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Quantum Computing Hardware

Which correctly describes the relationship between the dephasing time T2 and the energy relaxation time T1 of a qubit?

  1. AT2 is set independently of T1 and is often more than 100 times T1
  2. BT2 is equal to T1 for every qubit
  3. CT2 does not exceed 2T1
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Answer: C. T2 does not exceed 2T1

T2 is the time until the information on the relative phase of a superposition α|0⟩ + β|1⟩ is lost. Energy relaxation also destroys phase information, so 1/T2 = 1/(2T1) + 1/Tφ, where Tφ is the pure dephasing time due to frequency fluctuations and similar causes, and therefore T2 ≤ 2T1. For example, with T1 = 100 µs and Tφ = 150 µs, T2 is about 86 µs. In real qubits, frequency fluctuations caused by flux or charge noise often make T2 considerably shorter than 2T1.

  • A. Energy relaxation also destroys phase information, so T2 never exceeds 2T1.
  • B. Without pure dephasing T2 = 2T1, and with it T2 is shorter than 2T1; it is not necessarily equal to T1.
  • C. Correct. Since 1/T2 = 1/(2T1) + 1/Tφ, T2 ≤ 2T1.
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