Quantum Computing

Latest update: πŸ‡¦πŸ‡Ί 18:40 πŸ“† 21 Apr 2024

πŸ”Ί Sundar Pichai: CEO of Google, developer of the Sycamore 53 qubit quantum computer

Techinvestment.com invests in technology companies. This page includes a personalised self-tutorial from ChatGPT on quantum computing (as of the date of ChatGPT's training data). It is supported by lookups from Wikiwand and our own research. For more definitive and practical explanations of quantum computing, try IBM's Qiskit Documentation.

Our objective is not to become experts in the subject: we're not scientists or engineers. Our objective as investors is to understand a new area of investment opportunity directly (eg computer manufacturers and service providers) and indirectly (eg improving the capability and competitiveness of companies that use quantum computing, eg with artificial intelligence to develop new products, services and markets). That's how we see our job.

One of the classic tests is to compare the speed of solving specific tests against classical computers: eg claiming that Google's Sycamore 53 qubit quantum computer can perform a task in 200 seconds that would take IBM's supercomputer about 10,000 years: Nature: "Quantum supremacy using a programmable superconducting processor" 23 Oct 2019. This is referred to as ⏯️ "quantum supremacy" (ie quantum advantage - "supremacy" - over classical digital computing).

A simple explanation may be described this way. Take a pea and shell game, where a pea is placed under one of 3 shells and the task is to identify which shell the pea is placed under. A classical computer would start at one end and turn over one shell after another until the pea is found. Change the problem to one pea and a million shells. The quantum computer finds the pea by turning over all shells at the same time. [OK scientists, please feel free to give me a better example]. Quantum computing provides the opportunity to solve certain types of problems that cannot be solved by classical computers.

Beyond quantum computing, quantum physics technology provides exceptional opportunities for security - especially use of quantum keys in superposition based on the ⏯️ Schrâdinger principle.

A "personalised tutorial" from ChatGPT

Latest developments and future directions in quantum computing technology - in particular use of the attributes (eg spin) of sub-atomic particles

Gravitons: "While the matter particles of the Standard Model are spin 1/2 and the Standard Model force-carrying particles have a spin of 1, gravitons must have a spin of 2. This proceeds from the fact that gravity stems from the distribution of energy and momentum in the universe. It turns out that this spin thing can prove that any massless spin-2 particle must act exactly as a graviton is predicted to behave. Thus if we find a spin-2 massless particle, we'll know it's a graviton. This spin-2 behavior also explains the fact that conventional gravity only attracts, unlike electromagnetism, which both attracts and repels." Fermilab

22 Mar 2024: South China Morning Post reports that "Scientists from China, US and Germany find electrons to have spin only expected in gravitons", a long-sought-after particle that gives rise to gravity.


In quantum computing there seems to be an interest in sub-atomic particles, such as bosons that spin in integer values (0, 1, 2, etc.) and fermions that spin in odd half integer values (1/2, 3/2, and 5/2, but not 2/2 or 6/2).

Could you explain, please, what it means for fermions to spin in half integer values?


In quantum mechanics, particles like electrons, protons, and neutrons are classified into two main categories: fermions and bosons. One of the key distinguishing characteristics between fermions and bosons is their intrinsic angular momentum, commonly referred to as "spin”.

Spin is a quantum mechanical property that doesn't have a direct analog in classical physics but can be loosely thought of as the intrinsic angular momentum of a particle. However, it's important to note that spin isn't really spinning in the classical sense; it's a fundamental property of particles in the quantum world.

Fermions are particles that obey the Pauli Exclusion Principle, which states that no two fermions can occupy the same quantum state simultaneously. This principle is crucial in understanding the behavior of electrons in atoms, for example.

Fermions have spin values that are half-integer multiples of Δ§ (the Reduced Planck Constant), such as 1/2, 3/2, 5/2, and so on. This means that when you measure the spin of a fermion along a particular axis (say, the z-axis), you can only get one of two possible results: either +1/2 or -1/2 times Δ§.

