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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\/the-quest-to-quantify-quantumness-20231019\/#comments<\/a><\/br> In other words, he showed that an entanglement-free quantum circuit was easy to simulate on a classical computer. In a computational sense, the circuit wasn\u2019t intrinsically quantum. The collection of all such non-entangling circuits (or, equivalently, all arrangements of qubits that might come out of these non-entangling circuits) formed something of a classically simulable island in a vast quantum sea.<\/p>\n In this sea were the states resulting from truly quantum circuits, the ones for which a classical simulation might take billions of years. For this reason, researchers came to regard entanglement not just as a quantum property, but as a quantum resource: It was what you needed to reach the uncharted depths, where powerful quantum algorithms like Shor\u2019s resided.<\/p>\n Today, entanglement is still the most studied quantum resource. \u201cIf you ask 99 out of 100 physicists [what makes quantum circuits powerful], the first thing that comes to mind is entanglement,\u201d Fefferman said.<\/p>\n And active research into entanglement\u2019s relationship with complexity continues. Fefferman and his collaborators, for instance, showed last year<\/a> that for one particular class of quantum circuits, entanglement fully determines how hard the circuit is to classically simulate. \u201cAs soon as you get to a certain amount of entanglement,\u201d Fefferman said, \u201cyou can actually prove hardness. There\u2019s no [classical] algorithm that will work.\u201d<\/p>\n But Fefferman\u2019s proof holds for only one flavor of circuits. And even 20 years ago, researchers were already recognizing that entanglement alone failed to capture the richness of the quantum ocean.<\/p>\n \u201cDespite the essential role of entanglement,\u201d Jozsa and his collaborator wrote in their 2002 paper, \u201cwe argue that it is nevertheless misleading to view entanglement as a key resource for quantum computational power.\u201d<\/p>\n The quest for quantumness, it turned out, was just beginning.<\/p>\n Jozsa knew that entanglement was not the final word on quantumness, because four years before his work, the physicist Daniel Gottesman<\/a> had shown otherwise. At a 1998 conference in Tasmania, Gottesman explained<\/a> that, in a specific type of quantum circuit, the seemingly quintessential quantum quantity became a trifle for a classical computer to simulate.<\/p>\n In Gottesman\u2019s method (which he discussed with the mathematician Emanuel Knill), the entangling operation cost essentially nothing. You could entangle as many qubits as you liked, and a classical computer could still keep up.<\/p>\n \u201cThis was one of the first surprises, the Gottesman-Knill theorem, in the \u201990s,\u201d Korzekwa said.<\/p>\n The ability to classically simulate entanglement seemed like a bit of a miracle, but there was a catch. The Gottesman-Knill algorithm couldn\u2019t handle all quantum circuits, just those that stuck to the so-called Clifford gates. But if you added a \u201cT gate,\u201d a seemingly innocuous gadget that rotates a qubit in a particular way, their program would choke on it.<\/p>\n This T gate seemed to manufacture some sort of quantum resource \u2014 something intrinsically quantum that can\u2019t be simulated on a classical computer. Before long, a pair of physicists would give the quantum essence produced by the forbidden T-gate rotation a catchy name: magic.<\/p>\n In 2004, Sergey Bravyi, then of the Landau Institute for Theoretical Physics in Russia, and Alexei Kitaev of the California Institute of Technology worked out two schemes for pulling off any quantum calculation: You could include T gates in the circuit itself. Or you could take a \u201cmagic state<\/a>\u201d of qubits that had been prepared with T gates by another circuit and feed it into a Clifford circuit. Either way, magic was essential for achieving full quantumness.<\/p>\n A decade later, Bravyi and David Gosset<\/a>, a researcher at the University of Waterloo in Canada, worked out how to measure the amount of magic in a set of qubits. And in 2016, they developed<\/a> a classical algorithm for simulating low-magic circuits. Their program took exponentially longer for every additional T gate, although the exponential growth isn\u2019t quite as explosive as it is in other cases. They finally flexed the efficiency of their method by classically simulating a somewhat magical circuit with hundreds of Clifford gates and nearly 50 T gates.<\/p>\n<\/div>\n <\/br><\/br><\/br><\/p>\n
\nThe Quest to Quantify Quantumness<\/br>
\n2023-10-23 21:58:24<\/br><\/p>\n\u00a0<\/strong>A Little Bit of Magic<\/strong><\/h2>\n