutually orthogonal goals. For a binary quantum system we propose an error estimation method that can aid in reducing the number of error correcting blocks via sparse scheduling. For ternary quantum systems, we propose an approximate code that can correct errors with high probability while significantly reducing the circuit cost. These techniques are expected to be helpful for error mitigation in near-term systems in the absence of fault tolerance.