Quantum Computing

Latest update: 🇦🇺 23:35 📆 6 May 2024

🔺 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 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).

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).

Sidebar Sycamore is the world's 4th fastest supercomputer. "Hewlett Packard Enterprise's Frontier, or OLCF-5, is the world's first exascale supercomputer. It is hosted at the Oak Ridge Leadership Computing Facility (OLCF) in Tennessee, United States and became operational in 2022. As of December 2023, Frontier is the world's fastest supercomputer. It is based on the Cray EX and is the successor to Summit (OLCF-4). Frontier achieved an Rmax of 1.102 exaFLOPS, which is 1.102 quintillion floating-point operations per second (FLOPS), using AMD CPUs and GPUs." More

A simple explanation of how a quantum computer solves problems faster than a supercomputer 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 supercomputer 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 thousand 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 ⏯️ Schrödinger principle.

Examples of strategies used in quantum computers:

• ⏯️ Trapped Ion Quantum: IonQ,
• Quantinuum (Honeywell+Cambridge)
• ⏯️ Photonic Quantum: Xanadu
• ⏯️ Quantum Annealing: D-wave
• ⏯️ Quantum Dot Qubits: Intel
• ⏯️ Silicon Spin Qubits:
  • Intel Tunnel Falls
  • Silicon Quantum Computing
• ⏯️ Superconducting Qubits: Bleximo, QuEra
• ⏯️ Topological Majorana Fermion
• ⏯️ Transmon Qubits: Google, IBM, Rigetti

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

• Bosons
• Fermions
• Gravitons

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.

𝐋𝐋𝐎𝐘𝐃

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?

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

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 a class of elementary particles that obey the Pauli Exclusion Principle. Fermions are characterized by having half-integer values of spin (such as 1/2, 3/2, etc.) according to quantum mechanics. The Pauli Exclusion Principle states that no two fermions within the same quantum system can occupy the same quantum state simultaneously. This principle is crucial in understanding the behavior of electrons in atoms, for example.

About spin: "Spin is quantized, meaning it can only take certain discrete values. Particles are categorized based on the value of their spin. Fermions, such as electrons and quarks, have half-integer spin values (e.g., 1/2, -1/2), while bosons, like photons and gluons, have integer spin values (e.g., 0, 1, 2)."

Source: Wikipedia

Some examples of fermions include:

• Quarks: Quarks are fundamental constituents of matter. There are six types, or "flavors," of quarks: up, down, charm, strange, top, and bottom. Quarks combine to form particles such as protons and neutrons.
• Leptons: Leptons are another class of elementary particles. Examples include the electron, muon, and tau particles, as well as their associated neutrinos.
• Baryons: Baryons are composite particles made up of three quarks. Baryons are also classified as fermions because they have half-integer spin. Protons and neutrons are examples of baryons.
• Atomic Nuclei: Nuclei, composed of protons and neutrons, are also made up of fermions.
• Some Atoms and Molecules: Atoms and molecules composed of an odd number of fermions are also considered fermions due to the properties of their constituent particles.

Fermions have spin values that are half-integer multiples of ħ (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 ħ.

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

𝐋𝐋𝐎𝐘𝐃

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

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

OK, 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:

• Position: If one electron is located at a specific point in space, the other electron cannot occupy that exact same point simultaneously. This prevents them from being on top of each other in the same place.
• Spin: If one electron has a spin of +1/2 along a certain axis, the other electron cannot have the same spin along that axis. The second electron must have a spin of -1/2 along that axis or some other spin state. This ensures that they don't have identical spin configurations.
• Energy and Momentum: If one electron has a specific energy and momentum, the other electron cannot have precisely the same energy and momentum. They may have similar values, but they cannot be exactly the same.

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.

𝐋𝐋𝐎𝐘𝐃

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).'”

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

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:

• Low Temperatures: Creating a BEC requires extremely low temperatures, typically only a fraction of a degree above absolute zero. At these temperatures, the thermal energy is so low that the quantum effects dominate the behavior of the particles.
• Quantum Mechanical Effects: In the quantum world, particles don't behave like classical objects with well-defined positions and velocities. Instead, they have wave-like properties described by wave functions. When many bosons are cooled to extremely low temperatures, their wave functions start to overlap, and they can occupy the same quantum state.
• Macroscopic Quantum Phenomenon: The Bose-Einstein Condensate (BEC) is a macroscopic manifestation of quantum mechanics. Even though individual particles are subject to quantum uncertainty, when many of them come together in a BEC, their collective behavior becomes more predictable and coherent.
• Unique Properties: BEC exhibit fascinating properties, such as superfluidity and coherence times over macroscopic distances. Superfluidity means that the condensate can flow without any viscosity, meaning it flows forever without dissipating energy. Coherence refers to the fact that all the particles in the condensate act in unison, like one giant quantum wave.
• Experimental Realization: BECs were first experimentally realized in dilute atomic gases cooled to ultra-low temperatures using techniques like laser cooling and evaporative cooling. Since their discovery, BECs have been studied extensively in physics laboratories around the world for their unique properties and potential applications in fields like quantum computing and precision measurement.

