What is Quantum Computing ?

I chose Quantum computing for my Literature review project in Smart materials, for which I had to read about 10 research papers along with a variety of blogs and resources(All of them are mentioned at the end).

In this blog, I will be covering the basics of quantum mechanics and principles of quantum mechanics used in quantum computing, the basics of quantum computing and the principles of quantum computing, Qubits vs bits, Qubit gates and Qubit Circuits.

Q.What do you mean by Quantum Mechanics?

Quantum mechanics can be thought of roughly as the study of physics on very small length scales, although there are also certain macroscopic systems it directly applies to.

The descriptor “quantum” arises because, in contrast with classical mechanics, certain quantities take on only discrete values. However, some quantities still take on continuous values.

Q.What do you mean by Quantum Computing?

Quantum computing is essentially harnessing and exploiting the laws of quantum mechanics to process information. In traditional computers, we use “bits,” which encode either a zero or a one. In quantum computers, we use quantum bits or qubits. A qubit is a quantum system that encodes the zero and the one into two distinguishable quantum states. We can capitalize on the phenomena of “superposition” and “entanglement.”

What do you mean by these terms?

1. Superposition is essentially the ability of a quantum system to be in multiple states at the same time.
2. Entanglement is an extremely strong correlation that exists between quantum particles, that two or more quantum particles can be inextricably linked in perfect unison, even if separated by great distances.

Q.How can these terms help in quantum computers?

Thanks to superposition and entanglement, a quantum computer can process a vast number of calculations simultaneously. A classical computer works with ones and zeros, a quantum computer will have the advantage of using ones, zeros and “super-positions” of ones and zeros. Certain difficult tasks that have long been thought impossible for classical computers will be achieved quickly and efficiently by a quantum computer.

A few Quantum terminologies to know,

1.Quantum Interference: Quantum interference is the intrinsic behaviour of a qubit, due to superposition, to influence the probability of it collapsing one way or another. Quantum computers are designed and built to reduce interference as much as possible and ensure the most accurate results.

Algorithms can use interference effects to make the wrong answers cancel out quickly and give us a high probability of measuring the right answer. This is the idea behind quantum computing.

2.Coherence: Quantum coherence deals with the idea that all objects have wave-like properties. If an object’s wave-like nature is split in two, then the two waves may coherently interfere with each other in such a way as to form a single state that is a superposition of the two states.

Coherence also lies at the heart of quantum computing, in which a qubit is in a superposition of the “0” and “1” states, resulting in a speed-up over various classical algorithms.

3.Decoherence: The interaction of qubits with their environment in ways that causes damage to their quantum behaviour is called decoherence.

The slightest vibration or change in temperature disturbances known as “noise” in quantum-speak can cause them to tumble out of superposition before their job has been properly done. That’s why researchers do their best to protect qubits from the outside world in those supercooled fridges and vacuum chambers.

But despite their efforts, noise still causes lots of errors to creep into calculations. Smart quantum algorithms can compensate for some of these, and adding more qubits also helps.

Q.How does a Quantum Computer work?

Quantum computers perform calculations based on the probability of an object’s state before it is measured, so instead of just 1s or 0s, which means they have the potential to process exponentially more data compared to classical computers.

Rather than having a clear position, unmeasured quantum states occur in a mixed ‘superposition’, not unlike a coin spinning through the air before it lands in your hand.

An Example, If the qubit is in a superposition of the 1 state and the 0 state, and it performed a calculation with another qubit in the same superposition, then one calculation actually obtains 4 results: a 1/1 result, a 1/0 result, a 0/1 result, and a 0/0 result. This is a result of the mathematics applied to a quantum system when in a state of decoherence, which lasts while it is in a superposition of states until it collapses down into one state. The ability of a quantum computer to perform multiple computations simultaneously (or in parallel, in computer terms) is called quantum parallelism.

Q.How can we measure the probability of an object’s state before it is measured?

British Physicist Thomas Young in 1801 performed an experiment known as Young’s Double Slit Experiment to demonstrate the wave behaviour of light in which he placed two very thin slits in front of a source of light.

That light is diffracted through those pair of vertical slits. Then they interfere with each other to form an interference pattern on a screen where he found many vertical lines being spread out horizontally. When light passes through narrow slits, it is diffracted into semicircular waves.

