BEGIN:VCALENDAR
PRODID:-//AddEvent Inc//AddEvent.com v1.7//EN
VERSION:2.0
BEGIN:VTIMEZONE
TZID:America/New_York
BEGIN:STANDARD
DTSTART:20261101T010000
RRULE:FREQ=YEARLY;BYDAY=1SU;BYMONTH=11
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:EST
END:STANDARD
BEGIN:DAYLIGHT
DTSTART:20260308T030000
RRULE:FREQ=YEARLY;BYDAY=2SU;BYMONTH=3
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:EDT
END:DAYLIGHT
END:VTIMEZONE
BEGIN:VEVENT
DESCRIPTION:Cloning is as Hard as Learning for Stabilizer States\nNikhil Bansal | University of Warwick\nThe impossibility of simultaneously cloning non-orthogonal states lies at the foundations of quantum theory. Even when allowing for approximation errors\, cloning an arbitrary unknown pure state requires as many initial copies as needed to fully learn the state. Rather than arbitrary unknown states\, modern quantum learning theory often considers structured classes of states and exploits such structure to develop learning algorithms that outperform general-state tomography. This raises the question: How do the sample complexities of learning and cloning relate for such structured classes?We answer this question for an important class of states. Namely\, for n-qubit stabilizer states\, we show that the optimal sample complexity of cloning is Θ(n). Thus\, also for this structured class of states\, cloning is as hard as learning. To prove these results\, we use representation-theoretic tools in the recently proposed Abelian State Hidden Subgroup framework and a new structured version of the recently introduced random purification channel to relate stabilizer state cloning to a variant of the sample amplification problem for probability distributions that was recently introduced in classical learning theory. This allows us to obtain our cloning lower bounds by proving new sample amplification lower bounds for classes of distributions with an underlying linear structure. Our results provide a more fine-grained perspective on No-Cloning theorems\, opening up connections from foundations to quantum learning theory and quantum cryptography.\nLocation\n\n• QNC 4104\n• Online on Zoom\n\n
X-ALT-DESC;FMTTYPE=text/html:Cloning is as Hard as Learning for Stabilizer States<br />Nikhil Bansal | University of Warwick<br />The impossibility of simultaneously cloning non-orthogonal states lies at the foundations of quantum theory. Even when allowing for approximation errors, cloning an arbitrary unknown pure state requires as many initial copies as needed to fully learn the state. Rather than arbitrary unknown states, modern quantum learning theory often considers structured classes of states and exploits such structure to develop learning algorithms that outperform general-state tomography. This raises the question: How do the sample complexities of learning and cloning relate for such structured classes?We answer this question for an important class of states. Namely, for n-qubit stabilizer states, we show that the optimal sample complexity of cloning is Θ(n). Thus, also for this structured class of states, cloning is as hard as learning. To prove these results, we use representation-theoretic tools in the recently proposed Abelian State Hidden Subgroup framework and a new structured version of the recently introduced random purification channel to relate stabilizer state cloning to a variant of the sample amplification problem for probability distributions that was recently introduced in classical learning theory. This allows us to obtain our cloning lower bounds by proving new sample amplification lower bounds for classes of distributions with an underlying linear structure. Our results provide a more fine-grained perspective on No-Cloning theorems, opening up connections from foundations to quantum learning theory and quantum cryptography.<br />Location<br /><ul><li>QNC 4104</li><li>Online on Zoom</li></ul>
UID:57683a97b19040d59329b6bf5cb6858baddeventcom
SUMMARY:IQC Math and CS seminar featuring Nikhil Bansal
DTSTART;TZID=America/New_York:20260520T110000
DTEND;TZID=America/New_York:20260520T120000
DTSTAMP:20260624T144737Z
TRANSP:OPAQUE
STATUS:CONFIRMED
SEQUENCE:0
LOCATION:QNC 4104
X-MICROSOFT-CDO-BUSYSTATUS:BUSY
BEGIN:VALARM
TRIGGER:-PT30M
ACTION:DISPLAY
DESCRIPTION:Reminder
END:VALARM
END:VEVENT
END:VCALENDAR