{ "cells": [ { "cell_type": "markdown", "source": [ "# MBQC Quick Start Guide\n", "\n", " Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. " ], "metadata": { "tags": [] } }, { "cell_type": "markdown", "source": [ "## Introduction\n", "\n", "Quantum computation utilizes the peculiar laws in the quantum world and provides us with a novel and promising way of information processing. The essence of quantum computation is to evolve the initially prepared quantum state into another expected one, and then make measurements on it to obtain the required classical results. However, the approaches of quantum state evolution are varied in different computation models. The widely used **quantum circuit model** [1,2] completes the evolution by performing quantum gate operations, which can be regarded as a quantum analog of the classical computing model. In contrast, **measurement-based quantum computation (MBQC)** provides a completely different approach for quantum computing.\n", "\n", "As its name suggests, the entire evolution in MBQC is completed via quantum measurements. There are mainly two variants of measurement-based quantum computation in the literature: **teleportation-based quantum computing (TQC)** model[3-5] and **one-way quantum computer (1WQC)** model [6-9]. The former requires joint measurements on multiple qubits, while the latter only requires single-qubit measurements. After these two variants were proposed, they were proved to be highly correlated and admit a one-to-one correspondence [10]. So without further declaration, **all of the following discussions about MBQC will refer to the 1WQC model.**\n", "\n", "MBQC is a unique model in quantum computation and has no classical analog. The model controls the computation by measuring part of the qubits of an entangled state, with those remaining unmeasured undergoing the evolution correspondingly. By controlling measurements, we can complete any desired evolution. The computation in MBQC is mainly divided into three steps. The first step is to prepare a resource state, which is a highly entangled many-body quantum state. This state can be prepared offline and can be independent of specific computational tasks. The second step is to sequentially perform single-qubit measurements on each qubit of the prepared resource state, where subsequent measurements can depend on previous measurement outcomes, that is, measurements can be adaptive. The third step is to perform byproduct corrections on the final state. Finally, we do classical data processing on measurement outcomes to obtain the required computation results. \n", "\n", "A typical example of MBQC algorithms is shown in Figure 1. The grid represents a commonly used quantum resource state (called cluster state, see below for details). Each vertex on the grid represents a qubit, while the entire grid represents a highly entangled quantum state. We measure each qubit one by one in a specific measurement basis (In the vertices, X, Y, Z, XY, etc. represent the corresponding measurement basis), and then perform byproduct corrections (to eliminate the effect of Pauli X and Pauli Z operators), to complete the computation.\n", "\n", "![MBQC example](./figures/mbqc-fig-general_pattern.jpg)\n", "