wp-plugin-hostgator domain was triggered too early. This is usually an indicator for some code in the plugin or theme running too early. Translations should be loaded at the init action or later. Please see Debugging in WordPress for more information. (This message was added in version 6.7.0.) in /home4/scienrds/scienceandnerds/wp-includes/functions.php on line 6114ol-scrapes domain was triggered too early. This is usually an indicator for some code in the plugin or theme running too early. Translations should be loaded at the init action or later. Please see Debugging in WordPress for more information. (This message was added in version 6.7.0.) in /home4/scienrds/scienceandnerds/wp-includes/functions.php on line 6114Source:https:\/\/www.quantamagazine.org\/machine-learning-aids-classical-modeling-of-quantum-systems-20230914\/#comments<\/a><\/br> Understanding the quantum universe is not an easy thing. Intuitive notions of space and time break down in the tiny realm of subatomic physics, allowing for behavior that seems, to our macro sensibilities, downright weird.<\/p>\n Quantum computers<\/a> should allow us to harness this strangeness. Such machines could theoretically explore molecular interactions to create new drugs and materials<\/a>. But perhaps most important, the world itself is built upon this quantum universe \u2014 if we want to understand how it works, we probably need quantum tools.<\/p>\n However, current near-term quantum devices<\/a> are still far from fulfilling that promise, since they can\u2019t reliably execute a large number of quantum interactions. Until researchers can overcome this issue, classical computers remain the best way to solve real-world problems, however inefficiently they do so.<\/p>\n But maybe there\u2019s a workaround, a kind of quantum compromise. A spate of recent papers suggests that it may be possible to take the quantum system you\u2019d like to understand, input its properties into classical machines, and use those machines to predict the quantum system\u2019s behavior. By combining a new way of modeling quantum systems with increasingly sophisticated machine learning algorithms, researchers have established<\/a> a method for classical machines to model and predict quantum behavior.<\/p>\n \u201cI think the work is very significant,\u201d said Yi-Zhuang You<\/a>, a physicist at the University of California, San Diego who is unaffiliated with the studies. \u201cIt fundamentally changes the field in the sense that it\u2019s the right way to combine quantum computation and machine learning.\u201d<\/p>\n Researchers have been trying<\/a> to use classical computers to predict quantum states since at least 1989. Typically, a quantum system with n<\/em> qubits \u2014 the quantum equivalent of a bit \u2014 can be represented by a classical array of 2n <\/sup><\/em>numbers. The size of this array increases exponentially with the number of qubits, meaning that the required computing power quickly becomes prohibitive.<\/p>\n In late 2017, the computer scientist Scott Aaronson<\/a> suggested<\/a> that it\u2019s not necessary to know the full classical representation of a quantum system. Instead, you might be able to learn about a given quantum state and predict its properties using only a subset of the representation.<\/p>\n Then in 2020, the physicists Hsin Yuan (Robert) Huang<\/a> and Richard Kueng<\/a> pioneered a practical approach to Aaronson\u2019s method. Their technique allowed them to predict many characteristics of the quantum state of a system from very few measurements using classical methods. The process involved constructing a \u201cclassical shadow<\/a>\u201d from these measurements: a succinct classical representation of the quantum system, akin to an actual shadow, which conveys a lot of information \u2014 but not everything \u2014 about the object casting it.<\/p>\n \u201cYou have to lower your sights and only try to predict certain quantum observables,\u201d said John Preskill<\/a>, a theoretical physicist at the California Institute of Technology who worked with Huang and Kueng on the project.<\/p>\n With this model, if you want to predict a certain number of properties of the system, you need just enough measurements \u2014 specifically, a number of measurements that scales as the logarithm of the number of properties. \u201cRobert\u2019s idea is brilliant,\u201d said Xie Chen<\/a>, a colleague of Preskill\u2019s at Caltech who was not associated with the study. \u201cThat is going to give us a big advantage to learn the system by doing some random sampling.\u201d<\/p>\n The approach has already seen some success. Scientists have already used these classical shadows to conduct the largest simulation<\/a> of quantum chemistry ever undertaken, using a classical algorithm with a noisy, error-prone quantum computer to study the forces experienced by atoms in a diamond crystal.<\/p>\n But perhaps it could do more. Huang and others wanted to study a quantum system not just at one static moment \u2014 as in a crystal \u2014 but as it changed over time. That would give researchers far more insight into how these systems behave, at the cost of far more data to process. Luckily, by this time another tool had become popular for such a task: machine learning.