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

𝐋𝐋𝐎𝐘𝐃

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?

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

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.

𝐋𝐋𝐎𝐘𝐃

Just as atoms have atomic weights, do subatomic particles (such as bosons) have "physical substance" or are they parcels of attributes such as spin?

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

Subatomic particles, including bosons such as photons, W and Z bosons, gluons, and the Higgs boson, don't have a "physical substance" in the classical sense like macroscopic objects do. Instead, they are best understood as excitations or manifestations of quantum fields.

In quantum field theory, particles are often described as excitations of underlying fields that permeate space. These fields are more fundamental than the particles themselves. For example, the photon is the quantum of the electromagnetic field, and the Higgs boson is associated with the Higgs field.

The properties of subatomic particles, such as mass, charge, and spin, are indeed fundamental attributes that characterize them. However, it's important to note that these properties emerge from the behavior of the underlying quantum fields rather than being intrinsic properties of "tiny objects" with definite size and shape.

The concept of "physical substance" becomes somewhat ambiguous at the subatomic scale due to the principles of quantum mechanics. Subatomic particles can exhibit wave-particle duality, meaning they can behave both as particles and waves depending on the experimental context.

So, while subatomic particles don't possess physical substance in the way macroscopic objects do, they do have attributes such as spin, charge, and mass that define their behavior and interactions. These attributes arise from the properties of the underlying quantum fields.

𝐋𝐋𝐎𝐘𝐃

So what does it mean for a boson to be cooled to a very low temperature?

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

Cooling a boson to very low temperatures typically refers to the process of reducing the thermal motion of the particles, thereby bringing them to a state where their quantum behavior dominates. This is often achieved through techniques like laser cooling and evaporative cooling.

At very low temperatures, close to absolute zero (-273.15°C or 0 Kelvin), the kinetic energy of the particles is minimized, and they start to exhibit behaviors dictated by quantum mechanics rather than classical physics. For bosons, this can lead to the formation of a Bose-Einstein condensate (BEC), a state of matter in which a large fraction of bosons occupy the lowest quantum state available to them.

In a BEC, bosons lose their individual identities to a certain extent and behave collectively as a single quantum entity. This results in fascinating phenomena such as superfluidity and superconductivity, where the material flows without resistance or conducts electricity without energy loss, respectively.

Cooling bosons to very low temperatures allows researchers to study these quantum phenomena and explore fundamental aspects of quantum mechanics. It also has practical applications in fields like precision measurement, quantum computing, and atom interferometry.

𝐋𝐋𝐎𝐘𝐃

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

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

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:

• Quantum Gates: BECs can serve as qubits, the basic units of quantum information in a quantum computer. The quantum states of BECs can be manipulated using techniques such as laser cooling and trapping. By controlling the interactions between the atoms or particles comprising the BEC, it's possible to perform quantum logic operations, such as quantum gates, which are the building blocks of quantum algorithms.
• Quantum Entanglement: BECs can be used to generate and manipulate entangled states, which are a fundamental resource for quantum computing. Entanglement allows for correlations between qubits that are stronger than any classical correlation, enabling quantum computers to perform certain tasks more efficiently than classical computers.
• Quantum Simulation: BECs can be used to simulate the behavior of complex quantum systems, which is useful for understanding phenomena such as superfluidity, magnetism, and phase transitions. Quantum simulation involves encoding the properties of a quantum system into the states of qubits and manipulating those qubits to emulate the behavior of the original system.
• Quantum Sensing and Metrology: BECs can be used as ultra-sensitive detectors for measuring various physical quantities, such as magnetic fields, gravitational fields, and accelerations. This capability can be harnessed for quantum-enhanced sensing and metrology applications, which have potential applications in fields such as navigation, medical imaging, and fundamental physics research.
• Quantum Communication: BECs can be employed in the development of quantum communication protocols, which enable secure transmission of information over long distances using quantum principles. BECs could serve as the basis for quantum repeaters, which are devices that extend the range of quantum communication by mitigating the effects of signal loss in optical fibers.

