Deferred measurement principle: Difference between revisions
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[[File:MeasurementCommutesWithControls.png|thumb|Two equivalent quantum logic circuits. One where measurement happens first, and one where an operation conditioned on the to-be-measured qubit happens first.]] |
[[File:MeasurementCommutesWithControls.png|thumb|Two equivalent quantum logic circuits. One where measurement happens first, and one where an operation conditioned on the to-be-measured qubit happens first.]] |
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The '''Deferred Measurement Principle''' is a result in [[quantum computing]] which states that delaying measurements until the end of a quantum computation doesn't affect the probability distribution of outcomes.<ref name="NielsenChuang2010">{{cite book|author1=Michael A. Nielsen|author2=Isaac L. Chuang|title=Quantum Computation and Quantum Information: 10th Anniversary Edition|url=https://books.google.com/books?id=-s4DEy7o-a0C|date=9 December 2010|publisher=Cambridge University Press|isbn=978-1-139-49548-6 |page=186 |section=4.4 Measurement}}</ref><ref name="Cross2012">{{cite book|author=Odel A. Cross|title=Topics in Quantum Computing|url=https://books.google.com/books?id=b_D9flK2h8QC&pg=PA348|date=5 November 2012|publisher=O. A. Cross|isbn=978-1-4800-2749-7|page=348 |section=5.2.2 Deferred Measurement}}</ref> |
The '''Deferred Measurement Principle''' is a result in [[quantum computing]] which states that delaying measurements until the end of a quantum computation doesn't affect the [[probability distribution]] of outcomes.<ref name="NielsenChuang2010">{{cite book|author1=Michael A. Nielsen|author2=Isaac L. Chuang|title=Quantum Computation and Quantum Information: 10th Anniversary Edition|url=https://books.google.com/books?id=-s4DEy7o-a0C|date=9 December 2010|publisher=Cambridge University Press|isbn=978-1-139-49548-6 |page=186 |section=4.4 Measurement}}</ref><ref name="Cross2012">{{cite book|author=Odel A. Cross|title=Topics in Quantum Computing|url=https://books.google.com/books?id=b_D9flK2h8QC&pg=PA348|date=5 November 2012|publisher=O. A. Cross|isbn=978-1-4800-2749-7|page=348 |section=5.2.2 Deferred Measurement}}</ref> |
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A consequence of the deferred measurement principle is that measuring commutes with conditioning. |
A consequence of the deferred measurement principle is that measuring commutes with conditioning. |
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The choice of whether to measure a qubit before, after, or during an operation conditioned on that qubit will have no observable effect on a circuit's final expected results. |
The choice of whether to measure a [[qubit]] before, after, or during an operation conditioned on that qubit will have no observable effect on a circuit's final expected results. |
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Thanks to the deferred measurement principle, measurements in a quantum circuit can often be shifted around so they happen at better times. |
Thanks to the deferred measurement principle, measurements in a [[quantum circuit]] can often be shifted around so they happen at better times. |
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For example, measuring qubits as early as possible can reduce the maximum number of simultaneously stored qubits; potentially enabling an algorithm to be run on a smaller quantum computer or to be simulated more efficiently. |
For example, measuring qubits as early as possible can reduce the maximum number of simultaneously stored qubits; potentially enabling an algorithm to be run on a smaller quantum computer or to be simulated more efficiently. |
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Alternatively, deferring all measurements until the end of circuits allows them to be analyzed using only [[pure state]]s. |
Alternatively, deferring all measurements until the end of circuits allows them to be analyzed using only [[pure state]]s. |
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Revision as of 17:09, 6 March 2018
The Deferred Measurement Principle is a result in quantum computing which states that delaying measurements until the end of a quantum computation doesn't affect the probability distribution of outcomes.[1][2]
A consequence of the deferred measurement principle is that measuring commutes with conditioning. The choice of whether to measure a qubit before, after, or during an operation conditioned on that qubit will have no observable effect on a circuit's final expected results.
Thanks to the deferred measurement principle, measurements in a quantum circuit can often be shifted around so they happen at better times. For example, measuring qubits as early as possible can reduce the maximum number of simultaneously stored qubits; potentially enabling an algorithm to be run on a smaller quantum computer or to be simulated more efficiently. Alternatively, deferring all measurements until the end of circuits allows them to be analyzed using only pure states.
References
- ^ Michael A. Nielsen; Isaac L. Chuang (9 December 2010). "4.4 Measurement". Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press. p. 186. ISBN 978-1-139-49548-6.
- ^ Odel A. Cross (5 November 2012). "5.2.2 Deferred Measurement". Topics in Quantum Computing. O. A. Cross. p. 348. ISBN 978-1-4800-2749-7.
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