BGLS: A Python Package for the Gate-by-Gate Sampling Algorithm to Simulate Quantum Circuits

The classical simulation of quantum computers is in general a computationally hard problem. To emulate the behavior of realistic devices, it is sufficient to sample bitstrings from circuits. Recently, arXiv:2112.08499 introduced the so-called gate-by-gate sampling algorithm to sample bitstrings and showed it to be computationally favorable in many cases. Here we present bgls, a Python package which implements this sampling algorithm. bgls has native support for several states and is highly flexible for use with additional states. We show how to install and use bgls, discuss optimizations in the algorithm, and demonstrate its utility on several problems.Comment: 7 pages, 9 figures, included in Workshops of The International Conference on High Performance Computing, Network, Storage, and Analysis (SC-W 2023

Digital zero noise extrapolation for quantum error mitigation

Zero-noise extrapolation (ZNE) is an increasingly popular technique for mitigating errors in noisy quantum computations without using additional quantum resources. We review the fundamentals of ZNE and propose several improvements to noise scaling and extrapolation, the two key components in the technique. We introduce unitary folding and parameterized noise scaling. These are digital noise scaling frameworks, i.e. one can apply them using only gate-level access common to most quantum instruction sets. We also study different extrapolation methods, including a new adaptive protocol that uses a statistical inference framework. Benchmarks of our techniques show error reductions of 18X to 24X over non-mitigated circuits and demonstrate ZNE effectiveness at larger qubit numbers than have been tested previously. In addition to presenting new results, this work is a self-contained introduction to the practical use of ZNE by quantum programmers.Comment: 11 pages, 7 figure

Testing platform-independent quantum error mitigation on noisy quantum computers

We apply quantum error mitigation techniques to a variety of benchmark problems and quantum computers to evaluate the performance of quantum error mitigation in practice. To do so, we define an empirically motivated, resource-normalized metric of the improvement of error mitigation which we call the improvement factor, and calculate this metric for each experiment we perform. The experiments we perform consist of zero-noise extrapolation and probabilistic error cancellation applied to two benchmark problems run on IBM, IonQ, and Rigetti quantum computers, as well as noisy quantum computer simulators. Our results show that error mitigation is on average more beneficial than no error mitigation - even when normalized by the additional resources used - but also emphasize that the performance of quantum error mitigation depends on the underlying computer

Quantum-assisted quantum compiling

Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential overhead of classical simulation of quantum dynamics will allow compilation of larger algorithms, and a strategy for this is to evaluate an algorithm's cost on a quantum computer. To this end, we propose a variational hybrid quantum-classical algorithm called quantum-assisted quantum compiling (QAQC). In QAQC, we use the overlap between a target unitary $U$ and a trainable unitary $V$ as the cost function to be evaluated on the quantum computer. More precisely, to ensure that QAQC scales well with problem size, our cost involves not only the global overlap ${\rm Tr} (V^\dagger U)$ but also the local overlaps with respect to individual qubits. We introduce novel short-depth quantum circuits to quantify the terms in our cost function, and we prove that our cost cannot be efficiently approximated with a classical algorithm under reasonable complexity assumptions. We present both gradient-free and gradient-based approaches to minimizing this cost. As a demonstration of QAQC, we compile various one-qubit gates on IBM's and Rigetti's quantum computers into their respective native gate alphabets. Furthermore, we successfully simulate QAQC up to a problem size of 9 qubits, and these simulations highlight both the scalability of our cost function as well as the noise resilience of QAQC. Future applications of QAQC include algorithm depth compression, black-box compiling, noise mitigation, and benchmarking.Comment: 19 + 10 pages, 14 figures. Added larger scale implementations and proof that cost function is DQC1-har

Variational Quantum Linear Solver

Previously proposed quantum algorithms for solving linear systems of equations cannot be implemented in the near term due to the required circuit depth. Here, we propose a hybrid quantum-classical algorithm, called Variational Quantum Linear Solver (VQLS), for solving linear systems on near-term quantum computers. VQLS seeks to variationally prepare $|x\rangle$ such that $A|x\rangle\propto|b\rangle$. We derive an operationally meaningful termination condition for VQLS that allows one to guarantee that a desired solution precision $\epsilon$ is achieved. Specifically, we prove that $C \geq \epsilon^2 / \kappa^2$, where $C$ is the VQLS cost function and $\kappa$ is the condition number of $A$. We present efficient quantum circuits to estimate $C$, while providing evidence for the classical hardness of its estimation. Using Rigetti's quantum computer, we successfully implement VQLS up to a problem size of $1024\times1024$. Finally, we numerically solve non-trivial problems of size up to $2^{50}\times2^{50}$. For the specific examples that we consider, we heuristically find that the time complexity of VQLS scales efficiently in $\epsilon$, $\kappa$, and the system size $N$.Comment: 13 + 8 pages, 15 figures, 7 table

Framing and visual type: Effect on future Zika vaccine uptake intent

Introduction: The Zika virus is associated with the birth defect microcephaly, and while a vaccine was not available in early- 2017, several were under development. This study’s purpose was to identify effective communication strategies to promote uptake of a new vaccine, particularly among women of reproductive age.Design and methods: In order to study the effects of Zika message framing (gain vs. loss) and visual type (photo vs. infographic) on future Zika vaccine uptake intent, a 2×2 between-subjects experiment was performed via an online survey in 2017 among 339 U.S. women of reproductive age (18-49 years). Participants were exposed to one of four messages, all resembling Instagram posts: gain-framed vs. loss-framed infographic, and gain-framed vs. loss-framed photo. These messages were followed by questions about Zika vaccine uptake intent as well as intermediate psychosocial variables that could lead to intent. Results: There was no interaction between framing and visual type (P=0.116), and there was no effect for framing (P=0.185) or visual type (P=0.724) on future Zika vaccine uptake intent, which is likely indicative of insufficient dosage of the intervention. However, when focusing on intermediate psychosocial constructs that are known to influence behavior and intent, gain-framed messages were more effective in increasing subjective norms (P=0.005) as related to a future Zika vaccine, as well as perceived benefits (P=0.016) and self-efficacy (P=0.032). Conclusions: Gain-framed messages seem to be more effective than loss-framed messages to increase several constructs that could, in turn, affect future Zika vaccine uptake intent. This is a novel finding since, traditionally, loss-framed messages are considered more beneficial in promoting vaccine-related health behaviors