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.

𝐋𝐋𝐎𝐘𝐃

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

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

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:

• H: Hadamard Gate: The Hadamard gate is a fundamental gate in quantum computing that creates superposition. When applied to a qubit in the state |0⟩, it puts it into an equal superposition of |0⟩ and |1⟩. Mathematically, it transforms the state |0⟩ to (|0⟩ + |1⟩) / √2 and |1⟩ to (|0⟩ - |1⟩) / √2.
• Ry: Rotation Gates: Rotation gates rotate the qubit's state vector around the Y-axis on the Bloch sphere. The parameter 'y' in Ry(theta) determines the angle of rotation around the Y-axis. These gates are used to manipulate the phase of a qubit.
  
  
• The U2 gate is a single-qubit quantum gate that belongs to the family of universal single-qubit gates. It's closely related to the more general U3 gate. The U2 gate performs a specific type of rotation on the Bloch sphere, similar to the U3 gate, but with fewer parameters. The U2 gate is parametrized by two angles, denoted as φ and λ. Mathematically, the U2 gate can be represented as:
  
  The U2 gate performs a rotation about the Bloch sphere axis defined by the angles φ and λ. The U2 gate is useful in quantum algorithms and circuits, providing a convenient way to manipulate qubit states. It's worth noting that while the U2 gate is more limited compared to the U3 gate in terms of the range of rotations it can perform, it still offers significant flexibility in quantum computations.
• U3: The U3 gate is a general single-qubit quantum gate that allows arbitrary rotations around the Bloch sphere. It's defined by three parameters: θ, φ, and λ. It's capable of implementing any single-qubit operation. About the Bloch sphere.

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 Quantum™ 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.

𝐋𝐋𝐎𝐘𝐃

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⟩ = α|↑⟩ + β|↓⟩

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

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

• |ψ⟩ is the symbol representing the quantum state.
• α and β are numbers called probability amplitudes.
• |0⟩ and |1⟩, or α|↑⟩ and β|↓⟩ represent two possible states of a quantum system. These are often called "qubits," and they can be thought of as being in two different states at the same time due to a property called superposition.

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

𝐋𝐋𝐎𝐘𝐃

Entanglement: Whereas quantum experiments entangle two subatomic particles (say we're referring to bosons) can 3 subatomic particles become entangled?

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

Yes, it's possible for more than two subatomic particles to become entangled in a phenomenon known as multipartite entanglement. In quantum mechanics, entanglement is a phenomenon where the quantum states of multiple particles are correlated with each other, even when they are separated by large distances. This means that the state of one particle cannot be described independently of the state of the others.

Multipartite entanglement involves entangling three or more particles. The entangled state of multiple particles can exhibit complex correlations and behaviors that are not possible with just two particles.

For example, in experiments involving photons or other quantum particles, researchers have demonstrated multipartite entanglement involving three or more particles. These states are crucial for various quantum information processing tasks such as quantum cryptography, quantum teleportation, and quantum computing.

Entanglement among multiple particles can be more intricate than entanglement between pairs of particles and can lead to novel phenomena and applications in quantum technology.

𝐋𝐋𝐎𝐘𝐃

What is the largest number of the same type of subatomic particles that have been entangled, and what type of particles were they?

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

As of my last update in January 2022, the largest number of identical particles that have been experimentally entangled is 20. These particles were photons, entangled in a multipartite state in a laboratory experiment.

This experiment was conducted by a team of researchers led by Jian-Wei Pan at the University of Science and Technology of China. They published their findings in the journal Nature Photonics in 2020. The experiment demonstrated the entanglement of 20 photons, surpassing the previous record of 15 entangled photons.

Entangling such a large number of particles is a significant achievement in the field of quantum mechanics and quantum information science. It opens up possibilities for exploring complex quantum phenomena and developing new applications in quantum communication, quantum computing, and quantum metrology.

𝐋𝐋𝐎𝐘𝐃

Can different types of particles (eg bosons and fermions) become entangled?

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

In principle, yes, different types of particles can become entangled with each other, including bosons and fermions. However, there are some important distinctions to consider.

Bosons and fermions are two fundamental classes of particles in quantum mechanics, distinguished by their quantum statistics:

• Bosons follow Bose-Einstein statistics, which means they are indistinguishable and can occupy the same quantum state simultaneously. Examples of bosons include photons, gluons, and certain types of atomic nuclei.
• Fermions follow Fermi-Dirac statistics, which dictate that no two fermions can occupy the same quantum state simultaneously. Examples of fermions include electrons, protons, neutrons, and quarks.

