The Map of Quantum Computing - Quantum Computing Explained

Summary

This video script offers an insightful exploration into the world of quantum computing, tracing its evolution since the 1980s and highlighting the recent surge in industry growth. It simplifies complex concepts such as superposition, entanglement, and interference, which are fundamental to understanding how quantum computers operate differently from classical ones. The script delves into various quantum computing models, including the gate model, adiabatic quantum computing, and topological quantum computing, each with unique approaches to harnessing qubits. It also discusses the practical challenges of building quantum computers, such as decoherence and scalability, and touches on potential applications in optimization, machine learning, and quantum simulation. The video is sponsored by Qiskit, an educational resource for those eager to learn more about quantum computing.

Takeaways

• 🌟 The quantum computing industry has seen significant growth since the 1980s, with many companies investing heavily in the development of advanced quantum computers.
• 🚀 Quantum computers operate differently from classical computers, leveraging principles like superposition, entanglement, and interference to solve problems that are difficult or impossible for classical computers.
• 📊 Qubits, the fundamental units of quantum information, can exist in multiple states simultaneously, unlike classical bits which are either 0 or 1.
• 🔗 Entanglement is a key quantum phenomenon where qubits become interconnected, affecting the state of the entire system when any single qubit is altered.
• 🌐 Superposition allows qubits to exist in a state that is a combination of 0 and 1, influencing the probability of the output when measured.
• 🔍 Quantum algorithms, such as Shor's algorithm, can solve complex problems like integer factorization more efficiently than classical algorithms, potentially impacting security protocols.
• 🛠 Quantum computers have a wide range of potential applications, including optimization, machine learning, financial modeling, and quantum simulation for material science and drug development.
• 💡 Quantum simulation is highlighted as a particularly promising application, offering exponential speedup over classical computers for simulating quantum systems.
• 🌐 Quantum computing models include the gate model, adiabatic quantum computing, quantum annealing, and topological quantum computing, each with unique approaches to manipulating qubits.
• 🔬 Physical implementations of qubits vary widely, with superconducting qubits, quantum dots, linear optical quantum computing, trapped ion, color centers, and neutral atoms in optical lattices among the leading methods.
• 🔄 The challenges of building quantum computers include decoherence, noise, and scalability, which are being addressed through techniques like quantum error correction and advanced engineering.

Q & A

What is the main focus of the video 'Map of Quantum Computing'?

The video aims to provide a comprehensive overview of different types of quantum computing, how they work, and why there is significant investment in the quantum computing industry.

What are the three fundamental concepts needed to understand how quantum computers work?

The three fundamental concepts are superposition, entanglement, and interference, which are the building blocks of quantum computing.

How do quantum bits, or qubits, differ from classical bits in terms of their states?

While classical bits can only be in one state at a time (0 or 1), qubits can be in a superposition state, allowing them to be in a combination of 0 and 1 states simultaneously.

What is the significance of entanglement in quantum computing?

Entanglement allows qubits to become part of one large quantum state, making them interdependent. Changes to one qubit can affect the probability distribution of the entire system, which is crucial for quantum computing's power.

How does the concept of interference play a role in quantum computing?

Interference, through the constructive and destructive addition of wavefunctions, influences the probabilities of different states in a quantum computer. It is used in quantum algorithms to increase the likelihood of the correct answer and decrease the likelihood of incorrect ones.

What is Shor's algorithm and why is it significant in the field of quantum computing?

Shor's algorithm is a quantum algorithm that can efficiently find the factors of large integers. It is significant because it demonstrated the potential of quantum computing to solve problems considered intractable on classical computers, such as integer factorization, which has implications for cryptography.

What is quantum complexity theory and how does it relate to the efficiency of quantum algorithms?

Quantum complexity theory is a subfield that categorizes algorithms based on their efficiency on quantum computers. It helps in understanding how much harder it is to solve a problem as the problem size increases and classifies problems like factorization into complexity classes, showing which are more efficiently solvable by quantum computers.

What are some potential applications of quantum computers beyond cryptography?

Beyond cryptography, potential applications include quantum simulation for studying chemical reactions or material properties, optimization problems, machine learning, financial modeling, weather forecasting, and climate change research.

What are some of the challenges faced in building a practical quantum computer?

Challenges include decoherence, where information leaks due to interaction with the outside world, noise from various sources that can cause errors, and scalability issues as the number of qubits increases, requiring more complex control and measurement systems.

What is the difference between the gate model and adiabatic quantum computing?

The gate model involves a sequence of quantum gates applied to entangled qubits to perform computations, while adiabatic quantum computing leverages the natural tendency of physical systems to move towards the minimum energy state to solve problems, with the solution being the lowest energy state of the system.

Can you explain the concept of quantum error correction and its importance?

Quantum error correction is a scheme that uses multiple entangled qubits to represent a single noise-free qubit. It is important because it helps create fault-tolerant quantum computers by protecting against decoherence and noise, which are major obstacles in building practical quantum computers.

What are some of the physical implementations of qubits that are being explored in quantum computing?

Some of the physical implementations being explored include superconducting qubits, quantum dot or silicon spin qubits, linear optical quantum computing with photons, trapped ion quantum computers, color center or nitrogen vacancy quantum computers, and neutral atoms in optical lattices.

