Quantum Computing Hardware
When the state of a single qubit is represented on the Bloch sphere, what state does a point on the equator represent?
- AA superposition that gives 0 and 1 with 50% probability each when measured; the position on the equator (the longitude) represents the relative phase between |0⟩ and |1⟩
- BThe state |0⟩, which always gives 0 when measured; every point on the equator represents the same state
- CA state that has lost its energy and can no longer be used as a qubit
Show answer and explanation
Answer: A. A superposition that gives 0 and 1 with 50% probability each when measured; the position on the equator (the longitude) represents the relative phase between |0⟩ and |1⟩
The Bloch sphere represents a single-qubit state cos(θ/2)|0⟩ + e^{iφ} sin(θ/2)|1⟩ as a point on a sphere, with the angle θ playing the role of latitude and φ that of longitude. The north pole is |0⟩ and the south pole is |1⟩; on the equator (θ = 90°) the amplitudes of |0⟩ and |1⟩ have equal magnitude, so a measurement gives 0 and 1 with 50% probability each. Points on the equator differ in the relative phase φ: (|0⟩ + |1⟩)/√2 and (|0⟩ − |1⟩)/√2 have the same measurement probabilities but are different states. Quantum gate operations can be represented as rotations of this sphere.
- A. Correct. On the equator the probabilities of 0 and 1 are equal, and a different longitude means a different relative phase.
- B. |0⟩ is a single point, the north pole. Points on the equator are superpositions in which the amplitudes of |0⟩ and |1⟩ have equal magnitude.
- C. Every point on the surface is a valid qubit state. Losing energy moves the state toward |0⟩ at the north pole, and losing phase information moves it into the interior of the sphere.