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Quantum Computing Hardware

How many probability amplitudes (complex numbers) are needed to describe a general state of a system of 10 qubits?

  1. A10
  2. B100
  3. C1,024
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Answer: C. 1,024

The state of n qubits is a superposition of the 2ⁿ basis states from |00…0⟩ to |11…1⟩, each with its own probability amplitude. For 10 qubits that is 2 to the power of 10, or 1,024. Each additional qubit doubles the number of amplitudes, so 50 qubits need about 10¹⁵. However, a measurement yields only a single string of n zeros and ones, and the amplitudes cannot all be read out.

  • A. This is just the number of qubits. Describing a superposition requires one amplitude per basis state.
  • B. This is 10 squared. The number of amplitudes grows as a power of 2, not as the square of the number of qubits.
  • C. Correct. Each of the 2 to the power of 10 = 1,024 basis states has an amplitude.
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More Quantum Computing Hardware questions

  1. 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?
  2. Two qubits are in the entangled state (|00⟩ + |11⟩)/√2. Which statement is correct?
  3. Which correctly describes what a single-qubit X gate does?
  4. A qubit in the state |0⟩ has a Hadamard (H) gate applied once and is then measured. What is the probability of getting 1?
  5. 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?