What is the current state of quantum computers in terms of their ability to solve real-world problems?

As of the video's information, quantum computers have not yet reached the stage where they can consistently solve real-world problems better than classical computers. Current quantum computers are still in the development phase, and much research is focused on overcoming technical challenges and scaling up the technology.

Outlines

00:00

🌟 Introduction to Quantum Computing and Its Growth

The video script introduces the concept of quantum computing, tracing its origins back to 1980 and highlighting the significant growth in the industry over the past decade. It mentions the substantial investments made by numerous companies and startups in the race to develop superior quantum computers. The script aims to provide viewers with a comprehensive understanding of quantum computing, its various types, operational principles, and the reasons behind the substantial interest and investments in the field. The fundamental quantum concepts of superposition, entanglement, and interference are introduced as keys to understanding how quantum computers differ from classical computers, with their ability to exist in multiple states simultaneously due to quantum bits, or qubits, which are the basic units of quantum information.

05:02

📚 Quantum Computing Basics and Algorithms

This paragraph delves deeper into the foundational aspects of quantum computing, explaining the role of qubits and their behavior in contrast to classical bits. It discusses the phenomenon of superposition, where qubits can exist in multiple states, and entanglement, which links qubits in a unified quantum state. The script then explores the concept of interference, which is essential for manipulating the probabilities of qubits' states. The explanation transitions into the discussion of quantum algorithms, particularly Shor's algorithm, which is famous for its potential to efficiently solve the factorization problem, a task that is computationally intensive for classical computers. The video also touches on quantum complexity theory, contrasting the capabilities of classical and quantum computers in solving complex problems, and emphasizes the theoretical potential of quantum computers to tackle problems deemed intractable by classical standards.

10:02

🛡️ Current State of Quantum Computers and Security Implications

The script addresses the current limitations of quantum computing, noting that existing quantum computers are not yet capable of running complex algorithms like Shor's on large numbers. It discusses the need for approximately a million qubits to achieve this, whereas the most advanced quantum computers currently have around 100 qubits. The video also mentions ongoing efforts in developing post-quantum encryption schemes to counteract the potential decryption capabilities of future quantum computers. Additionally, it introduces the concept of quantum cryptography as an alternative security measure. The script acknowledges the theoretical nature of the discussion thus far and indicates a shift towards addressing the practical aspects of building quantum computers in the remainder of the video.

15:05

🛠️ Exploring Quantum Computing Models and Their Implementations

This paragraph provides an overview of the various models and physical implementations involved in quantum computing. It starts by discussing skepticism regarding the feasibility of building large-scale quantum computers due to challenges like decoherence and noise. The script then outlines different models of quantum computing, including the gate model, adiabatic quantum computing, quantum annealing, and topological quantum computing. Each model has its unique approach to manipulating qubits and solving problems. The gate model, for instance, uses a sequence of quantum gates to perform operations on qubits, while adiabatic quantum computing leverages the natural tendency of systems to seek the lowest energy state. Quantum annealing is a variation of this approach, tailored for specific problems like optimization. Lastly, topological quantum computing is highlighted as a highly theoretical model that uses quasi-particles for increased stability. The script emphasizes the diversity of approaches within the field and the ongoing debate about which model will ultimately prove most successful.

20:06

🔬 Challenges in Building Practical Quantum Computers

The script discusses the practical challenges faced in building quantum computers, focusing on issues like decoherence, noise, and scalability. Decoherence occurs when qubits become entangled with the environment, leading to information loss. Noise from external factors such as cosmic rays, radiation, and heat can also disrupt qubits. The need for quantum error correction is highlighted as a strategy to create fault-tolerant quantum computers by using multiple entangled qubits to represent a single noise-free qubit. The scalability challenge is addressed, noting the exponential increase in the complexity of wiring and control mechanisms as the number of qubits grows. The paragraph outlines various physical implementations of qubits, including superconducting circuits, quantum dots, linear optical quantum computing, trapped ions, color centers in diamonds, and neutral atoms in optical lattices, each with its own set of advantages and challenges.

25:10

🌐 Overview of Quantum Computing Approaches and Future Prospects

In the concluding paragraph, the script provides a summary of the main approaches to building quantum computers and acknowledges the uncertainty surrounding which approach will ultimately prevail. It briefly mentions other qubit designs that are not as widely scaled as the ones discussed in detail. The script also teases upcoming content that will explore companies and startups in the quantum computing field, their approaches, and their future roadmaps. Additionally, it provides information about the availability of the 'Map of Quantum Computing' for purchase or digital download and mentions other educational resources available in the store. The video concludes with a note of thanks to Patreon supporters for their valuable contributions to the creation of these informative videos.

Keywords

💡Quantum Computing

Quantum computing refers to the use of quantum-mechanical phenomena, such as superposition and entanglement, to perform computation. Unlike classical computing where bits exist as either 0 or 1, quantum computing uses quantum bits, or qubits, which can exist in multiple states simultaneously. The video discusses the growth and investment in the quantum computing industry and its potential to solve problems that are currently intractable for classical computers.

💡Superposition

Superposition is a fundamental concept in quantum mechanics where a quantum system can exist in multiple states at the same time until it is measured. In the context of quantum computing, superposition allows qubits to represent a combination of 0 and 1, enabling quantum computers to process a vast number of possibilities concurrently. The video uses the analogy of an arrow pointing in various directions in 3D space to illustrate the superposition state of a qubit.

