deferred measurement principle

File:Qcircuit measurement-commute.svg. One where measurement happens first, and one where an operation conditioned on the to-be-measured qubit happens first.]]

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| footer = Example: Two variants of the teleportation circuit. The 2-qubit states $|\backslash Phi^\{+\}\backslash rangle$ and $|\backslash beta\_\{00\}\backslash rangle$ refer to the same Bell state.

| image1 = Quantum_teleportation_circuit.svg

| caption1 = Measurement is performed early and the resulting classical bits are sent. The classical bits control if the 1-qubit X and Z gates are executed, allowing teleportation.{{Cite book|title=Quantum Computation and Quantum Information|last1=Nielsen|first1=Michael A.|last2=Chuang|first2=Isaac|date=2010|publisher=Cambridge University Press|isbn=978-1-10700-217-3|location=Cambridge|oclc=43641333|author-link=Michael Nielsen|author-link2=Isaac Chuang|url=https://www.cambridge.org/9781107002173|pages=26–28}}

| image2 = AltTeleport.jpg

| caption2 = By moving the measurement to the end, the 2-qubit controlled-X and -Z gates need to be applied, which requires both qubits to be near (i.e. at a distance where 2-qubit quantum effects can be controlled), and thus limits the distance of the teleportation. While logically equivalent, deferring the measurement have physical implications.

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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.{{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}}{{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}}

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.