The fact that fermions have half-integer spin values is a consequence of their quantum nature and the underlying principles of quantum mechanics. It's one of the fundamental properties that distinguishes fermions from bosons.

In contrast, bosons, such as photons and gluons, have integer values of spin (0, 1, 2, etc.). Unlike fermions, bosons do not obey the Pauli Exclusion Principle and can occupy the same quantum state simultaneously.

So, in summary, when we say that fermions have spin values in half-integer increments, it means that their intrinsic angular momentum is quantized in a specific way dictated by the rules of quantum mechanics, and this property has profound implications for the behavior of matter at the subatomic level.

Pauli Exclusion Principle

Reduced Planck Constant


Could you illustrate (in words obviously) the Pauli Exclusion Principle: "no two fermions can occupy the same quantum state simultaneously"?


Certainly! Let's imagine a scenario with two identical fermions, such as two electrons. The Pauli Exclusion Principle states that these two electrons cannot occupy the exact same quantum state simultaneously.

Now, what does it mean for two particles to occupy the same quantum state? In quantum mechanics, particles are described by various properties, including their energy, momentum, position, and spin. A quantum state is essentially a complete description of these properties for a particle.

So, if two fermions cannot occupy the same quantum state, it means that they cannot have identical values for all of their quantum properties at the same time. For example:

This principle is crucial in understanding the behavior of fermions in various systems, particularly in atoms. It's what gives rise to the structure of the periodic table, as electrons arrange themselves in different quantum states around atomic nuclei, each obeying the Pauli Exclusion Principle. Without this principle, matter as we know it wouldn't exist in its current form, and the stability of atoms would be fundamentally different.


Could you please explain this statement: "Several bosons in the same quantum state can collect into what is known as a 'Bose-Einstein Condensate(BEC).'”


When multiple bosons, such as photons or certain types of atoms, occupy the same quantum state, they can exhibit a phenomenon called a "Bose-Einstein Condensate (BEC)". This is a fascinating state of matter predicted by Satyendra Nath Bose and Albert Einstein in the early 1920s.

In a Bose-Einstein Condensate (BEC), a large number of bosons, often cooled to extremely low temperatures, all occupy the lowest possible energy state, known as the ground state, and essentially behave as a single quantum entity. At such low temperatures, the individual wave functions of the bosons start to overlap significantly, leading to the collective behavior.

Here's a breakdown of the key points:

Overall, the Bose-Einstein Condensate (BEC) represents one of the most remarkable manifestations of quantum mechanics at the macroscopic scale, offering insights into the nature of matter at its most fundamental level.

Macroscopic Quantum Phenomenon


In your statement "When many bosons are cooled to extremely low temperatures, their wave functions start to overlap, and they can occupy the same quantum state." Does this mean that the bosons become entangled?


Yes, indeed. When many bosons are cooled to very low temperatures and start to occupy the same quantum state, they can become entangled with each other. entanglement is a fundamental phenomenon in quantum mechanics where the quantum states of two or more particles become correlated in such a way that the state of one particle is dependent on the state of another, even when they are physically separated. In the context of a Bose-Einstein Condensate (BEC), the individual particles lose their distinct identities to some extent as they overlap and occupy the same quantum state. This overlapping of wave functions leads to a high degree of entanglement among the particles within the condensate. The entanglement in a BEC contributes to its unique properties, such as coherence and superfluidity. For example, the entanglement allows the particles in the condensate to behave collectively, exhibiting coherent behavior over macroscopic distances without losing their quantum correlations. This coherence is crucial for the superfluidity observed in BECs, where the particles flow without resistance and act as a single entity. So, in summary, the formation of a Bose-Einstein Condensate involves not only the overlapping of wave functions but also the entanglement of the particles within the condensate, leading to the emergence of macroscopic quantum phenomena.


How could Bose-Einstein Condensate be used in the architecture of a quantum computer?