💡Entanglement

Entanglement is a quantum phenomenon where pairs or groups of particles interact in such a way that the state of each particle cannot be described independently of the state of the others, even when the particles are separated by a large distance. In quantum computing, entanglement is crucial as it allows qubits to be interconnected, creating a complex quantum state that can be manipulated to perform computations. The script explains how entanglement affects the probability distribution of a system of qubits.

💡Interference

Interference in the context of quantum computing pertains to the ability to manipulate the probability amplitudes of quantum states, which can either constructively or destructively interfere with each other. This property is used to amplify the probability of correct answers and diminish the probability of incorrect ones in a quantum algorithm. The video describes how interference is essential for solving computation problems on a quantum computer.

💡Qubits

Qubits, short for quantum bits, are the basic units of quantum information in quantum computing. Unlike classical bits that are in a state of 0 or 1, qubits can be in a superposition of both states, and when entangled, can exhibit correlations that are not possible in classical systems. The script explains that qubits are more complex than classical bits and are visualized as arrows pointing in 3D space.

💡Shor's Algorithm

Shor's algorithm is a quantum algorithm developed by Peter Shor that can efficiently factor large integers. This is significant because factoring is considered a hard problem for classical computers, and Shor's algorithm demonstrates the potential of quantum computing to solve problems exponentially faster than classical counterparts. The video discusses the impact of Shor's algorithm on the field of cryptography and its role in the advancement of quantum computing.

💡Quantum Complexity Theory

Quantum complexity theory is a subfield of computational complexity theory that categorizes quantum algorithms based on their efficiency. It deals with the difficulty of solving problems as they scale in size and is concerned with how quantum computers can tackle problems that are intractable for classical computers. The script uses quantum complexity theory to explain the difference in problem-solving capabilities between classical and quantum computers.

💡Quantum Simulation

Quantum simulation refers to the use of quantum computers to simulate quantum systems, such as chemical reactions or the behavior of electrons in materials. This is an area where quantum computers are expected to outperform classical computers due to their inherent ability to represent and manipulate quantum states. The video highlights the potential of quantum simulation to revolutionize fields like materials science and drug development.

💡Decoherence

Decoherence is a process in quantum systems where the delicate quantum states, such as superposition and entanglement, lose their quantum properties and begin to behave more classically due to interactions with the environment. In the context of quantum computing, decoherence is a major challenge as it leads to loss of information and errors in computation. The script discusses the importance of protecting qubits from decoherence to build functional quantum computers.

💡Scalability

Scalability in the context of quantum computing refers to the ability to increase the number of qubits in a quantum system while maintaining control and coherence. As the number of qubits grows, the complexity of the system and the engineering challenges associated with it also increase. The script mentions scalability as a critical issue for the practical implementation of quantum computers.

💡Quantum Error Correction

Quantum error correction is a set of techniques used to protect quantum information from errors due to decoherence and other quantum noise. It involves encoding quantum information across multiple physical qubits to create a logical qubit that is more robust against errors. The script discusses quantum error correction as a strategy to build fault-tolerant quantum computers capable of performing reliable computations.

💡Qiskit

Qiskit is an open-source software framework sponsored by IBM that provides tools for quantum computing. It includes an online textbook, tutorials, and the ability to run quantum circuits on simulators or actual quantum hardware. The video script mentions Qiskit as an educational resource for those interested in learning about quantum computing and gaining hands-on experience.

Highlights

Sponsored video by Qiskit providing details on quantum computing industry growth since 1980.

Quantum computers have advantages over classical computers due to their ability to be in multiple states simultaneously.

Introduction to quantum bits (qubits) as the fundamental building blocks of quantum computers.

Explanation of superposition, where qubits can exist in a combination of 0 and 1 states.

Entanglement concept, where qubits become interconnected and influence each other's state.

Interference in quantum computing, which is used to manipulate probabilities of qubit states.

Quantum algorithms, such as Shor's algorithm, that can solve problems intractable on classical computers.

Quantum complexity theory and the difference between problems solvable by classical and quantum computers.

Potential applications of quantum computers in optimization, machine learning, financial modeling, and more.

Quantum simulation as a promising application for quantum computers to model complex quantum systems.

Challenges in building quantum computers, including decoherence and noise affecting qubit stability.

Overview of different models of quantum computing, including gate model, adiabatic, and topological quantum computing.

Introduction to physical implementations of qubits using superconducting circuits, quantum dots, and other methods.

Discussion on quantum error correction to create fault-tolerant quantum computers.

Scalability issues in quantum computing and the need for efficient control and measurement of qubits.

Current state of quantum computing technology and the various approaches being pursued by companies and startups.

Qiskit as an educational resource for learning quantum computing and gaining hands-on experience.

Transcripts

Video is sponsored by Qiskit,  more details later in the video.  

From the first idea of a quantum computer in 1980  to today there has been huge growth in the quantum  

computing industry, especially in the last 10  years. With dozens of companies and startups  

spending hundreds of millions of dollars in a  race to build the world’s best quantum computers.  

