Row 4835

Row ID: 4835 | Dataset Entry | Axioma AXP Content Repository

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So in Shor’s algorithm I was taught that |1> is a sum of all possible eigenvectors for gate U. This allows for phase estimation of a random eigenvalue of one of those eigenvectors which we can use to find r etc etc… But why does using |1> work this way? I’ve seen proofs showing how |1> is a sum of eigenvectors and can understand the math behind it but I don’t understand how phase kickback can occur if |1> itself is not an eigenvector. U|1> = |a mod n>, not |1>, so how does phase kickback even happen?

Any help with this would be much appreciated. I’ve been stuck trying to wrap my head around this for almost a week now 😅

Edit: for clarification the unitary gate I’m referring to here is U|y> = |ay mod n>

FieldValue
text So in Shor’s algorithm I was taught that |1> is a sum of all possible eigenvectors for gate U. This allows for phase estimation of a random eigenvalue of one of those eigenvectors which we can use to find r etc etc… But why does using |1> work this way? I’ve seen proofs showing how |1> is a sum of eigenvectors and can understand the math behind it but I don’t understand how phase kickback can occur if |1> itself is not an eigenvector. U|1> = |a mod n>, not |1>, so how does phase kickback even ha…
label r/quantumcomputing
dataType post
communityName r/QuantumComputing
datetime 2024-04-22
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{
  "text": "So in Shor’s algorithm I was taught that |1> is a sum of all possible eigenvectors for gate U. This allows for phase estimation of a random eigenvalue of one of those eigenvectors which we can use to find r etc etc… But why does using |1> work this way? I’ve seen proofs showing how |1> is a sum of eigenvectors and can understand the math behind it but I don’t understand how phase kickback can occur if |1> itself is not an eigenvector. U|1> = |a mod n>, not |1>, so how does phase kickback even happen? \n\nAny help with this would be much appreciated. I’ve been stuck trying to wrap my head around this for almost a week now 😅\n\nEdit: for clarification the unitary gate I’m referring to here is U|y> = |ay mod n>",
  "label": "r/quantumcomputing",
  "dataType": "post",
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  "datetime": "2024-04-22",
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