Bose-Einstein Condensate (BECs) have been proposed as a potential component in the architecture of quantum computers due to their unique quantum properties. Here are a few ways in which BECs could be utilized:

In summary, Bose-Einstein Condensates offer a versatile platform for realizing various components of quantum computers, including qubits, quantum gates, quantum simulators, and sensors. Integrating BECs into the architecture of quantum computers could enable the development of more powerful and efficient quantum technologies with a wide range of applications.


Please describe a qubit and how it is used in a quantum computer.


A qubit, short for quantum bit, is the fundamental unit of quantum information in a quantum computer. Unlike classical bits, which can be either 0 or 1, a qubit can exist in a superposition of both states simultaneously. This property of superposition allows quantum computers to perform many calculations in parallel, potentially enabling them to solve certain problems much faster than classical computers.

The state of a qubit is described by a quantum state vector, which can be represented as a linear combination of the basis states α|0⟩ and |1⟩.

Mathematically, a qubit can be written as:
|ψ⟩ = α|0⟩ + β|1⟩
where α and β are complex numbers called probability amplitudes, and |α|^2 and |β|^2 represent the probabilities of measuring the qubit in the states |0⟩ and |1⟩, respectively. Notably, the sum of the squares of the probability amplitudes must equal 1, ensuring that the total probability of finding the qubit in any state is 1.

Qubits can be manipulated using quantum gates, which are analogous to classical logic gates but operate on quantum states. Quantum gates perform transformations on the quantum state of one or more qubits, allowing for the implementation of quantum algorithms.

The diagram shows various quantum gates which are fundamental building blocks used to manipulate qubits (quantum bits) to perform quantum computations. Here's a brief explanation of some common types:

These gates, along with others like the Pauli gates (X, Y, Z), Controlled NOT (CNOT) gate, and others, form the basis of quantum circuits and algorithms. They allow for the manipulation and transformation of quantum states, enabling quantum computations and algorithms to be executed.

OpenQASM (Open Quantum Assembly Language) is "a machine-independent programming interface compatible with IBM Quantumβ„’ systems, is an imperative programming language for describing quantum circuits. OpenQASM uses the quantum circuit model to express quantum programs as ordered sequences of parameterized operations (such as gates, measurements, and resets) and real-time classical computation. In addition to quantum algorithms, OpenQASM can describe circuits intended to characterize, validate, or debug quantum systems." QASM Tutorials

One of the most important properties of qubits is quantum entanglement. When qubits become entangled, the state of one qubit becomes dependent on the state of another qubit, even when they are separated by large distances. This entanglement enables quantum computers to perform operations that are not possible with classical computers and forms the basis of many quantum algorithms, such as quantum teleportation and quantum key distribution (QKD).

In summary, qubits are the building blocks of quantum computers, and their unique properties, including superposition and entanglement, enable quantum computers to perform complex calculations and solve problems that are intractable for classical computers. By manipulating the quantum states of qubits using quantum gates, quantum algorithms can be executed to perform tasks ranging from optimization and cryptography to simulation and machine learning.


Whoa - let's go back to "Mathematically, a qubit can be written as: |ψ⟩ = α|0⟩ + β|1⟩"

A qubit can also be written as |ψ⟩ = Ξ±|β†‘βŸ© + Ξ²|β†“βŸ©


That formula is describing a quantum state. Let me break it down for you:

So, the formula is saying that the quantum state |ψ⟩ is a combination of two states, |0⟩ and |1⟩, with coefficients α and β respectively. The squares of the absolute values of α and β give the probabilities of finding the system in the states |0⟩ and |1⟩ when measured.

In simpler terms, imagine you have a quantum system, like a qubit (which can represent, say, the spin of an electron). This formula is saying that the quantum state of that qubit, |ψ⟩, can be a mixture of two basic states, |0⟩ and |1⟩. The α and β values tell you how much of each state is in the mixture. When you measure the qubit, you'll find it in state |0⟩ with probability |α|² and in state |1⟩ with probability |β|².

⏯️ Quantum Computers, Explained With Quantum Physics


OK: Got that, thanks.

What coding languages are used in quantum computing?

Is Qiskit a commonly used language?


