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Quantum Computing Hardware

Learn quantum computing hardware with multiple-choice questions: qubit superposition and measurement, entanglement, calculations with quantum gates such as X, H, Z and CNOT, T1, T2 and gate fidelity, quantum error correction and the surface code, the superconducting (transmon), trapped-ion, neutral-atom, silicon spin and photonic platforms, and dilution refrigerators and control and readout electronics. Shor's algorithm and post-quantum cryptography are also covered.

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Quantum Computing Hardware: key points

A quantum computer computes using superpositions of 0 and 1 and quantum entanglement. Its performance is not set by the number of qubits alone, but by gate error rates, how long quantum states can be kept (the coherence time), how the qubits are connected, and how many qubits can be devoted to quantum error correction.

After checking qubit states, measurement probabilities and the effect of quantum gates with small calculations, this topic covers T1, T2 and fidelity and the ideas of the surface code and its threshold. It then turns to the hardware challenges of scaling up: the strengths and weaknesses of superconducting qubits based on Josephson junctions, trapped ions, neutral atoms, silicon spin qubits that can draw on CMOS fabrication, and photonic qubits; dilution refrigerators that cool to about 10 mK; microwave control and dispersive readout; and cryo-CMOS and the heat load of wiring. Why Shor's algorithm threatens public-key cryptography, and post-quantum cryptography as the response, are also covered in relation to the scale of hardware they require.

All Quantum Computing Hardware questions (40)
  1. Which statement about a qubit is correct?
  2. A qubit is in the state (√3/2)|0⟩ + (1/2)|1⟩. What is the probability of getting 1 when it is measured?
  3. When the state of a single qubit is represented on the Bloch sphere, what state does a point on the equator represent?
  4. How many probability amplitudes (complex numbers) are needed to describe a general state of a system of 10 qubits?
  5. The state vector (all the probability amplitudes) of 50 qubits is stored in the memory of a classical computer as double-precision complex numbers of 16 bytes each. Which is closest to the memory required?
  6. Two qubits are in the entangled state (|00⟩ + |11⟩)/√2. Which statement is correct?
  7. Which correctly describes what a single-qubit X gate does?
  8. A qubit in the state |0⟩ has a Hadamard (H) gate applied once and is then measured. What is the probability of getting 1?
  9. Starting from the two-qubit state |00⟩ (the left digit is the first qubit), an H gate is applied to the first qubit, followed by a CNOT gate with the first qubit as control and the second as target. What is the resulting state?
  10. Gates H, Z and H are applied in that order to a qubit in |0⟩, which is then measured. What is the probability of getting 1?
  11. Why can't quantum error correction directly use the classical approach of making three copies of the data and taking a majority vote?
  12. Which correctly describes the energy relaxation time T1 of a qubit?
  13. Which correctly describes the relationship between the dephasing time T2 and the energy relaxation time T1 of a qubit?
  14. 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?
  15. Which is the most appropriate reason why the performance of quantum computers cannot be compared by their number of qubits alone?
  16. Which element is essential for a superconducting qubit (transmon) to work as a qubit?
  17. What is the main reason superconducting qubits are cooled to about 10–20 mK in a dilution refrigerator?
  18. 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.
  19. 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)?
  20. 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?
  21. 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?
  22. 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?
  23. Which correctly describes dispersive readout, which is widely used to read out superconducting qubits?
  24. What is the main purpose of frequency multiplexing in the readout of superconducting qubits, where several readout resonators with different frequencies are connected to a single transmission line?
  25. Which is closest to the minimum power required by the Carnot limit to pump 1 µW of heat out of a 10 mK stage and reject it at 300 K?
  26. Which correctly describes a change in MOSFET characteristics at low temperature that must be considered when designing cryo-CMOS circuits that run qubit control electronics at about 4 K?
  27. Which correctly describes a trapped-ion quantum computer?
  28. Which is the most appropriate comparison of superconducting and trapped-ion platforms?
  29. Which correctly describes a neutral-atom quantum computer?
  30. What is the main reason silicon spin qubits are expected to suit large-scale systems?
  31. Why is silicon enriched in the isotope ²⁸Si (isotopically purified silicon) used for silicon spin qubits?
  32. Which correctly describes photonic quantum computing, which uses photons as qubits?
  33. A rotated surface code of code distance d uses, for one logical qubit, d² physical data qubits and d² − 1 physical measurement qubits that check for errors. For d = 15, how many physical qubits does one logical qubit need?
  34. Suppose the logical error rate p_L of a surface code can be approximated as p_L ∝ (p/p_th)^((d+1)/2), using the physical error rate p, the threshold p_th and the code distance d. With p = 0.1% and p_th = 1%, which is closest to the ratio of logical error rates when d is increased from 5 to 9 (the value at d = 5 divided by the value at d = 9)?
  35. Which correctly describes the kind of quantum computer called NISQ?
  36. When searching 1 million items in no particular order for the one item that meets a condition, which is closest to the order of the number of queries (oracle calls) needed by Grover's algorithm?
  37. Once large fault-tolerant quantum computers are built, which ciphers are expected to have their security seriously undermined by Shor's algorithm?
  38. Which is the most appropriate main reason why quantum computers as of the mid-2020s cannot break RSA-2048 with Shor's algorithm?
  39. Which correctly describes post-quantum cryptography (PQC)?
  40. Which is the most appropriate reason to hurry the migration to post-quantum cryptography even before large quantum computers exist?

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