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Register a new userEstablishing the Quantum Supremacy Frontier with a 281 Pflop/s Simulation
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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.
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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 worlds 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 simulators 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.
Recent advances on quantum computing hardware have pushed quantum computing to the verge of quantum supremacy. Random quantum circuits are outstanding candidates to demonstrate quantum supremacy, which could be implemented on a quantum device that supports nearest-neighbour gate operations on a two-dimensional configuration. Here we show that using the Projected Entangled-Pair States algorithm, a tool to study two-dimensional strongly interacting many-body quantum systems, we can realize an effective general-purpose simulator of quantum algorithms. This technique allows to quantify precisely the memory usage and the time requirements of random quantum circuits, thus showing the frontier of quantum supremacy. With this approach we can compute the full wave-function of the system, from which single amplitudes can be sampled with unit fidelity. Applying this general quantum circuit simulator we measured amplitudes for a $7times 7$ lattice of qubits with depth $1+40+1$ and double-precision numbers in 31 minutes using less than $93$ TB memory on the Tianhe-2 supercomputer.
Quantum computing is of high interest because it promises to perform at least some kinds of computations much faster than classical computers. Arute et al. 2019 (informally, the Google Quantum Team) report the results of experiments that purport to demonstrate quantum supremacy -- the claim that the performance of some quantum computers is better than that of classical computers on some problems. Do these results close the debate over quantum supremacy? We argue that they do not. We provide an overview of the Google Quantum Teams experiments, then identify some open questions in the quest to demonstrate quantum supremacy.
Fundamental questions in chemistry and physics may never be answered due to the exponential complexity of the underlying quantum phenomena. A desire to overcome this challenge has sparked a new industry of quantum technologies with the promise that engineered quantum systems can address these hard problems. A key step towards demonstrating such a system will be performing a computation beyond the capabilities of any classical computer, achieving so-called quantum supremacy. Here, using 9 superconducting qubits, we demonstrate an immediate path towards quantum supremacy. By individually tuning the qubit parameters, we are able to generate thousands of unique Hamiltonian evolutions and probe the output probabilities. The measured probabilities obey a universal distribution, consistent with uniformly sampling the full Hilbert-space. As the number of qubits in the algorithm is varied, the system continues to explore the exponentially growing number of states. Combining these large datasets with techniques from machine learning allows us to construct a model which accurately predicts the measured probabilities. We demonstrate an application of these algorithms by systematically increasing the disorder and observing a transition from delocalized states to localized states. By extending these results to a system of 50 qubits, we hope to address scientific questions that are beyond the capabilities of any classical computer.
Buhrman, Cleve and Wigderson (STOC98) observed that for every Boolean function $f : {-1, 1}^n to {-1, 1}$ and $bullet : {-1, 1}^2 to {-1, 1}$ the two-party bounded-error quantum communication complexity of $(f circ bullet)$ is $O(Q(f) log n)$, where $Q(f)$ is the bounded-error quantum query complexity of $f$. Note that the bounded-error randomized communication complexity of $(f circ bullet)$ is bounded by $O(R(f))$, where $R(f)$ denotes the bounded-error randomized query complexity of $f$. Thus, the BCW simulation has an extra $O(log n)$ factor appearing that is absent in classical simulation. A natural question is if this factor can be avoided. H{o}yer and de Wolf (STACS02) showed that for the Set-Disjointness function, this can be reduced to $c^{log^* n}$ for some constant $c$, and subsequently Aaronson and Ambainis (FOCS03) showed that this factor can be made a constant. That is, the quantum communication complexity of the Set-Disjointness function (which is $mathsf{NOR}_n circ wedge$) is $O(Q(mathsf{NOR}_n))$. Perhaps somewhat surprisingly, we show that when $ bullet = oplus$, then the extra $log n$ factor in the BCW simulation is unavoidable. In other words, we exhibit a total function $F : {-1, 1}^n to {-1, 1}$ such that $Q^{cc}(F circ oplus) = Theta(Q(F) log n)$. To the best of our knowledge, it was not even known prior to this work whether there existed a total function $F$ and 2-bit function $bullet$, such that $Q^{cc}(F circ bullet) = omega(Q(F))$.
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