Quantum Phase Estimation

Vamsi Parasa, Marek A. Perkowski

This papers presents the generalization of the quantum phase estimation (QPE) algorithm to multivalued logic. QPE is a very important subroutine used in many quantum algorithms of practical importance. The QPE using qudits has certain advantages when compared to the version using qubits. The QPE using qudits is more accurate and requires lesser number of qudits (as the value of the radix d increases) to estimate the phase up to a given accuracy with a given success probability. Since the existing quantum computer implementations use only few qubits, it is important to have alternative versions of the QPE which use as few qubits as possible. In this regard, the iterative quantum phase estimation algorithm (IQPE) which uses only single qubit to store the phase information has been developed. The number of iterations involved in the IQPE is directly proportional to the required accuracy in the estimated phase. In this regard, IQPE using qudits requires (logarithmically) lesser number of iterations (and hence is faster) compared to the one using qubits. In this paper, we also develop the multivalued logic version of the IQPE and describe its implementation.

Hiu Yung Wong

Nicholas J. C. Papadopoulos, J. Reilly, John Drew Wilson +1 more

Estimating a quantum phase is a necessary task in a wide range of fields of quantum science. To accomplish this task, two well-known methods have been developed in distinct contexts, namely, Ramsey interferometry (RI) in atomic and molecular physics and quantum phase estimation (QPE) in quantum computing. We demonstrate that these canonical examples are instances of a larger class of phase estimation protocols, which we call reductive quantum phase estimation (RQPE) circuits. Here, we present an explicit algorithm that allows one to create an RQPE circuit. This circuit distinguishes an arbitrary set of phases with a smaller number of qubits and unitary applications, thereby solving a general class of quantum hypothesis testing to which RI and QPE belong. We further demonstrate a tradeoff between measurement precision and phase distinguishability, which allows one to tune the circuit to be optimal for a specific application. Published by the American Physical Society 2024

Hiu Yung Wong

Jincheng Zhang

Quantum phase estimation (QPE) is a fundamental technique for determining the phase of a quantum state, crucial for various quantum algorithms and quantum measurements. This paper introduces a novel adaptive optimization algorithm, dubbed the "Adaptive Quantum Phase Estimation" (AQPE) algorithm, designed to enhance the efficiency of QPE by dynamically adjusting parameters during the state estimation process. We demonstrate the effectiveness of AQPE through rigorous theoretical analysis and extensive numerical simulations, achieving significantly improved convergence rates compared to traditional optimization techniques. The algorithm leverages a feedback mechanism based on the observed phase error during the estimation, allowing it to iteratively refine the parameter set and ultimately locate the optimal phase estimation. We present preliminary results demonstrating the algorithm's capability to mitigate the challenges associated with conventional QPE, particularly in the presence of noisy data. The implications of this research extend to broader advancements in quantum algorithm design and computational power.

Ugo Marzolino