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Bennett’s trick

As explained in Quantum Programming in Depth

Bennett’s trick is a reversible computation technique that copies an output to a separate register and then runs the computation backward to reset intermediate qubits.

Bennett’s trick disentangles auxiliary qubits in a reversible computation without measuring them. It copies the computed basis-state output into a separate register, then runs the original computation backward to reset its intermediate qubits. section 6.5.1

For an input encoded as |x⟩ and an existing output register |y⟩:

  • Initialize input, auxiliary, and temporary output registers as |x⟩, |0⟩, and |0⟩, with the final output in |y⟩. section 6.5.1
  • Use CNOT gates to copy the basis-state output into the final register, changing it to |y ⊕ f(x)⟩. section 6.5.1
  • Apply the computation backward, returning the auxiliary and temporary output registers to |0⟩. section 6.5.1

Measuring only the auxiliary qubits can collapse part of a superposition and discard input basis states. Bennett’s trick preserves the full superposition; its copying step copies basis states, not an arbitrary quantum state. section 6.5.1

How Quantum Programming in Depth covers it

How deep it goes
Derives a four-register sequence through computation, basis-state copying, and reverse execution.
Examples
Uses input, auxiliary, temporary-output, and final-output registers with states |x⟩, |0⟩, |0⟩, and |y⟩.
What it assumes
Assumes basis-state registers, superposition measurement, CNOT copying, and reversible computation.
What you can do after
Build reversible function evaluations that return intermediate qubits to |0⟩ without measuring them.
How it connects
Connects reversible computation with quantum measurement, entanglement, CNOT gates, and the no-cloning theorem.
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Related concepts

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