“Hadamard test (quantum computation)”的意思、由来-开放百科全书

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Hadamard test (quantum computation)

释义

In quantum computation the Hadamard test is a method used to create a random variable whose expected value is the expected real part of the observed value of a state with respect to some unitary operator.

Let be a state which can be efficiently generated, and let be a unitary gate. The Hadamard test produces a random variable whose image is in and whose expected value is exactly . A variant of the test produces a random variable whose expected value is .

To perform the Hadamard test we first calculate the state . We then apply the unitary operator on conditioned on the first qubit to obtain the state . We then apply the Hadamard gate to the first qubit, yielding .

Measuring the first qubit, the result is with probability , in which case we output . The result is with probability , in which case we output . The expected value of the output will then be the difference between the two probabilities, which is

To obtain a random variable whose expectation is follow the exact same procedure but start with .

The Hadamard test has many applications in quantum algorithms such as the Aharonov-Jones-Landau algorithm.

1 : Quantum computing

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