Abstract Noisy intermediate-scale quantum (NISQ) computers are entering an era in which they can perform computational tasks beyond the capabilities of the most powerful classical computers, thereby achieving ‘quantum supremacy’, a major milestone in quantum computing. NISQ supremacy requires comparison with a state-of-the-art classical simulator. We report HPC simulations of hard random quantum circuits (RQC), which have been recently used as a benchmark for the first experimental demonstration of quantum supremacy, sustaining an average performance of 281 Pflop/s (true single precision) on Summit, currently the fastest supercomputer in the world. These simulations were carried out using qFlex, a tensor-network-based classical high-performance simulator of RQCs. Our results show an advantage of many orders of magnitude in energy consumption of NISQ devices over classical supercomputers. In addition, we propose a standard benchmark for NISQ computers based on qFlex.
Abstract Noisy intermediate-scale quantum (NISQ) computers are entering an era in which they can perform computational tasks beyond the capabilities of the most powerful classical computers, thereby achieving ‘quantum supremacy’, a major milestone in quantum computing. NISQ supremacy requires comparison with a state-of-the-art classical simulator. We report HPC simulations of hard random quantum circuits (RQC), which have been recently used as a benchmark for the first experimental demonstration of quantum supremacy, sustaining an average performance of 281 Pflop/s (true single precision) on Summit, currently the fastest supercomputer in the world. These simulations were carried out using qFlex, a tensor-network-based classical high-performance simulator of RQCs. Our results show an advantage of many orders of magnitude in energy consumption of NISQ devices over classical supercomputers. In addition, we propose a standard benchmark for NISQ computers based on qFlex.
Abstract Here we present qFlex, a flexible tensor network-based quantum circuit simulator. qFlex can compute both the exact amplitudes, essential for the verification of the quantum hardware, as well as low-fidelity amplitudes, to mimic sampling from Noisy Intermediate-Scale Quantum (NISQ) devices. In this work, we focus on random quantum circuits (RQCs) in the range of sizes expected for supremacy experiments. Fidelity f simulations are performed at a cost that is 1/f lower than perfect fidelity ones. We also present a technique to eliminate the overhead introduced by rejection sampling in most tensor network approaches. We benchmark the simulation of square lattices and Google’s Bristlecone QPU. Our analysis is supported by extensive simulations on NASA HPC clusters Pleiades and Electra. For our most computationally demanding simulation, the two clusters combined reached a peak of 20 Peta Floating Point Operations per Second (PFLOPS) (single precision), i.e., 64% of their maximum achievable performance, which represents the largest numerical computation in terms of sustained FLOPs and the number of nodes utilized ever run on NASA HPC clusters. Finally, we introduce a novel multithreaded, cache-efficient tensor index permutation algorithm of general application.
Abstract The achievement of quantum computational advantage, also known as quantum supremacy, is a major milestone at which a quantum computer can solve a problem significantly faster than the world's most powerful classical computers. Two tasks, boson sampling and random quantum circuit sampling, have experimentally exhibited quantum advantages on photonic and superconducting platforms respectively. Classical benchmarking is essential, yet challenging, because these tasks are intractable for classical computers. This study reviews models, algorithms and large‐scale simulations of these two sampling tasks. These approaches continue to hold substantial significance for research in both current noisy intermediate‐scale quantum (NISQ) systems and future fault‐tolerant quantum computing.
