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

• URL: http://arxiv.org/abs/2502.15928v1
• Date: Fri, 21 Feb 2025 20:52:16 GMT
• Title: EHands: Quantum Protocol for Polynomial Computation on Real-Valued Encoded States
• Authors: Jan Balewski, Mercy G. Amankwah, E. Wes Bethel, Talita Perciano, Roel Van Beeumen,
• Abstract summary: EHands protocol defines a universal set of quantum operations for multivariable transformations on quantum processors.<n>We present a detailed implementation of $P_(x)$ using IBM's Heron-class quantum processors and an ideal Qiskit simulator.
• Score: 0.18641315013048299
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The novel constructive EHands protocol defines a universal set of quantum operations for multivariable polynomial transformations on quantum processors by introducing four basic subcircuits: multiplication, addition, negation, and parity flip, and by using expectation-value encoding (EVEN) to represent real numbers in quantum states. These elementary arithmetic operations can be systematically composed to compute degree-$d$ polynomials, $P_d(x)$, on a QPU. The resulting quantum circuit structure closely mirrors the stepwise evaluation of polynomials on a classical calculator, providing an intuitive and efficient approach to polynomial computation on quantum hardware. By enabling direct, predictable polynomial and nonlinear data transformations on a QPU, our method reduces dependence on classical post-processing in hybrid quantum-classical algorithms, enabling advancements in many quantum algorithms. The EHands quantum circuits are compact enough to deliver meaningful and accurate results on today's noisy quantum processors. We present a detailed implementation of $P_4(x)$ and report experimental results for polynomial approximations of common functions, obtained using IBM's Heron-class quantum processors and an ideal Qiskit simulator.

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