Entanglement can occur between particles of the same type (e.g., entangled photons) or between particles of different types (e.g., entangled photons and entangled electrons). However, the behavior of entangled systems involving different types of particles can be more complex due to their different properties and interactions.

For example, in experiments involving quantum dots, researchers have demonstrated entanglement between an electron (a fermion) and a photon (a boson). These types of entanglement can have important implications for quantum communication and quantum information processing.

Overall, while entanglement between different types of particles is possible, it introduces additional complexity and considerations compared to entanglement between particles of the same type.

𝐋𝐋𝐎𝐘𝐃

Are gravitons subatomic particles, and if so are they included in the Standard Model?

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

Gravitons are theoretical particles that are hypothesized to be carriers of the gravitational force in quantum field theory. They are postulated within the framework of quantum mechanics and general relativity, aiming to unify the description of gravity with the other fundamental forces described by the Standard Model of particle physics.

However, it's important to note that gravitons have not been directly detected or observed experimentally as of the last update. Unlike other particles such as photons (carriers of electromagnetic force) or gluons (carriers of the strong force), which have been detected and studied extensively, gravitons remain hypothetical.

In the Standard Model of particle physics, which describes the fundamental particles and their interactions, gravitons are not explicitly included. This is because the Standard Model primarily deals with three of the four fundamental forces: electromagnetism, the weak nuclear force, and the strong nuclear force. Gravity, described by general relativity, is not fully compatible with the quantum field theories that underpin the Standard Model.

Efforts to reconcile quantum mechanics with general relativity and incorporate gravity into the framework of the Standard Model have led to theories such as string theory and loop quantum gravity. These theories propose the existence of gravitons and aim to provide a quantum description of gravity. However, confirming the existence of gravitons and integrating gravity into the Standard Model remains one of the major challenges in theoretical physics.

𝐋𝐋𝐎𝐘𝐃

This is later than your Dec 2022 training data: "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

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

The information you provided highlights the reasoning behind the theoretical characteristics of gravitons, particularly their spin and behavior as predicted by quantum field theory. It's indeed crucial to consider these theoretical foundations when discussing the nature of gravitons.

The FermiLab article you referenced discusses ongoing research efforts to find evidence for particles behaving like gravitons. If these findings are confirmed, it could provide significant support for the existence of gravitons and further our understanding of quantum gravity.

In light of this, while gravitons remain theoretical and have not yet been directly detected, ongoing research in experimental physics and theoretical frameworks such as quantum field theory and general relativity continues to explore the nature of gravity at the quantum level.

𝐋𝐋𝐎𝐘𝐃

Staying with the issue of gravitons and the standard model, as I understand it, while the particles in the standard model repel, gravitons attract. Can you provide any explanation for these differences? How would gravitons attract?

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

The difference in behavior between the particles described by the Standard Model of particle physics and gravitons, which are hypothesized carriers of the gravitational force, arises from their fundamental properties and the nature of the forces they mediate.

Spin and Force Mediation:

Particles in the Standard Model, such as photons (mediators of the electromagnetic force) and gluons (mediators of the strong nuclear force), have a spin of 1 and mediate forces that can both attract and repel.

Gravitons, on the other hand, are hypothesized to have a spin of 2. This difference in spin leads to distinct behavior. Theoretical considerations suggest that a massless particle with spin 2, like the graviton, would necessarily lead to a force that only attracts, rather than repels. This is a consequence of the mathematical structure of general relativity, where gravity arises from the curvature of spacetime caused by the distribution of mass and energy.

Curvature of Spacetime:

In general relativity, gravity is not described as a force between two objects in the same way as electromagnetism or the strong force. Instead, gravity is a consequence of the curvature of spacetime caused by the presence of mass and energy. Objects with mass or energy "curve" the fabric of spacetime around them, and the motion of other objects is influenced by this curvature. This is what we perceive as the force of gravity.

Gravitons, if they exist, would be the quantum excitations of this curved spacetime. They would carry the gravitational force, but instead of "pulling" objects toward each other in the way that particles mediating other forces do, they would transmit the effects of the curvature of spacetime, resulting in what we observe as gravitational attraction.

So, while particles in the Standard Model can mediate both attractive and repulsive forces, the behavior of gravitons is fundamentally different due to the unique nature of gravity as described by general relativity. Gravitons would transmit the effects of curved spacetime, leading to the attractive behavior we observe as gravitational attraction.

