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DESCRIPTION:Random dimension reduction and learning symmetric properties of quantum states\nAngus Lowe | MIT\nWe introduce a procedure called random dimension reduction that simultaneously reduces the dimensions of many\, potentially distinct quantum states while preserving properties invariant under the tensor power action of an isometry. This provides a black-box method to replace the dimension with the maximum rank in the sample complexity of learning symmetric properties\, even those depending on multiple input states. We show that dimension reduction followed by full state tomography yields improved upper bounds for estimating distances\, fidelities\, and relative entropies between pairs of states. \n\nWe also give an efficient quantum circuit implementation of the procedure using the Schur transform.Expressing the action of our procedure through the Choi-Jamiolkowski isomorphism reveals an intimate connection with the recently introduced random purification channel by Tang\, Wright\, and Zhandry. This perspective also completes an end-to-end analysis of sample-optimal tomography without requiring a reference to the Schur transform or Schur polynomials. Finally\, we prove that there does not exist a random purification channel that simultaneously purifies copies of multiple\, potentially different input states. Hence\, random dimension reduction is related to\, but distinct from\, random purification.\n\nLocation\n\n• QNC 4104\n• Online on ZoomMeeting ID: 912 8146 6256 \nPasscode\n: 494237\n\n
X-ALT-DESC;FMTTYPE=text/html:Random dimension reduction and learning symmetric properties of quantum states<br />Angus Lowe | MIT<br />We introduce a procedure called random dimension reduction that simultaneously reduces the dimensions of many, potentially distinct quantum states while preserving properties invariant under the tensor power action of an isometry. This provides a black-box method to replace the dimension with the maximum rank in the sample complexity of learning symmetric properties, even those depending on multiple input states. We show that dimension reduction followed by full state tomography yields improved upper bounds for estimating distances, fidelities, and relative entropies between pairs of states. <br><br>We also give an efficient quantum circuit implementation of the procedure using the Schur transform.Expressing the action of our procedure through the Choi-Jamiolkowski isomorphism reveals an intimate connection with the recently introduced random purification channel by Tang, Wright, and Zhandry. This perspective also completes an end-to-end analysis of sample-optimal tomography without requiring a reference to the Schur transform or Schur polynomials. Finally, we prove that there does not exist a random purification channel that simultaneously purifies copies of multiple, potentially different input states. Hence, random dimension reduction is related to, but distinct from, random purification.<br><br>Location<br /><ul><li>QNC 4104</li><li>Online on Zoom<ul><li>Meeting ID: 912 8146 6256 <br />Passcode<br />: 494237</li></ul></li></ul>
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SUMMARY:IQC Math and CS seminar featuring Angus Lowe
DTSTART;TZID=America/New_York:20260805T140000
DTEND;TZID=America/New_York:20260805T150000
DTSTAMP:20260731T185716Z
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LOCATION:QNC 4104
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