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Mean

As explained in Quantum Programming in Depth

The mean is the equal-superposition quantum state over all basis states in a specified search space.

The mean is the equal-superposition quantum state over every basis state in a specified search space: |mean⟩ = (1/√N) Σₓ |x⟩. Each of the N states has the same amplitude. section 7.2.1

Use the mean to represent:

  • An unrestricted n-qubit search space, where N = 2ⁿ and every possible bit string is included. section 7.2.1
  • A structured search space containing only bit strings that could be solutions, potentially reducing its size and simplifying oracle implementation. section 7.2.1

How Quantum Programming in Depth covers it

How deep it goes
Defines the normalized state mathematically and relates it to unrestricted and structured search spaces, without detailing its circuit implementation.
Examples
Uses all n-qubit basis states, structured search spaces, and the partition into solution and non-solution states.
What you can do after
Understand how Grover’s algorithm models and transforms a search space through its mean state.
How it connects
Connects equal superposition with basis states, Grover’s algorithm, quantum oracles, and solution and non-solution states.
Cover of Quantum Programming in Depth
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This explainer was generated by Manning's knowledge graph from the text of Quantum Programming in Depth. The section links point to the parts of the book it draws on.