A Modular Framework for Generic Quantum Algorithms

Abstract

We describe a general-purpose framework to design quantum algorithms. This framework relies on two pillars: a basic data structure called quantum matrix and a modular structure based on three quasi-independent modules. These latter include a loading module, a tool-kit of basic quantum arithmetic operations and a read-out module. We briefly discuss the loading and read-out modules, while the arithmetic module is analyzed in more depth. Eventually, we give explicit examples regarding the manipulation of generic oracles and hint at possible applications.

Real quantum amplitude estimation

“…In particular, RQAE utilizes a set of auxiliary amplitudes which allow to shift in a controlled fashion the amplitude to be retrieved. Such shift can be easily and efficiently implemented following the methods presented in [18]. Relying on this, we propose a specific strategy to iteratively choose the amplification factor k (i.e.…”

“…We give an example on how to build such a shifted oracle in Appendix B. In particular, its implementation is straightforward in the framework described in [18].…”

Real Quantum Amplitude Estimation

“…We give an example on how to build such a shifted oracle in Appendix B. In particular, its implementation is straightforward in the framework described in [Man+22].…”

“…The sign of b 1 has to be decided at the start of the algorithm to have a clear reference. In practice, in some setups it is possible to measure at the same time both states taking advantages of Hadamard gates as in the quantum arithmetic techniques discussed in [Man+22] (more details are given in Appendix B). As a and b 1 are real numbers, we have the identity:…”

“…In particular, RQAE utilizes a set of auxiliary amplitudes which allow to shift in a controlled fashion the amplitude to be retrieved. Such shift can be easily and efficiently implemented following the methods presented in [Man+22]. Relying on this, we propose a specific strategy to iteratively choose the amplification factor k (i.e.…”