For most of us it’s quite hard to get our  heads around the world of quantum computing,  

and a lot of information about it glosses over  important details. This video aims to clear all  

this up and if you watch the whole thing you’ll  have a very good overview of all the different  

kinds of quantum computing, how they work, and  why so many people are investing in the quantum  

computing industry. This is the map of quantum  computing. Quantum computers solve problems in  

a different way to the computers we are familiar  with, which, from now on I’ll be referring to as  

classical computers. Quantum computers have  certain advantages over normal computers for  

certain problems which comes from their ability  to be in a huge number of states at the same time  

whereas classical computers can only be in  one state at a time. To understand this,  

and to understand how quantum computers work you  need to understand three things: superposition,  

entanglement and interference. The building  blocks of a classical computer are called bits,  

and the building blocks of a quantum computer are  called quantum bits, or qubits for short, and they  

work in fundamentally different ways. A classical  bit is kind of like a switch that can either be  

a 0 or a 1 which you are probably already  familiar with as binary or binary information.  

When we measure a bit we just get back the state  that it’s currently in, but we’ll see this isn’t  

true of qubits. A qubit is more complicated. For  a useful visualisation you can think of them as  

an arrow pointing in 3D space. If they point  up they are in the 0 state and if they point  

down they are in the 1 state, just like a  classical bit, but they also have the option to  

be in a thing called a superposition state which  is when the arrow points in any other direction.  

This superposition state is a combination state of  0 and 1. Now, when you measure a qubit the output  

it gives will still end up being either a 0 or a  1, but which one you get depends on a probability  

which is set by the direction of the arrow. If the  arrow is pointing more upwards you are more likely  

to get back a 0 than a 1, and if it is pointing  downwards you are more likely to get a 1 than a 0,  

and if it is exactly on the equator  you’ll get either state with a 50%  

probability. So that’s the effect of superposition  explained, now we’ll move on to entanglement.  

In a classical computer the bits  are independent from each other.  

The state of one bit is not influenced  by the state of any of the other bits.  

But in quantum computers the qubits can be  entangled with each other which means they  

become part of one large quantum state together.  For an example let’s look at two qubits which are  

each in different superposition states, but aren’t  entangled yet. You can see the probabilities next  

to them, and these probabilities are  currently independent of each other.  

But when we entangle them, we have to throw away  those independent probabilities and calculate a  

probability distribution of all of the possible  states we can get out. Either 00, 01, 10, or 11.  

The important point here is because the qubits  are entangled, if you change the direction of  

the arrow on one qubit, it changes the probability  distribution for the whole system, so the qubits  

are no longer independent of each other, they are  all part of the same large state. And this is true  

no matter how many qubits you have. You’ll also  note that for one qubit you have a probability  

distribution over 2 states. For two qubits you  have a probability distribution over 4 states.  

For three qubits you have a distribution over  8 states, and this keeps on doubling each time  

you add another qubit. In general, a quantum  computer of n qubits can be in a combination of  

2^n states. So I’d say this is the core difference  between classical computers and quantum computers.  

Classical computers can be in any state you want,  but can only be in one state at a time, whereas  

quantum computers can be in a superposition  of all of those states at the same time. But  

you may wonder how being in this superposition  state can be useful in a computer. Well for that  

we need the final component: interference.  To explain the effect of interference we  

need to go back and look at my picture of  a qubit technically called a Bloch sphere.  

A qubit doesn’t actually look like this,  this is just a really nice way of visualising  

the state of a qubit. In reality the state of  a qubit is described by a more abstract entity  

known as a quantum wavefuncion. Wavefunctions  are the fundamental mathematical description  

of everything in quantum mechanics which I’ve  described in more detail in a previous video.  

When you have many qubits entangled together all  of their wavefunctions are added together into an  

overall wavefunction describing the state  of the quantum computer. This adding  

together of wavefunctions is the interference  because, just like with say ripples of water,  

when we add waves together they can constructively  interfere and add together to make a bigger wave,  

or destructively interfere to cancel each  other out. The overall wavefunction of the  

quantum computer is what sets the different  probabilities of the different states,  

and by changing the states of different qubits  we can change the probabilities that different  

states will come out when we measure the quantum  computer. Remember that even though the quantum  

computer can be in a superposition of millions  of states at the same time, when we measure it,  

we only get a single state out. So when you are  using a quantum computer to solve a computation  

problem you need to use constructive interference  to increase the probability of the correct answer,  

and use destructive interference to decrease  the probabilities of the incorrect answers  

so that when you measure it the correct answer  will come out. Now how you do this is the realm  

of quantum algorithms, and the whole motivation  behind quantum computing is that, theoretically,  

there are a bunch of problems that you can solve  on a quantum computer that are thought to be  

intractable on classical computers. Let’s take a  look at them. There are many quantum algorithms,  

too many to describe in this video, so we’ll  just focus on the most famous and historically  

important: Shor’s algorithm. If you have two large  numbers and you multiply them together there is  

a very fast, efficient, classical algorithm for  finding the answer. However, if you start with the  

answer and ask, what are the original numbers that  multiply together to make this number? It is a lot  

more difficult. This is known as factorization,  and these numbers are called factors,  

and the reason finding them is so hard is because  the search space of possible factors is so large.  

And there is no efficient classical algorithm  for finding the factors of large numbers.  

