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How to compare a noisy quantum processor to a classical computer

🤖 Intelligence Artificielle

✍️ Auteur(s)

Sergio Boixo and Vadim Smelyanskiy

📅 Publication

2023-08-24T15:10:00.000-07:00

📖 Longueur

800 mots

Source: https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1m1RqJqScz...

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Posted by Sergio Boixo and Vadim Smelyanskiy, Principal Scientists, Google Quantum AI Team A full-scale error-corrected quantum computer will be able to solve some problems that are impossible for classical computers, but building such a device is a huge endeavor. We are proud of the milestones that we have achieved toward a fully error-corrected quantum computer, but that large-scale computer is still some number of years away. Meanwhile, we are using our current noisy quantum processors as flexible platforms for quantum experiments. In contrast to an error-corrected quantum computer , experiments in noisy quantum processors are currently limited to a few thousand quantum operations or gates, before noise degrades the quantum state. In 2019 we implemented a specific computational task called random circuit sampling on our quantum processor and showed for the first time that it outperformed state-of-the-art classical supercomputing. Although they have not yet reached beyond-classical capabilities, we have also used our processors to observe novel physical phenomena, such as time crystals and Majorana edge modes , and have made new experimental discoveries, such as robust bound states of interacting photons and the noise-resilience of Majorana edge modes of Floquet evolutions. We expect that even in this intermediate, noisy regime, we will find applications for the quantum processors in which useful quantum experiments can be performed much faster than can be calculated on classical supercomputers — we call these "computational applications" of the quantum processors. No one has yet demonstrated such a beyond-classical computational application. So as we aim to achieve this milestone, the question is: What is the best way to compare a quantum experiment run on such a quantum processor to the computational cost of a classical application? We already know how to compare an error-corrected quantum algorithm to a classical algorithm. In that case, the field of computational complexity tells us that we can compare their respective computational costs — that is, the number of operations required to accomplish the task. But with our current experimental quantum processors, the situation is not so well defined. In “ Effective quantum volume, fidelity and computational cost of noisy quantum processing experiments ”, we provide a framework for measuring the computational cost of a quantum experiment, introducing the experiment’s “effective quantum volume”, which is the number of quantum operations or gates that contribute to a measurement outcome. We apply this framework to evaluate the computational cost of three recent experiments: our random circuit sampling experiment , our experiment measuring quantities known as “out of time order correlators” (OTOCs) , and a recent experiment on a Floquet evolution related to the Ising model . We are particularly excited about OTOCs because they provide a direct way to experimentally measure the effective quantum volume of a circuit (a sequence of quantum gates or operations), which is itself a computationally difficult task for a classical computer to estimate precisely. OTOCs are also important in nuclear magnetic resonance and electron spin resonance spectroscopy . Therefore, we believe that OTOC experiments are a promising candidate for a first-ever computational application of quantum processors. Plot of computational cost and impact of some recent quantum experiments. While some (e.g., QC-QMC 2022 ) have had high impact and others (e.g., RCS 2023 ) have had high computational cost, none have yet been both useful and hard enough to be considered a “computational application.” We hypothesize that our future OTOC experiment could be the first to pass this threshold. Other experiments plotted are referenced in the text. Random circuit sampling: Evaluating the computational cost of a noisy circuit When it comes to running a quantum circuit on a noisy quantum processor, there are two competing considerations. On one hand, we aim to do something that is difficult to achieve classically. The computational cost — the number of operations required to accomplish the task on a classical computer — depends on the quantum circuit’s effective quantum volume : the larger the volume, the higher the computational cost, and the more a quantum processor can outperform a classical one. But on the other hand, on a noisy processor, each quantum gate can introduce an error to the calculation. The more operations, the higher the error, and the lower the fidelity of the quantum circuit in measuring a quantity of interest. Under this consideration, we might prefer simpler circuits with a smaller effective volume, but these are easily simulated by classical computers. The balance of these competing considerations, which we want to maximize, is called the "computational resource", shown below. Graph of the tradeoff between quantum volume and noise in a quantum circuit, captured in a quantity called the “computational resource.” For a noisy quantum circuit, this will initially increase with the computational cost, but eventually, noise will overrun the circuit and cause it to decrease. We can see how these...

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