English
Menu

Quantum Computing Hardware

A circuit uses a two-qubit gate with a fidelity of 99.5% per operation (an error rate of 0.5%) 100 times in a row. Assuming errors occur independently, which is closest to the probability that no error occurs at all?

  1. AAbout 37%
  2. BAbout 61%
  3. CAbout 99.5%
Show answer and explanation

Answer: B. About 61%

The probability of no error in each operation is 0.995, so the probability of no error in 100 operations in a row is 0.995 to the power of 100, about 0.61, or about 61%. Even with an error rate as small as 0.5%, the success rate drops quickly as the circuit gets deeper: for 1,000 operations it is about 0.7%. This is why the depth of circuit that a device without error correction can run is roughly set by its gate error rate. Real errors are not necessarily independent, and measurement and idle errors add to them, so this is a rough estimate.

  • A. This is the value for an error rate of 1% (0.99 to the power of 100 ≈ 0.37).
  • B. Correct. 0.995 to the power of 100 ≈ 0.61.
  • C. This takes the fidelity of a single operation as the success rate of the whole circuit.
Practice this topic Back to topic

Books on Quantum Computing Hardware Ad

As an Amazon Associate I earn from qualifying purchases.

More Quantum Computing Hardware questions

  1. Which is the most appropriate reason why the performance of quantum computers cannot be compared by their number of qubits alone?
  2. Which element is essential for a superconducting qubit (transmon) to work as a qubit?
  3. What is the main reason superconducting qubits are cooled to about 10–20 mK in a dilution refrigerator?
  4. 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.
  5. 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)?