In quantum computing, several programming languages and frameworks are used for developing quantum algorithms, simulating quantum systems, and interfacing with actual quantum hardware. Some of the commonly used languages and frameworks include:

Regarding your question about Qiskit, yes, Qiskit is indeed a commonly used language/framework in the quantum computing community. It has gained popularity due to its ease of use, comprehensive documentation, and support from IBM, one of the leading companies in quantum computing research and development.

This is a very simple example of a quantum circuit written using Qiskit. This example creates a basic quantum circuit with one qubit and one classical bit, applies a Hadamard gate to the qubit to put it in a superposition, and then measures the qubit to obtain a classical outcome.

This example demonstrates the basic structure of a quantum circuit and how to execute it using Qiskit.


What are the most commonly used quantum computers?


This can vary depending on factors such as availability, performance, and research interests. Some of the prominent quantum computing platforms and companies include:

These are just a few examples of companies and platforms involved in quantum computing research and development. The landscape of quantum computing is evolving rapidly, with many companies and research institutions contributing to the advancement of the field.


List of Quantum Logic Gates


π’π­πžπ© 1

π’π­πžπ© 2


Please provide a very simple example of the code a Qiskit program (if possible)


Here's a very simple example of a quantum circuit written using Qiskit. This example creates a basic quantum circuit with one qubit and one classical bit, applies a Hadamard gate to the qubit to put it in a superposition, and then measures the qubit to obtain a classical outcome.

Qiskit Code

Quantum Computer Manufacturers

Techinvestment has investments in Google (quantum and ai) and IonQ (trapped ion quantum).
Here are these and other developers:

Other companies:

πŸ‡¦πŸ‡Ί Other researchers: Several universities build research versions of quantum computers. One of these is the University of NSW:

ChatGPT explains the suspended structure of quantum computers

⏯️ Sweden's Wallenberg Center for Quantum Technology's $100m quantum computer: removing the outer shell to expose the cooling system and quantum computer at the bottom.

Physical architecture

Google's Sycamore quantum computer

Most of what you see in this picture is the cryostat, the mechanism for progressively maintaining a near zero Kelvin environment for the quantum computer at the bottom of the structure (more). The structure is usually inside a tube to manage temperature and other external environmental factors. When the tube is in place the circular horizontal plates divide the upper structure into cooling zones, to create and maintain near absolute zero temperature at the bottom: the mixing chamber.

The quantum computer chip is in the little brown box in the mixing chamber at the bottom of the structure. The mixing chamber provides the necessary cooling power for the chip to function.
Here is Google's Sycamore 53 qubit quantum computer (the 54th failed) - the chip is inside the silver box surrounded by connectors. The Scientific American describes what's inside the box:

Google quantum processor

Below the box containing the quantum computer chip is the quantum computing readout system. This is used to read the state of the qubits at the end of a quantum computing calculation.

⏯️ Google's Quantum Campus

⏯️ IBM's Quantum Campus

⏯️ Quantum Supremacy: Benchmarking Sycamore 53 qubit processor

"Whereas both IBM and Google are using superconductors to create their qubits, another approach relies on trapped ionsβ€”charged atoms suspended in a vacuum and manipulated by laser beams." Scientific American

𝐂𝐇𝐀𝐓𝐆𝐏𝐓: More about the suspended, chandelier structure

The images above typically depict quantum computers based on certain architectures, such as ion traps or superconducting circuits. These designs often involve delicate and precisely engineered components that need to be isolated from external disturbances, including vibrations and electromagnetic interference, to maintain the coherence of quantum states.

The suspended structure you see in these images serves multiple purposes:

Overall, the suspended structure is a practical design choice aimed at preserving the delicate quantum states and optimizing the performance of the quantum computing system.

Trapped Ion Computers

In addition to its investments in Google's quantum computing strategy described above, Techinvestment invests in IonQ, whose computers use the trapped ion design strategy.

IBM is partnering with Quantinuum with its H1 and H2 trapped ion computers.

ℹ️ How does IonQ's trapped ion quantum computer work?