For this reason we use this mathematical property  for internet encryption: secure websites,  

emails and bank accounts. If you know these  factors you can easily decrypt the information,  

but if you don’t you’d need to find them first  which is intractable on the world’s most powerful  

computers. Which is why in 1994, when Peter  Shor published a fast quantum algorithm that can  

efficiently find the factors of large integers,  it caused quite the stir. This is the moment  

that a lot of people started to take the idea  of quantum computing seriously because it was  

the first application to a real world problem with  potentially huge real world security implications.  

But when I say a ‘fast’ quantum algorithm,  how fast, and how much faster than a classical  

computer would it be? To answer these questions  we need to take a little detour into the world  

of quantum complexity theory. Quantum  complexity theory is a subfield of the  

world of computational complexity theory which  deals with the categorisation of algorithms,  

sorting them into bins according to how well they  run on computers. The categorisation is based on  

how much harder it is to solve the problem as the  problem gets larger. Here any problem inside the P  

box is easy to solve with a classical computer,  but anything outside it means we don’t have  

efficient classical algorithms to solve them and  factoring large numbers is one of these. But there  

is a box, BQP which is efficient for a quantum  computer, but not a classical computer. And these  

are the problems that quantum computers will be  better than classical computers at solving. As I  

said, complexity theory looks at how difficult it  is to solve a problem as the problem gets larger.  

So if you factorize a number with 8 digits, then  you add another digit on, how much harder is  

it to factor the new number compared to the old  one? Is it twice as hard? Exponentially harder?  

And what is the trend as you add more and more  digits? This is called its complexity or scaling,  

and for factorisation it is exponential. Anything  with the N in the exponent is exponentially hard.  

These exponential problems are the problems that  really screw you over as the problems get bigger,  

and in the world of computer science you can win  respect and renown if you find a better algorithm  

to solve these hardest problems. One example of  this was Shor’s algorithm which took advantage  

of the special features of quantum computers  to create an algorithm that could solve  

integer factorisation with a scaling much  better than the best classical algorithm.  

The best classical algorithm is exponential,  whereas Shor’s algorithm is polynomial which  

is a huge deal in the world of complexity theory  and computer science in general because it turns  

an intractable problem into a problem that can  be solved. Solved, that is, if you have a working  

quantum computer, which is what people are working  on building. But you don’t need to worry about the  

security of your bank account yet because today’s  quantum computers are not able to run Shor’s  

algorithm on large numbers yet. I’ve estimated  they would need about a million qubits to do so,  

but so far the most advanced universal quantum  computers have around 100. Also, people are  

working on what’s known as post-quantum encryption  schemes which don’t use integer factorization,  

and another technology from the world of quantum  physics can help here too, a cryptographic scheme  

known as quantum cryptography. So that  was a look at just one quantum algorithm,  

but there are many more each with different levels  of speedup. Another notable example is Grover’s  

algorithm which can search unstructured lists of  data faster than the best classical algorithm.  

But I should be careful here to make sure I  don’t mischaracterize classical computers.  

They are very versatile devices, and there  is nothing to say that someone may find a  

very clever classical algorithm that could solve  the hardest problems like integer factorization  

more efficiently. People think it is  very unlikely, but it is not ruled out.  

Also, there are problems that we can prove are  impossible to solve on classical computers,  

called non-computable problems, like the halting  problem, but these are also impossible to solve  

on a quantum computer. So computationally  classical computers and quantum computers  

are equivalent to each other, the differences  all come from the algorithms that they can run.  

You can even simulate a quantum computer on a  classical computer and vice versa. But simulating  

a quantum computer on a classical computer gets  exponentially harder to do the more qubits you  

are trying to simulate. This is because classical  computers struggle to simulate quantum systems,  

but because quantum computers are already quantum  systems, they don’t have this problem which  

brings me to my favourite application of quantum  computers: quantum simulation. Quantum simulation  

is simulating things like chemical reactions  or how electrons behave in different materials  

with a computer. Here quantum computers also have  an exponential speedup over classical computers  

because classical computers really struggle to  simulate quantum systems. Now I’ve made a whole  

other video about quantum simulation which you  can watch here, but basically simulating quantum  

systems with as few as 30 particles is difficult  even on the world’s most powerful supercomputers.  

We also can’t do this on quantum computers yet,  but as they mature a main goal is to simulate  

larger and larger quantum systems. These include  areas like the behaviour of exotic materials at  

low temperatures like understanding what makes  some materials superconduct, or study important  

chemical reactions to improve their efficiency,  one example aims to produce fertiliser in a way  

that emits way less carbon dioxide as fertiliser  production contributes to around 2% of global  

carbon emissions. Other potential applications  of quantum simulation include, improving solar  

panels, improving batteries, developing new  drugs, chemicals or materials for aerospace.  

In general quantum simulation would mean that we  would be able to rapidly prototype many different  

materials inside a quantum computer and test all  their physical parameters, instead of having to  

physically make them and test them in a lab which  is a much more laborious and expensive process.  

