BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Robert Huang (California Institute of Technology) DTSTART:20240326T203000Z DTEND:20240326T213000Z DTSTAMP:20260423T021135Z UID:MathPic/125 DESCRIPTION:Title: Certifying Almost All Quantum States with Few Single-qubit Measurements< /a>\nby Robert Huang (California Institute of Technology) as part of Mathe matical Picture Language Seminar\n\nLecture held in https://harvard.zoom.u s/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09.\n\nAbstract\nQuantum s ystems can exhibit highly complex entanglement. Certifying that an n-qubit state in the experimental lab is close to a highly-entangled target state typically requires deep entangling circuits or exponentially many single- qubit measurements. In this work\, we prove that almost all n-qubit target states\, including those with exponential circuit complexity\, can be cer tified from only O(n^2) single-qubit measurements. This result is establis hed by a new technique relating certification to a random walk's mixing ti me. Our protocol has applications for benchmarking the fidelity of quantum systems and for learning and verifying neural networks\, tensor networks\ , and various other representations of quantum states using only single-qu bit measurements. We show that such verified representations can be used t o efficiently predict highly non-local properties that would otherwise req uire an exponential number of measurements.\n\nPasscode: 657361\n LOCATION:https://researchseminars.org/talk/MathPic/125/ END:VEVENT END:VCALENDAR