What makes quantum computing so fast?


Quantum computing's speed primarily stems from its ability to perform calculations using qubits, which are quantum bits. Unlike classical bits, which can either be in a state of 0 or 1, qubits can exist in a superposition of both states simultaneously. This allows quantum computers to perform many calculations at once, exploiting the parallelism inherent in quantum mechanics.

Additionally, quantum computers can utilize a phenomenon called entanglement, where the state of one qubit is dependent on the state of another, even if they are physically separated. This allows for the manipulation of multiple qubits simultaneously and can lead to exponential speedups for certain types of problems.

Furthermore, quantum algorithms such as Shor's algorithm for factoring large numbers and Grover's algorithm for searching unsorted databases offer significant speed advantages over their classical counterparts for specific tasks.

However, it's important to note that quantum computing is not universally faster than classical computing for all types of problems. Quantum computers excel at certain types of calculations, such as factoring large numbers or optimizing complex systems, but they may not necessarily outperform classical computers for tasks like basic arithmetic or word processing.


⏯️ Elon Musk and Michio Kaku Aug 2023

⏯️ IBM Quantum Summit - Keynote: Entering the Era of Quantum Utility 4 Dec 2023

⏯️ IBM System Two Dec 2023

⏯️ 60 Minutes Report (Jan 2024)

⏯️ DW Mar 2024

⏯️ David Jamieson (UniMelb): The Journey to Quantum Computing

Use cases for quantum computing and AI in finance and banking

⏯️ "The Next Computing Revolution is with AI-Quantum" ft. Michio Kaku

Use case Quantum AI Suggested by
Equity and FX trading βœ… McKinsey
Cryptography βœ… McKinsey
Sales, marketing, distribution βœ… McKinsey

Cost to Buy or Use

How much does a quantum computer cost to buy? 10 Apr 2023: Article

What quantum computer services are available?

Our Investments in AI and Quantum Computing Companies

Investment in quantum technology has something in common with SchrΓΆdinger's principle: you invest your money but you don't know if that was a good idea or not until you measure the outcome. As of April 2024, many quantum computing companies are underperforming as investors adopt a "wait and see" strategy - waiting for the opening of SchrΓΆdinger's box. But after the box has been opened it's too late to place bets.

We've looked around at where committed and potential companies are in quantum computing and related AI development projects. We've invested in some, and sought to understand the decision drivrs of those who have looked and invested, and those who have looked and walked away. We share the view that quantum computing are powerful enablers for some companies - but not all - based on demand for what quantum computers are good at, and not intended for, such as general computing.

Company Invested Ticker Quantum AI Note
Alphabet βœ… GOOG/L βœ… βœ… Google Sycamore
Amazon AWS βœ… AMZN βœ… βœ… AWS Braket, Bedrock
Atos - βœ…-ATOS Quantum Learning Machine (QLM)
IBM βœ… IBM βœ… βœ… WatsonX
Intel βœ… INTC βœ… - Tunnel Falls Quantum Research Chip
IonQ βœ… IONQ βœ… - Aria, Forte, Tempo
Meta (Facebook) βœ… META βœ… βœ… Meta AI (Llama3)
Microsoft βœ… MSFT βœ… βœ… Azure AI
Nvidia βœ… NVDA βœ… βœ… Nvidia AI
Quantinuum (Honeywell) - HON βœ… - Quantinuum
Rigetti Computing βœ… RGTI βœ… - -
Taiwan Semiconductor Manufacturing Company Ltd - TSM βœ… - -

Quantum computer development requires a business case, budget, commitment, capability: not everyone stays the course, for example Alibaba and Baidu. Meta (Facebook) have also decided not to invest in quantum computing.

So we end this with a World Science Festival 2024 discussion (6 Apr 2024) with Brian Greene, Director of the Center for Theoretical Physics at Columbia University, and Eric Schmidt, former CEO of Google, and on the subject of AI (eg LLM) and quantum computing. Google is deeply engaged in both subjects. ⏯️ Here's the interview.