The authors define the QA-KS(φ) gate family embedding Toffoli with Hadamard sandwich and CP kickback, provide its exact 8x8 unitary, and demonstrate orthogonality to CCX on q0=1 inputs while agreeing on q0=0.
Exponentially cheaper coherent phase estimation via uncontrolled unitaries
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abstract
Phase kickback is a fundamental primitive that is used in many quantum algorithms, such as quantum phase estimation. Here we observe that by using information about the controlled unitary, we can replace the controlled unitary with an uncontrolled one at the cost of introducing controlled state preparations. We then show how this modified phase kickback can be used as part of the quantum phase estimation algorithm when the goal is to estimate the phase of an eigenstate whose preparation procedure is known. We prove that this yields an exponential reduction in the number of two-qubit gates for an m-bit phase estimation in the relevant limit. Examples of applications are also presented. Naturally, this can be adapted to any algorithm that uses the phase kickback phenomenon and satisfies the assumptions.
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quant-ph 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Quantum-Adaptive KS($\varphi$): A Parameterized Three-Qubit Gate Family Embedding Toffoli with Measurement-Free Phase Kickback and Intrinsic Error Non-Amplification
The authors define the QA-KS(φ) gate family embedding Toffoli with Hadamard sandwich and CP kickback, provide its exact 8x8 unitary, and demonstrate orthogonality to CCX on q0=1 inputs while agreeing on q0=0.