<\/p>\n In the last few years, classical machine learning models have made revolutionary strides in improving automated predictions. But when researchers tried using them to solve quantum problems, Preskill said, the models often got things right, but their accuracy was not guaranteed. Machine learning typically progresses via trial and error, so you\u2019d need just the right kind of data \u2014 and a lot of it \u2014 to get useful information.<\/p>\n A paper<\/a> by Huang and collaborators at Google Quantum AI underscored that intuition: Classical machine learning algorithms trained with enough quantum data can be computationally powerful enough to model quantum systems.<\/p>\n But there was still a problem. These machine learning models were still fundamentally classical, meaning that it\u2019s impossible for them to process truly quantum data and output quantum states. To get around this, Huang and colleagues showed in a Science<\/em><\/a> paper last year how to use classical shadows to convert quantum information into classical data. They could then train a machine learning model to predict properties of new quantum systems.<\/p>\n \u201cThe advantage they create is a quantum map between [quantum] inputs and [quantum] outputs, both of which are classical shadows \u2014 since you are never going to succeed if it blows up to the full quantum state,\u201d said Jarrod McClean<\/a>, a computer scientist at Google Quantum AI.<\/p>\n This seemed doable in practice, since the model only needed a polynomial number of data points to achieve accurate predictions. Unfortunately, it still wasn\u2019t ideal. \u201cThe polynomial was super large,\u201d Huang said. Basically, it was too difficult ever to obtain that much training data.<\/p>\n The final piece of the puzzle came in a workshop<\/a> in July this year at the Simons Institute for the Theory of Computing at the University of California, Berkeley. There, an undergraduate in Preskill\u2019s group named Laura Lewis<\/a> demonstrated a way around the obstacle.<\/p>\n While the previous models were agnostic about the geometry of the quantum system under study, Lewis\u2019 work wasn\u2019t. Rather than trying to keep track of the interactions between every combination of qubits in the system, her algorithm focused on the local interaction between qubits located next to each other. This approach now needed less training data \u2014 just a logarithmic function of the number of qubits \u2014 to accurately predict properties of the quantum system, making it finally practically feasible.<\/p>\n With these models, researchers can explore the composition and behavior of increasingly complicated quantum systems. But Lewis\u2019 result could also help improve this line of research itself: We now have better ways to understand how to reduce the scaling requirements for future predictions about other quantum systems.<\/p>\n Lewis\u2019 work reveals \u201chow much data [must] be collected from a physical system to make reliable predictions,\u201d McClean said.<\/p>\n Meanwhile, Huang has explored further. Building upon his work on classical shadows and machine learning, he recently used<\/a> an improved algorithm to study active quantum systems (such as the transformation of a quantum state to another) with a smaller amount of data. Preskill suspects it\u2019s just the start. \u201cWhat I expect over the next five to 10 years, the main impact of quantum computing will not be applications that are commercially important,\u201d he said. \u201cIt\u2019s going to be scientific exploration.\u201d<\/p>\n For now, the new methods developed by Huang and Lewis still need to be rigorously tested in laboratory experiments. Experimental systems come with extra baggage including measurement errors and inaccuracies, Chen said, which these models still can\u2019t handle.<\/p>\n But even though this work is still in progress, these classical shadows should allow researchers to improve their understanding of the quantum theoretical realm in new ways. Are classical shadows enough to capture quantum complexity, or do we need a fully quantum approach? Are there quantum properties or dynamics that will forever be out of reach? \u201cTheir work has been pioneering to start thinking about these questions,\u201d said Soonwon Choi<\/a>, a physicist at the Massachusetts Institute of Technology.<\/p>\n And maybe one day, Preskill said, researchers will collect enough experimental data to be able to predict system features that have never been encountered in the lab. \u201cThis is one of the big-picture goals of applying machine learning to quantum physics,\u201d he said. \u201cAnd we were able to show that at least in some settings, you can make accurate predictions.\u201d<\/p>\n Editor\u2019s note: Scott Aaronson is a member of <\/em>Quanta Magazine\u2019s <\/em>advisory board<\/em><\/a>.<\/em><\/p>\n<\/div>\n <\/br><\/br><\/br><\/p>\n
\nMachine Learning Aids Classical Modeling of Quantum Systems<\/br>
\n2023-09-18 21:58:39<\/br><\/p>\nWhat We Learn From the Shadows<\/strong><\/h2>\n
Training the Models<\/strong><\/h2>\n
Beyond Shadows<\/strong><\/h2>\n