This could be a lot faster and save a huge amount  of time and money. It is worth reiterating that  

these are all potential applications of quantum  computers, because we don’t have any quantum  

computers that can solve real world problems  better than our normal computers yet. But these  

are the kinds of problems quantum computers would  be well suited to. Other applications outside of  

quantum simulation are optimization problems,  machine learning and A.I. Financial modelling,  

weather forecasting and climate change, which  I’ll be honest I don’t really understand how  

this would work, and finally cybersecurity, which  I think just boils down to shor’s algorithm, which  

I already described. Now we need to be a little  careful about the potential of hype here, as a lot  

of the claims of what quantum computers will be  good for come from people who are actively raising  

money to build them and so it makes sense for them  to piggyback on topical subjects in their pitches.  

But my take on it is that historically, when a new  technology has come along, the people of the time  

aren’t the best at being able to tell what it’s  going to be used for. For example the people who  

invented the first computers never dreamed of the  internet, and all of the things on it. And this is  

likely to be the same for quantum computers.  But for me the application that I can really  

understand the value of is quantum simulation  which is why I've focused on it in this video.  

Anyway, so far I’ve described how quantum  computers work and what problems they can solve.  

But most of what I’ve talked about so far is  theoretical. For the rest of the video I want  

to focus on reality. How are people actually  building quantum computers, and what can they  

actually do? Now it’s worth mentioning here  that some physicists are sceptical that it will  

ever be possible to build quantum computers at  the scale needed to solve real world problems,  

but people working on all of the following  certainly don’t agree. Now quantum computing  

is often portrayed as if it is a single thing. But  inside the world of quantum computers there are  

a large range of approaches to turning different  kinds of quantum systems into quantum computers,  

and there are two layers of nuance I need to talk  about. First of all are the models of quantum  

computing: the overall approach to manipulating a  collection of qubits and then there’s the physical  

implementations: the actual quantum objects you  build your qubits from, like a superconducting  

loop, or individual atoms or photons. We’ll  start with the models of quantum computing.  

It is interesting that there are different  models of quantum computing, because this is  

not something we see with classical computers.  Practically all the computers we use today  

work in the same way, they have a bunch of bits  holding the binary information of ones and zeros,  

and we can do operations on these bits  using logical gates which are basically  

simple operations that flip a bit, called a  NOT gate, or compare bits like giving you a 1  

if two bits are both zero, and a 0 if they  are anything else this is called a NOR gate.  

Interestingly you can build a full general  purpose computer from just bits and NOR gates.  

In quantum computing there is a similar  model called gate model, or circuit model  

which is the most popular and most  understood model of quantum computing.  

In the circuit model you have your collection of  qubits which are entangled with each other, and  

then you have a bunch of gates which can perform  operations on small numbers of these qubits  

which change the states of the qubits without  measuring them. A quantum algorithm is built  

from a sequence of gates applied to the qubits in  a certain order, and then a measurement at the end  

when you get the final state, which hopefully is  the answer to the problem you are trying to solve.  

Simplistically you can think of these gates as  operations on the qubits that rotate the arrows  

to point in different directions. And these  operations change the probability of the final  

state of each qubit when it is finally measured.  Now there’s more to this which I don’t have time  

to explain here, but if you want to learn more  about them and do some quantum computing yourself  

I highly recommend the educational  website and YouTube channel called Qiskit.  

They are kindly sponsoring this video, and  honestly they are the best resource for people who  

want to learn more about quantum computing and get  some actual hands-on experience. Basically Qiskit  

is a software framework funded by IBM to make it  easier for people to get into the world of quantum  

computing. Everything there is free to access and  the code is all open source, there is an online  

text book which teaches you all the basics, so if  you don’t have a quantum physics background that  

is no problem at all, you can learn everything  you need there. Their Qiskit YouTube channel is  

also full of excellent tutorials and lectures,  I’ll link to all of this below. And in terms of  

quantum algorithms you can run through examples  of quantum circuits using their online tools.  

And if you want to run your own quantum  programs you can download their open-source  

SDK and run them on IBM hardware, either on  classical simulators of quantum computers, or  

on actual real world quantum computers, for free.  And the SDK is not only tied to IBM hardware. I  

used to work at another quantum computing company  called D-Wave, and there is an interface to their  

computers in the SDK as well if you want to learn  about their approach called quantum annealing and  

many other companies are available too. Personally  I’ve been using their website to learn gate model  

quantum computing deeper because my background is  in quantum annealing and I’m super happy that this  

educational resource exists, and is free to use so  please check that out if you want to dig deeper.  

Finally I just want to state that I’ve had  complete editorial control over the content  

of this video and my goal is always to be as  objective as I can, I just want to make sure you  

know that Qiskit is funded by IBM who are building  quantum computers, and I used to work for D-Wave  

who are making other quantum computers, just for  transparency so you know everyone’s backgrounds.  

Right, back to the models of quantum computing  we’ve already looked at the circuit model,  

but closely related to it is measurement based or  one-way quantum computing which involves setting  

up an initial entangled state, and then measuring  qubits one by one during the computation,  

and mathematically this has been shown  to be equivalent to the circuit model.  

Now let’s look at the models I’m most familiar  with: adiabatic quantum computing and quantum  

annealing. Adiabatic quantum computing works  in a very different way to the circuit model.  

In adiabatic quantum computing you are taking  advantage of one of the fundamental behaviours  

in physics, the fact that every system in physics  always moves towards the minimum energy state.  