This experiment predicted the probability of a light pattern being displayed at a particular location on the screen due to constructive and destructive interferences long before the light actually passed through the slits.

Q.What is required to build a quantum computer?

We need qubits that behave the way we want them to. These qubits could be made of photons, atoms, electrons, molecules or perhaps something else.

One method to create a qubit uses superconductivity to create and maintain a quantum state. To work with these superconducting qubits for extended periods of time, they must be kept very cold. Any heat in the system can introduce error, which is why quantum computers operate at temperatures close to absolute zero, colder than the vacuum of space.

Q. What do you mean by Qubit Gates?

Quantum gates are analogous to ordinary logic gates (the fundamental building blocks of circuits), but they must be unitary transformations.

1.Single-qubit gates: Any single-qubit gate is the rotation of our qubit’s state to a different point on the Bloch Sphere. The NOT gate is simple because it is reversible: NOT|0>=|1>, NOT|1>=|0>.

In quantum mechanics, the NOT transformation is usually called X.It is one of four useful unitary operations, called the Pauli matrices, which are worth remembering. On the standard basis

The X, Y,and Z operators get their names from the fact that they reflect state vectors along the x, y, z axes of the Bloch-sphere representation of a qubit, which we will not use in this book. Since they are reflections, they are Hermitian (their own inverses).

2.Multiple qubit gates: Multi qubit gates work on two qubits or more qubits. The controlled NOT( CNOT) gate has two inputs: the first determines what it does to the second (negate it or not).

Its first argument is called the control and its second is called the target, controlled, or data qubit. It is a simple example of conditional quantum computation. If the gate requires the control qubit to be in the |1〉 state, this is denoted by a filled-in circle on the control qubit’s wire. If the condition is set on the control qubit being in the |0> state instead.

Another useful gate is the three-input/output Tofoli gate or controlled-controlled-NOT. It negates the third qubit if and only if the first two qubits are both 1

Q.What do you mean by Quantum Circuits?

A quantum circuit is a sequential series of quantum transformations on a quantum register. The inputs are usually computational basis states. Quantum circuit diagrams are drawn with time going from left to right, with the quantum gates crossing one or more qubits as appropriate.

The circuit represents a sequence of unitary operations on a quantum register rather than physical wires. Quantum Circuit Diagrams rules are,

1. In a circuit diagram, time moves from left to right
2. Each qubit is represented by a single, horizontal line
3. Most gates are represented by boxes, the letters/symbols within giving us information about what kind of gate it is
4. Some gates can have multiple diagram elements (e.g. NOT)
5. The act of measuring a qubit causes any superpositions to collapse and its quantum properties to vanish, returning classical information. Hence, the measurement element below is seen to take in a qubit and output a classical bit.

Q.What are Applications of quantum computing?

The quantum computer is inherently faster than a classical computer is at searching through a space of potential solutions for the best solution or factoring really large numbers for cryptographical algorithms. Some of its applications are,

1. A processor with programmable superconducting qubits.
2. Machine Learning algorithms such as regression and classifications being performed on a quantum computer(Even normal algorithms like Divide and conquer).
3. Cryptography and security of data at rest and transit
4. Big data query optimization
5. A small programmable quantum computer with atomic qubits
6. A Router Implementation using a quantum computer

Although a fully functioning quantum computer is a longer-term goal, many fundamental and practical discoveries have been made in the name of quantum computing.

I think if we make use of quantum computing for the processing of data and classical computing for displaying the data or some other combination of both, our processing capacities can increase significantly.

I am still working on publishing my literature review, please reach out to me if you would like to read it. Also, let me me know where i could improve at.

Blog References:

1. https://arcb.csc.ncsu.edu/~mueller/qc/qc18-2/qc18/readings/quantum_circuits_part1.pdf
2. https://web.eecs.utk.edu/~bmaclenn/Classes/494-UC/handouts/LNUC-III.C.2-5.pdf
3. https://docs.microsoft.com/en-us/azure/quantum/overview-qdk
4. https://docs.microsoft.com/en-us/learn/paths/quantum-computing-fundamentals/
5. https://www.ibm.com/quantum-computing/learn/what-is-quantum-computing/
6. https://phoenixnap.com/blog/what-is-quantum-computing-how-works