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A qubit is in state [y) : Vo|0) +11) at time t = 0. It then evolves according to the Schrodinger quation with the Hamiltonian Ĥ defined by its action on the basis vectors: Ĥ|0) = 0|0) and 7|1) = E|1), where E is a constant with units of energy. ) Solve for the state of the qubit at time t. >) Find the probability to observe the qubit in state 0 at time t. Explain the result by referring o the way that the time-evolution transforms the Bloch sphere.

A qubit is in state [y) : Vo|0) +11) at time t = 0. It then evolves according to the Schrodinger quation with the Hamiltonian Ĥ defined by its action on the basis vectors: Ĥ|0) = 0|0) and 7|1) = E|1), where E is a constant with units of energy. ) Solve for the state of the qubit at time t. >) Find the probability to observe the qubit in state 0 at time t. Explain the result by referring o the way that the time-evolution transforms the Bloch sphere.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A qubit is in state |) = o|0) +₁|1) at time t = 0. It then evolves according to the Schrödinger equation with the Hamiltonian Ĥ defined by its action on the basis vectors: Ĥ0) = 0|0) and Ĥ|1) = E|1), where E is a constant with units of energy. a) Solve for the state of the qubit at time t. b) Find the probability to observe the qubit in state 0 at time t. Explain the result by referring to the way that the time-evolution transforms the Bloch sphere.
Transcribed Image Text:A qubit is in state |) = o|0) +₁|1) at time t = 0. It then evolves according to the Schrödinger equation with the Hamiltonian Ĥ defined by its action on the basis vectors: Ĥ0) = 0|0) and Ĥ|1) = E|1), where E is a constant with units of energy. a) Solve for the state of the qubit at time t. b) Find the probability to observe the qubit in state 0 at time t. Explain the result by referring to the way that the time-evolution transforms the Bloch sphere.
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