𝐋𝐋𝐎𝐘𝐃

What coding languages are used in quantum computing?

Is Qiskit a commonly used language?

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

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:

• Qiskit: Qiskit is an open-source quantum computing framework developed by IBM. It provides tools for writing quantum algorithms, simulating quantum circuits, and interfacing with IBM's quantum processors through the cloud. Qiskit offers a Python-based interface, making it accessible to both quantum researchers and software developers.
• Quipper: Quipper is a functional programming language for quantum computing developed at Microsoft Research and the University of Oxford. It is designed to express quantum algorithms in a high-level, functional style, allowing for concise and readable code.
• Cirq: Cirq is an open-source quantum computing framework developed by Google. It allows users to write quantum algorithms and simulate quantum circuits using Python. Cirq is designed to be flexible and suitable for both researchers and developers working on quantum computing projects.
• Quil instruction set: PyQuil is a Python library for writing and executing quantum programs using the Quil instruction set, which is the native language of Rigetti Computing's quantum processors. It provides tools for defining quantum circuits, compiling them into executable programs, and interfacing with Rigetti's quantum hardware.
• Q# Microsoft Quantum Development Kit: Microsoft provides a Quantum Development Kit, which includes the Q# programming language and associated tools for developing quantum algorithms. Q# is a domain-specific language designed for expressing quantum operations and algorithms in a high-level, structured manner.

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.

𝐋𝐋𝐎𝐘𝐃

What are the most commonly used quantum computers?

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

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

• IBM Quantum: IBM offers access to a fleet of quantum processors through the IBM Quantum Experience platform. These processors are based on superconducting qubits and are available for both research and educational purposes.
• Google Quantum AI: Google has developed its quantum processors based on superconducting qubits, which are used for both research and development of quantum algorithms. They have made significant advancements in areas such as quantum supremacy and error correction.
• Rigetti Computing: Rigetti Computing offers access to their quantum processors through their Quantum Cloud Services platform. Their processors are based on superconducting qubits, and they provide tools and resources for quantum algorithm development.
• IonQ: IonQ is known for its trapped-ion quantum computing platform. Trapped ions offer long coherence times, making them suitable for certain types of quantum computations. IonQ provides access to their quantum processors through Amazon Web Services Braket and Google cloud-based services.
• D-Wave Systems: D-Wave specializes in quantum annealing technology, which is particularly well-suited for optimization and sampling problems. Their quantum annealers are available for commercial use through cloud-based services.

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.

𝐐𝐈𝐒𝐊𝐈𝐓

List of Quantum Logic Gates

Qiskit

𝐒𝐭𝐞𝐩 1

• 1.1: How are your Python skills?
• 1.2: IBM Qiskit - Tutorials and courses
• 1.3: Learn about quantum computing, eg what is a Hadamard Gate?

𝐒𝐭𝐞𝐩 2

• # Install Qiskit
• !pip install qiskit
• !pip install qiskit-ibm-runtime

𝐋𝐋𝐎𝐘𝐃

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

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

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 Developers

Bureaux

Amazon Braket offers access to a range of gate-based quantum computers, including super-conducting: Rigetti and OQC, and ion-trap: IonQ

IBM Quantum Experience: IBM offers access to a fleet of quantum processors through IBM Quantum Experience: IBM Quantum Falcon, Hummingbird, Eagle, and Condor. These processors are based on superconducting qubits and are available for both research and educational purposes.

Developers and Manufacturers

Quantum computers are grouped by their computing strategy and ranked by fault tolerances. Assessments of their strategies are provided by ChatGPT (December 2022)

⏯️ Topological Majorana Fermion
This technology has the potential for high fault tolerance due to its topological protection against local errors. However, it's still in early stages of development and practical implementation.

⏯️ Superconducting Qubits: Bleximo, QuEra
Superconducting qubits have shown promising progress in fault tolerance, with various error correction techniques being developed to improve their performance.

⏯️ Trapped Ion Quantum: IonQ. Inc [NYSE:IONQ], Quantinuum (Honeywell+Cambridge)
Trapped ions have relatively long coherence times and low error rates, making them promising for fault-tolerant quantum computing. However, scaling remains a challenge.

⏯️ Transmon Qubits: Google Quantum AI [GOOG/L:NASDAQ], International Business Machines Corporation [NYSE:IBM], Rigetti Computing, Inc. [NASDAQ:RGTI]
Transmon qubits have seen significant development and are being actively pursued by major players in the field. Error rates have been decreasing steadily, but achieving fault tolerance still requires further advancements.

