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Quantum Computer

01 /Quantum Computers 02 /How to build a qubit 03 /Spin qubits (beginner level) 04 /Operations on spin qubits (beginner level) 05 /Electron spin qubits 06 /Capturing a single electron 07 /Quantum dot qubits 08 /Quantum control and readout 09 /Qubit errors 10 /NV center qubits 11 /Operations on NV center qubits 12 /The Transmon Qubit - A basis for the Quantum Computer 13 /Operations on the Transmon Qubit - Circuit QED 14 /Single-qubit operations on the Transmon qubit 15 /Measurements on the Transmon Qubit 16 /Two-qubit operations on the Transmon qubit 17 /Topological qubits: Anyons 18 /Operations on anyons: Braiding 19 /Operations on anyons: Real-life experiments 20 /Topological quantum computing: Majorana fermions and where to find them 21 /Majorana bound states in superconductors 22 /How do you measure Majorana bound states? 23 /A framework for the future Quantum Computer 24 /The Building Blocks of a Quantum Computer 25 /How to build a Quantum Algorithm - Quantum Circuits 26 /How do you program a quantum algorithm? 27 /The compiler of a quantum computer 28 /Micro-architectures 29 /How do we connect our quantum system to a classical interface? 30 /Assembling a Quantum Processor 31 /Microwave drivers for qubits 32 /Implementation of microwave drivers 33 /Quantum error correction 34 /Surface codes 35 /Fault-tolerant Quantum Error Correction with surface codes

How to build a Quantum Algorithm - Quantum Circuits

Introduction

One of the important tasks of a quantum compiler is to identify operations in some abstract quantum algorithm. The compiler then replaces them with sequences of operations which have the same effect on the qubits' states, and are composed of operations which can be executed 'on-chip.' But how do we know how to make such transformations? As usual, we will base our strategy on the operations in a classical computer. 

In this video, postdoctoral researcher Ben Criger will go over the standard mathematical techniques which allow us to express and manipulate quantum circuits. Furthermore, he will discuss methods for proving the equivalence of two circuits. We will see that if the circuits under consideration are small, you can often see this very quickly. However, as the circuits become larger, more technical methods are used to reduce the amount of mathematics to something we can handle.

Prerequisite knowledge

Further Thinking 

Consider the following circuits:

Which of the circuits above do you think performs a SWAP operation? (multiple answers might be correct)

Solution

Further reading