EHands: Quantum Protocol for Polynomial Computation on Real-Valued Encoded States

• URL: http://arxiv.org/abs/2502.15928v2
• Date: Mon, 06 Oct 2025 15:53:05 GMT
• Title: EHands: Quantum Protocol for Polynomial Computation on Real-Valued Encoded States
• Authors: Jan Balewski, C. Pestano, Mercy G. Amankwah, E. Wes Bethel, Talita Perciano, Roel Van Beeumen,
• Abstract summary: We present EHands, a quantum-native protocol for implementing multivariable transformations on quantum processors.<n>EHands operates directly on vectorized real-valued inputs prepared in the initial state.<n>The protocol's effectiveness is demonstrated through experimental validation on IBM's Heron-class quantum processors.
• Score: 0.08209843760716957
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present EHands, a quantum-native protocol for implementing multivariable polynomial transformations on quantum processors. The protocol introduces four fundamental, reversible operators: multiplication, addition, negation, and parity flip, and employs the Expectation Value ENcoding (EVEN) scheme to represent real numbers as quantum states. Unlike discretization or binary encoding methods, EHands operates directly on vectorized real-valued inputs prepared in the initial state and applies a shallow quantum circuit that depends only on the polynomial coefficients. The result is obtained from the expectation value measured on a single qubit, enabling efficient parallel evaluation of a polynomial across multiple data points using a single circuit. We introduce both a reversible implementation for degree-$d$ polynomials, requiring $3d$ qubits, and a non-reversible variant that uses qubit resets to reduce the requirements to $d+1$ qubits. Both implementations exhibit linear depth scaling in $d$ and are explicitly decomposed into one- and two-qubit gates for direct execution on current quantum processing units. The protocol's effectiveness is demonstrated through experimental validation on IBM's Heron-class quantum processors, showing reliable polynomial approximations of functions like ReLU and arctan.

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