Quantum Algorithms for Arithmetic and Function Composition

Abstract

Quantum circuits and associated methods use repeat until success (RUS) circuits to perform approximate multiplication and approximate squaring on input values ​​provided as rotations encoded on auxiliary qubits. So-called gearboxes and programmable auxiliary circuits are coupled to encode even or odd outcomes of input values ​​as rotations of the target qubits. In other examples, a quantum RUS circuit provides a target qubit rotation associated with an inverse expressed using a series expansion.

Description

Background technique [0001] Quantum computers promise dramatic speedups for a host of important problems such as factorization, quantum simulations, and optimization. Although quantum properties have proven to be a powerful resource for these algorithms, the basis of many of these algorithms is usually reduced to classical reversible logic with Hadamard gates. This is especially true for algorithms such as the quantum linear system algorithm, which promise exponential speedups but depend strongly on implementing classical arithmetic. For practical inversion problems, hundreds of auxiliary (ancilla) qubits may be required to implement the arithmetic operations required to reversibly perform arithmetic. In general, quantum implementations of arithmetic operations using reversible circuits are implemented by Kitaev in "Quantum computations: algorithms and error correction," Russian Math. Surveys 52: 1191-1249 (1998), and Cleve et al. in "Quantum algorithms revisited," Proc. The...

AI Technical Summary

Problems solved by technology

Unfortunately, methods based on classical algorithms and phase recoil require many qubits, so alternatives are needed

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