⏯️ Quantum Dot Qubits: Intel [NASDAQ:INTC
Quantum dot qubits show potential for fault tolerance, but they face challenges in scalability and coherence times compared to some other technologies.

⏯️ Silicon Spin Qubits: Silicon Quantum Computing
Silicon spin qubits hold promise due to their compatibility with existing semiconductor technology. However, achieving fault tolerance with silicon spin qubits is still an ongoing research area.

⏯️ Photonic Quantum: Xanadu
Photonic quantum computing has unique advantages such as low error rates and potential for high-fidelity operations. However, fault tolerance in photonic quantum computing is still an area of active research.

⏯️ Quantum Annealing: D-Wave Quantum, Inc: [NYSE:QBTS]
Quantum annealers like D-Wave's systems are designed for specific optimization problems rather than universal quantum computing. While fault tolerance is less of a concern for their targeted applications, they may not be suitable for fault-tolerant quantum computation in the general sense.

⏯️ Fusion: PSIQuantum
Fusion-based architectures, as proposed by PsiQuantum, are still theoretical and in early stages of development. While the fusion-based approach holds promise, its fault tolerance capabilities are yet to be fully explored and understood within the context of practical quantum computing implementations.

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.

Sycamore is a transmon superconducting quantum processor created by Google's Artificial Intelligence division. Google AI is a research division that offers free, open source products and services.

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:

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.

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

A transmon superconducting quantum processor is a type of quantum computing architecture based on superconducting circuits. It consists of superconducting qubits, which are the basic units of quantum information processing.

The transmon qubit is a variant of the superconducting qubit that has been optimized for coherence time and ease of control. It is typically composed of a Josephson junction (a device formed by two superconducting materials separated by a thin insulating barrier) and a capacitor. By tuning the parameters of the Josephson junction and capacitor, researchers can engineer the energy levels of the qubit, allowing for precise manipulation and readout of its quantum state.

Transmon qubits are designed to have longer coherence times compared to other types of superconducting qubits, making them more suitable for implementing quantum algorithms with many operations or for error correction schemes.

In a transmon superconducting quantum processor, multiple transmon qubits are interconnected through microwave resonators and control lines. These qubits can be manipulated through carefully designed microwave pulses, and their quantum states can be read out using similar techniques.

Overall, transmon superconducting quantum processors represent one of the leading approaches in the pursuit of practical and scalable quantum computing technologies.

⏯️ 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 ions—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:

• Isolation from vibrations: Hanging the components in a suspended manner helps isolate them from vibrations caused by nearby machinery or even footsteps, which can disrupt the fragile quantum states.
• Cryogenic cooling: Many quantum computing systems operate at extremely low temperatures, close to absolute zero. The suspended structure can allow for efficient cooling mechanisms, such as cryogenic cooling systems, to be implemented around the components.
• Electromagnetic shielding: Quantum computers are highly sensitive to electromagnetic interference. Suspending the components can help shield them from external electromagnetic fields.
• Accessibility for maintenance: Suspending the components can also make them more accessible for maintenance and adjustments without compromising their delicate nature.

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?

𝐋𝐋𝐎𝐘𝐃

What makes quantum computing so fast?

𝐂𝐇𝐀𝐓𝐆𝐏𝐓

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.

Discussion

⏯️ 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

Our investments in AI and quantum computing companies

Investment in quantum technology has something in common with Schrödinger's cat in the box: 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 Schrödinger'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 drivers 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.

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Company	Invested	Ticker	Quantum	AI	Note
Amazon AWS	✅	AMZN	✅	-	AWS Braket
Atos	-		✅	-	ATOS Learning Machine
Alphabet	✅	GOOG/L	✅	✅	Google Sycamore
D-Wave Quantum	✅	QBTS	✅	✅	-
IBM	✅	IBM		✅	Watson
Intel Corporation	✅	INTC	✅	-	Tunnel Falls Quantum Research Chip
IonQ	✅	IONQ	✅	-	Aria, Forte, Tempo
Microsoft	✅	MSFT	✅	✅	Azure
Nvidia	✅	NVDA	✅	✅	-
Quantinuum (Honeywell)	-	HON	✅	-	Quantinuum
Rigetti Computing	✅	RGTI	✅	-	-
Taiwan Semiconductor Manufacturing Company Ltd	-	TSM	✅	-	-

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.