From Quantum Biology to Quantum Computing
Erwin Schroedinger was a physicist that made several attempts to construct a unified field theory of our universe.
He is famous for a book called “What is Life?” where he described the problems of genetics, looking at the phenomenon of life from the point of view of physics.
He described an essence so small to be in any cell but so significant to contain the complete information of our body. That was the DNA.
Schroedinger announced the field of study in Quantum Biology with his book.
Quantum Mechanics has always been a great way to describe our universe and the world of biology. Indeed, in biology, Quantum Mechanics can explain many principles we couldn’t understand otherwise.
Let’s remember the theory of olfaction, our Vision, Magnetoreception to make birds flight accordingly, Photosynthesis and DNA mutations.
Those are just a few examples of what the field looks like.
In general, those systems are based on reducing the Gibbs energy and increasing Entropy.
To describe all that is present in biology, we need to define its fundamentals: Quantum Computing.
Quantum Computing
Quantum computing exploits collective properties of quantum states, such as superposition and entanglement, to perform computation. It’s handy when considering complex systems because it can represent nature as a whole.
When we work on numerical problems, we use numbers from 0 to 9, with classical computing, which becomes from 0 to 1.
Let’s imagine the number 2021; in binary, it would be 11111100101.
The binary syntax works everywhere, from Linkedin posts to Alexa’s answers. It’s how our world works.
With Quantum Computing, the game is entirely different, and we call “Qubit” the fundamental element present either in state 1 or in state 0 or any combination of values in between. You can imagine Classical computing as a switch and Quantum Computers as a sphere that can be in any position.
Bra-ket Notation
If we want to understand why that happens, we can develop a new computational way of describing the system called bra-ket notation, also called Dirac notation. The bra-ket notation is used to describe a quantum state in terms of vectors. It is divided into 2 different parts.
Having a vector v, we can define bra notatin and ket notation.
The bra notation is “bra v” written as ⟨v|
The ket notation is the conjugate transpose of bra written as |v⟩
It’s all about Probability
Since the states |0⟩ and |1⟩ form an orthonormal basis, we can represent any 2D vector combining these two states.
They are two-state linear combinations, each with its own coefficient. We can call those coefficients amplitudes of the states.
When solving a problem with Qubits, we need to define the differences in amplitude of those states.
The probability of each state is directly proportional to the square of the magnitude of its coefficient. We can’t be sure at 100% if what we want to do will happen. Indeed, that’s why Quantum Computers aren’t so much precise and need to repeat calculations at different times before finding a correct solution.
The Bloch Sphere
When we describe complex numbers, we have different ways to express them.
The best way of representing Qubits depends on the situation.
Since we cannot measure the global phase, we can only estimate the difference in phase between the states |0⟩ and |1⟩. Instead of having α and β be complex, we can confine them to the real numbers and add a term to tell us the relative phase between them:
Another way to describe them is
P.S. You can try this interactive system to visualise anything clearer
it’s easy to confuse the qubits statevector with its Bloch vector. Remember the statevector is the vector with the 2 parameters (α and β) in complex numbers, that holds the amplitudes for the two states our qubit can be in.
The Bloch vector is a visualisation tool that maps the 2D, complex statevector onto real, 3D space. It’s something used to understand Quantum Computing better
Quantum Entanglement
Quantum entanglement is a phenomenon that happens when different particles, also called qubits, are extremely close between each other and interact in a way that we cannot describe the quantum state of each particle of the group independently of the state of the others.
That also happens when a significant distance separates the particles.
Quantum entanglement, in physics, can be called linear combination in mathematics. They mean the same things, even if we say that in completely different ways.
It’s like when someone says Hello, Ciao or Salut. It means the same thing in different languages.
That links with Qubits is generally possible with different operations that we call Quantum Gates.
Quantum Gates are unitary matrices
Mathematically speaking, U is unitary if its conjugate transpose U* is also its inverse. Physically Speaking, unitary matrices don’t change the length of vectors. And that’s why they are so important Quantum Computing.
Quantum Algorithms
Quantum algorithms are the consequences of Quantum Gates.
Indeed, Quantum Gates and Qubits aren’t necessary by themselves. The union of them can make them more convenient than classical computing in specific tasks.
There are different Quantum Algorithms such as Shor’s Factoring Algorithm, Grover’s Algorithm and Deutsch-Jozsa Algorithm. Taking Shor’s Factoring Algorithm as an example, you can factor in large numbers in far less time than classical computers. The difference could be even 1000 times or more.
Let’s talk about what makes magic possible: Quantum Gates.
Quantum Gates
Quantum Gates are Quantum operations like are + — / and * in mathematics.
We can remember:
- The Pauli Gates (X Y and Z)
- The Hadamard Gate
- The P-gate
- The I, S and T-gates
- The U-gate
The X-Gate
the X-gate switches the amplitudes of the states |0⟩ and |1⟩
The Y-gates
The Y-gate performs rotations by π around the y-axis of the Bloch sphere.
The Z-gates
The Z-gate performs rotations by π around the z-axis of the Bloch sphere
Remember that Using only the Pauli-gates, it is impossible to move our initialised qubit to any state other than |0⟩ or |1⟩, i.e. we cannot achieve superposition.
This means we can see no behaviour different to that of a classical bit. To create more exciting states, we will need more gates!
The Hadamard Gate
It allows us to move away from the poles of the Bloch sphere and create a superposition of |0⟩ and |1⟩
The P-gate
The P-gate (phase gate) uses a parameter. It needs a number (ϕ) to tell it exactly what to do. The P-gate performs a rotation of ϕ around the Z-axis direction. It has the matrix form:
P.S. ϕ is a real number
Quantum Supremacy
Quantum supremacy or quantum advantage is the goal of demonstrating that a programmable quantum device can solve a problem that no classical computer can solve in any feasible amount of time.
It involves both the engineering task of building a powerful quantum computer and the computational-complexity-theoretic task of finding a problem that can be solved by that quantum computer (using Quantum gates) and has a speed over the best known or possible classical algorithm for that task.
In October 2019, engineers from Google claimed that they had achieved this fantastic milestone.
Their 54-qubit Sycamore processor performed a random sampling calculation in just 200 seconds, 1.58 billion times faster than their projection for how long it would take the fastest classical supercomputer to execute the same computation: 10,000 years. The experiment was published in Nature, and it made the history of Computer Science.
The Quantum Problem
Quantum computers can contain far more logic gates than regular classical computers, which have the potential to calculate and solve problems at speeds much faster than the computers we used today, as seen above.
Why aren’t Quantum Computers anywhere in the world?
It’s because of decoherence
Decoherence can be viewed as the loss of information from a system into the environment. Decoherence is caused by temperature change, electromagnetic waves, interactions with an outer environment, vibrations, and other minor disruption that destroys the computer’s quantum properties.
The way to avoid decoherence is by isolating quantum systems
If a quantum system were perfectly isolated, it would maintain coherence indefinitely, but it would be impossible to manipulate or investigate it. Michele Morello, for example, worked on a silicon quantum processor unit cell above one kelvin, far above the current possibilities. Taking that idea, in the future, we may have Quantum Computers at higher temperatures, too.
Conclusion
We described what Quantum Biology is going deeper on its principles. We talked about Qubit, the Quantum States and Logic Gates. When we define Quantum Computing, we are the beginning of it with incredible new possibilities in the future.