Here we present a flexible tensor network based simulator for quantum circuits on different topologies, including the Google Bristlecone QPU. Our simulator can compute both exact amplitudes, a task essential for the verification of the quantum hardware, as well as low-fidelity amplitudes to mimic Noisy Intermediate-Scale Quantum (NISQ) devices. While our simulator can be used to compute amplitudes of arbitrary quantum circuits, we focus on random quantum circuits (RQCs) [Boixo et al., Nature Physics 14] in the range of sizes expected for supremacy experiments. Our simulator enables the simulation of sampling on quantum circuits that were out of reach for previous approaches. For instance, our simulator is able to output single amplitudes with depth 1+32+1 for the full Bristlecone QPU in less than (f⋅4200) hours on a single core, where 0<f≤1 is the target fidelity, on 2×20-core Intel Xeon Gold 6148 processors (Skylake). We also estimate that computing 106 amplitudes (with fidelity 0.50\%) needed to sample from the full Bristlecone QPU with depth (1+32+1) would require about 3.5 days using the NASA Pleiades and Electra supercomputers combined. In addition, we discuss the hardness of the classical simulation of RQCs, as well as give evidence for the higher complexity in the simulation of Bristlecone topology as compared to other two-dimensional grids with the same number of qubits. Our analysis is supported by extensive simulations on NASA HPC clusters Pleiades and Electra. For the most computationally demanding simulation we had, namely the simulation of a 60-qubit sub-lattice of Bristlecone, the two HPC clusters combined reached a peak of 20 PFLOPS (single precision), that is 64% of their maximum achievable performance. To date, this numerical computation is the largest in terms of sustained PFLOPS and number of nodes utilized ever run on NASA HPC clusters.
It is believed that random quantum circuits are difficult to simulate classically. These have been used to demonstrate quantum supremacy: the execution of a computational task on a quantum computer that is infeasible for any classical computer. The task underlying the assertion of quantum supremacy by Arute et al. (Nature, 574, 505--510 (2019)) was initially estimated to require Summit, the world's most powerful supercomputer today, approximately 10,000 years. The same task was performed on the Sycamore quantum processor in only 200 seconds. In this work, we present a tensor network-based classical simulation algorithm. Using a Summit-comparable cluster, we estimate that our simulator can perform this task in less than 20 days. On moderately-sized instances, we reduce the runtime from years to minutes, running several times faster than Sycamore itself. These estimates are based on explicit simulations of parallel subtasks, and leave no room for hidden costs. The simulator's key ingredient is identifying and optimizing the "stem" of the computation: a sequence of pairwise tensor contractions that dominates the computational cost. This orders-of-magnitude reduction in classical simulation time, together with proposals for further significant improvements, indicates that achieving quantum supremacy may require a period of continuing quantum hardware developments without an unequivocal first demonstration.
The quest for quantum advantage, wherein quantum computers surpass the computational capabilities of classical computers executing state-of-the-art algorithms on well-defined tasks, represents a pivotal race in the domain of quantum computing. NISQ (Noisy Intermediate-Scale Quantum) computing has witnessed remarkable advancements, culminating in significant milestones on the journey towards the realization of universal fault-tolerant quantum computers. This transformative turning point, known as quantum supremacy, has been achieved amid a series of breakthroughs, signifying the dawn of the quantum era. Quantum hardware has undergone substantial integration and architectural evolution, contrasting with its nascent stages. In this review, we critically examine the quantum supremacy experiments conducted thus far, shedding light on their implications and contributions to the evolving landscape of quantum computing. Additionally, we endeavor to illuminate a range of cutting-edge proof-of-principle investigations in the realm of applied quantum computing, providing an insightful overview of the current state of applied quantum research and its prospective influence across diverse scientific, industrial, and technological frontiers.
A major milestone in the era of noisy intermediate scale quantum computers is \textit{quantum supremacy} [Nature \textbf{574}, 505 (2019)] claimed on the Sycamore quantum processor of 53 qubits, which can perform a random circuit sampling task within 200 seconds while the same task is estimated to require a runtime of 10,000 years on Summit. This record has been renewed with two recent experiments on the Zuchongzhi 2.0 (56 qubits) and Zuchongzhi 2.1 (60 qubits) quantum processors. On the other front of quantum supremacy comparison, there has also been continuous improvements on both the classical simulation algorithm as well as the underlying hardware. And a fair justification of the computational advantages for those quantum supremacy experiments would require to practically simulate the same problems on current top supercomputers, which is still in lack. Here we report the full-scale simulations of these problems on new generation Sunway supercomputer, based on a customized tensor network contraction algorithm. Our benchmark shows that the most challenging sampling task performed on Sycamore can be accomplished within 1 week, thus collapsing the quantum supremacy claim of Sycamore. Additionally, we show that the XEB fidelities of the \textit{quantum supremacy circuits} with up to 14 cycles can be verified in minutes, which also provides strong consistency check for quantum supremacy experiments. Our results redefine quantum supremacy baseline using the new generation Sunway supercomputer.