Quantum Algorithm Implementations for Beginners

Abstract

As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims to explain the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM’s quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations.

Quantum Program Synthesis Through Operator Learning and Selection

“…If multiple arrangements implement the same target, we choose to learn those with minimal costs. The following subsection (Section III-C) describes details on how we realize the two 1 The machine-learning model can be various models, and we demonstrate the use of neural networks in the evaluation (Section IV.A).…”

“…As such, a qubit is represented with a vector of two complex numbers (, ), as in notation 1 in Table II; their amplitudes indicate the probabilities of the qubit measured as 0 and 1, respectively, such that || 2 + || 2 = 1; the ratio between real and imaginary parts determines the phases. For example, (1,0) indicates that the qubit is 0 for sure, and (0, 1) indicates that it is definitely 1, both demonstrating zero phases. Another example (1/√2, −1/√2) indicates equal probabilities of being 0 and 1 with phases 0 and , respectively.…”

“…q [1] targets, but the resulting programs tend to use numerous stages and operators, exponentially proportional to the number of qubits [9]. Furthermore, to explore a different operator set, the rules must to be adjusted considering the peculiarities of the new operators; this adjustment takes time and effort even by experts.…”

“…Fig. 3 shows the input/output of this model and its utilization 1 . We aim to train the model, such that when it receives a target function as a matrix in phase 2, it produces a vector of probabilities p1 to pNoperator, one for each operator.…”

“…Quantum computers have been shown to perform certain operations faster than classical computers, including factorization, database search, and simulation [1]. As such, the two types of computers are expected to work together, enabling speedy processing of huge data [2].…”