What is Quantum superposition?

The ability of a quantum system such as a qubit to be in a state formed by adding several states, such as |0⟩ and |1⟩, with complex amplitudes. A measurement gives one of the outcomes at random, and differences in the phases of the amplitudes affect the results through interference.

Japanese name: 量子重ね合わせ

Quantum superposition appears in 10 practice questions across 1 topic, including Quantum Computing Hardware.

Field: Quantum Computing Hardware

Try it: questions about Quantum superposition

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?

  1. A25 ns
  2. B50 ns
  3. C100 ns
Show answer and explanation

Answer: A. 25 ns

Under continuous microwave driving, the probability of being in |1⟩ oscillates as sin²(Ωt/2) with Ω = 2π × 10 MHz, and the period of one round trip is 1 ÷ 10 MHz = 100 ns. The rotation angle Ωt reaches π/2 at t = 25 ns, when the probability of being in |1⟩ is 50%. A rotation angle of π (50 ns) is an X gate (π pulse) that swaps |0⟩ and |1⟩, and 2π (100 ns) returns the qubit to |0⟩. The rotation angle is set by the pulse amplitude and length, so errors in the microwave amplitude or timing translate directly into gate errors.

Quantum superposition in the explanations

Questions that mention Quantum superposition (10)

  1. 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?
  2. Which statement about a qubit is correct?
  3. How many probability amplitudes (complex numbers) are needed to describe a general state of a system of 10 qubits?
  4. Two qubits are in the entangled state (|00⟩ + |11⟩)/√2. Which statement is correct?
  5. Which correctly describes what a single-qubit X gate does?
  6. A qubit in the state |0⟩ has a Hadamard (H) gate applied once and is then measured. What is the probability of getting 1?
  7. 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?
  8. Why can't quantum error correction directly use the classical approach of making three copies of the data and taking a majority vote?
  9. Which correctly describes the energy relaxation time T1 of a qubit?
  10. Which correctly describes the relationship between the dephasing time T2 and the energy relaxation time T1 of a qubit?

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Related terms

Qubit Quantum entanglement Quantum error correction Time constant Decoherence Dilution refrigerator Ion trap Josephson junction NISQ Post-quantum cryptography

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