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What is the main reason superconducting qubits are cooled to about 10–20 mK in a dilution refrigerator?

  1. ATo make the wiring and junctions superconducting and to make thermal excitation of the qubits and thermal noise sufficiently small
  2. BBecause cooling widens the band gap of silicon and raises the qubit frequency
  3. CBecause electron mobility rises at low temperature, making gate operations 1,000 times faster than at room temperature
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Answer: A. To make the wiring and junctions superconducting and to make thermal excitation of the qubits and thermal noise sufficiently small

The aluminum used in transmons becomes superconducting below about 1.2 K, eliminating resistive losses. In addition, the energy hf of a qubit at a frequency of about 5 GHz corresponds to a temperature of about 0.24 K, so unless the thermal energy kT is made much smaller than this, the qubit is thermally excited to |1⟩ and thermal noise enters through the wiring. Liquid helium temperature, about 4 K, is therefore not enough, and the qubits are cooled to about 10 mK with a dilution refrigerator that uses a mixture of helium-3 and helium-4. Qubit speed is not set by mobility, and superconducting qubits do not use the band gap of silicon.

  • A. Correct. The purpose is to keep the circuit superconducting and make the thermal energy kT much smaller than the qubit energy hf.
  • B. Superconducting qubits do not use the band gap of silicon. Their frequency is set by the circuit parameters of the junction and capacitor.
  • C. The purpose of cooling is not speed but superconductivity and the suppression of thermal excitation and noise.
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More Quantum Computing Hardware questions

  1. For a superconducting qubit with a frequency of 5 GHz, which is closest to the energy difference hf between |0⟩ and |1⟩ expressed as a temperature, hf/k_B? Use Planck's constant h = 6.63×10⁻³⁴ J·s and Boltzmann's constant k_B = 1.38×10⁻²³ J/K.
  2. A qubit with a frequency of 5 GHz (hf/k_B ≈ 0.24 K) is in thermal equilibrium at an effective temperature of 50 mK. Which is closest to the ratio of the probabilities of being in |1⟩ and in |0⟩, exp(−hf/k_B T)?
  3. In a transmon, the frequency of the |0⟩→|1⟩ transition is 5.0 GHz and the anharmonicity (the |1⟩→|2⟩ frequency minus the |0⟩→|1⟩ frequency) is −200 MHz. What is the frequency of the |1⟩→|2⟩ transition?
  4. Among the factors that limit the energy relaxation time T1 of superconducting qubits, which is most closely related to fabrication processes such as thin-film deposition and surface treatment?
  5. A qubit is rotated with microwave pulses tuned to its resonance frequency, and the Rabi frequency (the frequency of one round trip between |0⟩ and |1⟩) is 10 MHz. What is the length of the π/2 pulse that takes |0⟩ to a superposition in which the amplitudes of |0⟩ and |1⟩ have equal magnitude?