This is a very general principle, and adiabatic  quantum computing takes advantage of this by  

posing the problems you want solved in such  a way so that the minimum energy state of the  

quantum system is the answer to the problem.  You can picture this as an energy landscape,  

where each point on the landscape is one of the  potential outputs of the computer. In adiabatic  

quantum computing you start off with a flat  landscape, and gradually introduce the energy  

landscape of your problem where the answer to  your problem is the lowest position on the map.  

If you do this slowly enough, the quantum  computer will always stay in the lowest  

energy state so that when you measure it you  are most likely to get the correct answer.  

I should mention that I’m having to simplify  things a bit here to make it easier to understand,  

but it gives you the right picture of what is  going on. In reality I would need to talk about  

Hamiltonian’s and eigenstates but that’s beyond  the scope of this video. Even though adiabatic  

quantum computing is so different to the circuit  model, they have been shown to be mathematically  

equivalent, and problems can be mapped from one  to the other. And they are both something called  

a universal quantum computing scheme which means  that theoretically they can simulate any quantum  

system. Strongly related to adiabatic quantum  computing is quantum annealing which is not a  

universal quantum computing scheme, but works on  the same principle as adiabatic quantum computing  

with the system finding the minimum energy  state of an energy landscape that you give it.  

The reason it is not universal is because it  doesn’t have the full degrees of freedom to  

represent any quantum state, but even with this  limitation it can still be used to solve certain  

energy landscape problems like optimization  problems and simulate certain quantum systems,  

and example is spin glasses which are grids  of magnetic fields connected to each other.  

And quantum annealing is a stepping stone to  building a universal adiabatic quantum computer.  

The last model we are going to look at is called  topological quantum computing which is currently  

the most theoretical model of quantum computing  because it builds its qubits from an entity in  

physics called a Majorana zero-mode quasi-particle  which is a type of non-abelian anyon.  

Which is a bit of a mouthful and obviously  quite confusing but the important term here is  

quasi-particle. Quasi-particles aren’t fundamental  particles like atoms, electrons or photons,  

quasi-particles are created from the collected  behaviour of many particles together, and end up  

having particle-like properties despite not being  actually real. The clearest example of this is an  

electron hole: if you have a grid of electrons  with a gap in the middle, as the electrons fill  

in the gap it looks like this hole moves in  the opposite direction. This hole isn’t real,  

it’s just a hole, but you can treat it like  a particle with particle-like properties.  

In condensed matter physics there are a large  range of different kinds of quasi-particle and  

a Majorana zero-mode quasti-particle is an entity  that has been theoretically predicted, but there  

is still significant debate over whether they’ve  actually been experimentally observed or not.  

Now the reason why physicists are excited about  this model is because these quasi-particles are  

predicted to be a lot more stable than other  qubits because they are made from parts which  

are physically separated from each other. This  is good because the main source of failure in  

a quantum computer is noise, which comes from  rogue forms of energy creeping into the quantum  

computer making the qubits drift away from  where they should be and causing errors.  

But these quasi-particles are special because they  are protected from the noise by an energy gap.  

Basically what this means is it takes a certain  energy to bring the parts of the Majorana particle  

back together, so any perturbations of noise which  have a lower energy than that energy gap is not  

felt by the quasi-particle. This might have been  a bit confusing, but that’s okay I’m still getting  

my head around them too, but that was just the  best boiled down description I could come up with.  

Okay so that rounds up the different models of  quantum computation, but how do you actually build  

them? There are a huge range of different physical  implementations of quantum computers because  

there are so many different quantum systems  that you could potentially build them from.  

The requirements to build a qubit is actually  fairly simple: all you need is a two state quantum  

system when one state will represent 0 and the  other will represent 1. The most obvious example  

of this is the spin of a particle: the spin can  be up or down, but as we shall see there are many  

properties of particles we can use. In fact, there  are too many for me to list them all, so I’m just  

going to focus on the implementations that are the  most widely used and have been the most successful  

so far. But no matter what the approach is, they  all face a similar set of obstacles which we need  

to take a look at first. In general it’s really  hard to control quantum systems because if you  

have got any slight interaction with the outside  world the information starts leaking away. This  

is called decoherence. You want your qubits to be  entangled with each other, but don’t want them to  

be entangled with anything else. But the trouble  is, your qubits will be made of physical stuff  

and you will need other physical stuff  nearby to control and measure them,  

and your qubits are dumb they’ll  entangle with anything they can. So,  

you need to design your qubits very carefully to  protect them from entangling with the environment.  

Then you need to shield your qubits from  any kind of noise: things like cosmic rays,  

or radiation from things like phone calls, or  heat energy or any other kind of rogue particle.  

Unfortunately some amount of decoherence and  noise is inevitable in any physical system,  

and is impossible to eliminate completely. And it  gets worse the more qubits you have entangled with  

each other. This is the big open question still  hanging over the whole field of quantum computing:  

is it ever possible to make a working quantum  computer with a large number of qubits, or will  

decoherence and noise ruin everything? There  are strong opinions on both sides, and I guess  

we won’t know for sure until we actually build  them. One plan to deal with decoherence and noise  

is quantum error correction. This is an error  correction scheme to make fault-tolerant quantum  

computers by using many entangled qubits together  to represent one noise free qubit. How many  

you need depends on how good the qubits are, but  estimates are in the range of 100 to 1000 physical  

qubits to make one fault-tolerant qubit. Which  is a lot of qubits. And this brings us to another  

major obstacle: scalability. For each qubit you  need to have a bunch of wires to manipulate and  

measure it. For a small number of qubits this  is all manageable, but as the number of qubits  

increases the amount of extra stuff you need  increases linearly, which is a massive engineering  

problem. So any quantum computer design needs to  somehow be able to entangle all of the qubits,  

and then control and measure them in a scalable  way. So those are all the problems with building a  

real quantum computer, let’s take a look at the  different approaches scientists are pursuing.  

Superconducting quantum computers are currently  the most popular approach. A superconducting qubit  

is made from superconducting wires with a break  in the superconductor called a josephson junction.  

The most popular type of superconducting  qubit is called a transmon where the two  

level system is encoded in pairs of the  electric charge moving across the junction,  

specifically the frequency at which charges  oscillate back and forth across the junction.  

But there have been other designs that  use the magnetic flux in a loop of wire,  

or the phase across a wire as a two level  system known as flux qubits or phase qubits.  

Physicists have also looked at ways of making  qubits out of fundamental entities like atoms, or  

electrons or photons. Next are quantum dot quantum  computers or silicon spin quantum computers.  

Here I’m using quantum dot quantum computers  to collect a range of qubit designs built from  

semiconductors, things like silicon. Here the  qubits are made from electrons or even groups  

of electrons and the two level system is encoded  into the spin or charge of the electrons. On the  

chip there’s a small area where the electron  is restricted to is called a quantum dot,  

and operations on the qubits are performed through  voltages on the chip, or microwaves or magnetic  

fields. As well as silicon, people have also  used other semiconducting materials like gallium  

arsenide, silicon carbide and also diamond amongst  others, which all have different properties.  

Next we have linear optical quantum computing.  Optical quantum computers use photons of light  

as the qubits and they operate on these  qubits using optical elements like mirrors,  

waveplates and interferometers. At scale this has  been accomplished by printing these elements into  

integrated photonics chips. The two level system  in an optical quantum computer can have different  

designs, either a superposition of different  paths a single photon takes through the chip,  

or a superposition of different numbers of photons  present in a path. And these can be manipulated by  

applying a voltage to a path. Now onto trapped  ion quantum computers which use charged atoms  

as qubits. These atoms are ionised, having a  missing electron, which makes them electrically  

charged and means they can be levitated and  moved about with electromagnetic fields.  

Here the two level state that encodes the qubit  are two specific energy levels of the atom which  

can be manipulated or measured with microwaves  or laser beams. Next we have colour centre or  

nitrogen vacancy quantum computers which are  similar to trapped ion quantum computers in  

that the qubits are made from atoms, but instead  of being trapped in an electromagnetic field,  

they are embedded in a gap of the material like  nitrogen embedded in diamond or silicon carbide.  

There are a few different ways to make  these, but typically the qubits are  

the nuclear spins of the embedded atoms and  they are entangled together with electrons.  

The final approach is called neutral atoms  in optical lattices. In this approach the  

qubits are atoms, and the design uses cold atom  physics capturing neutral atoms like caesium  

into an optical lattice which is a crisscrossed  arrangement of laser beams, which form energy  

wells shaped kind of like an egg box. These atoms  are cooled down with lasers to a few millionths of  

a kelvin and there are a number of ways to encode  the two level system the qubit is built from:  

either the hyperfine energy level of the atom  or excited states and they can also make use of  

Rydberg atoms. And the atoms can be controlled  and entangled with each other with lasers.  

They can also be used as quantum simulators  as well as quantum computers. In fact a 10,000  

atom quantum simulator has been made, but this  doesn’t look like a universal quantum computer.  

These are the main approaches I’m going to cover  in this video, but it is not an exhaustive list,  

some other qubit designs include:  Electron-on-helium qubit,  

Cavity quantum electrodynamics, Magnetic Molecule,  Molecular Spins, NMR quantum computers. But these  

have not been built at the same scale as the  other approaches I mentioned in more detail.  

So that was the map of quantum computing and  that should give you an excellent overview of the  

field. As you can see, there are many different  approaches to building a quantum computer,  

and what is so interesting is that it’s not yet  clear which approach will win out in the long run.  

Now one thing I haven’t covered in this video are  the companies and startups and which approach they  

are using, along with their current best quantum  computers, and their roadmaps into the future.  

But this is what I’ll look at in my next video  so keep your eyes peeled for that. You don’t  

need to subscribe or anything, but check back in a  couple of weeks if you think you’d be interested.  

And like all my maps this map of quantum  computing is available to buy at my store  

dosmaps dot com, or to download as a digital  image for educational purposes links to all  

of that in the description below. Quick note  though, due to logistics we can only get the  

map of quantum computing to you after the  holidays, but everything else in my store  

is ready to go. We also have many educational  posters and a range of engaging kids books about  

science called Professor Astro Cat, so if you  are looking for some gifts that will help your  

loved ones learn about science, check that out.  Dosmaps dot com. Finally, a massive thank you to  

all my patreon supporters. As you can  probably tell I put a huge amount of work  

into these map videos and the support on patreon  is invaluable. Thank you. And I’ll see you soon!