How can a quantum computer prove that it is superior?

Subject :Science and Tech

Section: Awareness in computers

Source: TH

Quantum Computing (QC):

QC technology promises more speed and more efficient problem-solving abilities, challenging the boundaries set by classical, conventional computing.
Quantum supremacy is the term used for these computing techniques as QCs have the ability to solve some problems much faster than a classical computer.

Facing the quantum challenge:

Quantum computers use quantum bits, or qubits, whereas classical computers use binary bits (0 and 1).
Qubits are fundamentally different from classical bits as they can have the value 0 or 1, as a classical bit can, or a value that’s a combination of 0 and 1, called a superposition.
- Superposition states allow qubits to carry more information. This capacity of quantum computers allows them to perform a disproportionately greater number of operations.
Qubits also exhibit entanglement, meaning that two qubits can be intrinsically linked regardless of their physical separation. This property allows quantum computers to tackle complex problems that may be out of reach of classical devices.
Scalability- Biggest advantage of QCs:
- In classical computers, the processing power grows linearly with the number of bits. While in QCs it grows exponentially as 2ⁿ, where n is the number of qubits.

#P-hard problems:

Quantum circuits (core of QCs) consist of qubits and quantum gates.
In such a circuit, a quantum gate could manipulate the qubits to perform specific functions, leading to an output.
Classical computers struggle with #P-hard problems – a set of problems that includes estimating the probability that random quantum circuits will yield a certain output.
#P-hard problems are a subset of #P problems, which are all counting problems.
If a problem is #P-hard, then it is so challenging that if you can efficiently solve it, you can also efficiently solve every other problem in the #P class by making certain types of transformations.

Taking the Cayley path:

Cayley path is a mathematical construct developed by Dr. Movassagh to prove that certain classes of problems can be solved by quantum computers but not by classical computers.

Quantum complexity theory:

Dr. Mossavagh’s paper shows that there exists a problem that presents a computational barrier to classical computers but not to quantum computers (assuming a quantum computer can crack a #P-hard problem).
The theory also challenges the extended Church-Turing thesis, which is the idea that classical computers can efficiently simulate any physical process.
The establishment of quantum supremacy will have a positive impact in the field of cryptography.

Quantum Technology

Quantum Technology is based on the principles of Quantum mechanics that was developed in the early 20th century to describe nature at the scale of atoms and elementary particles.
The first phase of this revolutionary technology has provided the foundations of our understanding of the physical world, including the interaction of light and matter, and led to ubiquitous inventions such as lasers and semiconductor transistors.
A second revolution is currently underway with the goal of putting properties of quantum mechanics in the realms of computing.

Properties of Quantum Computing

Superposition – It is the ability of a quantum system to be in multiple states simultaneously.
Entanglement– It means the two members of a pair (Qubits) exist in a single quantum state. Changing the state of one of the qubits will instantaneously change the state of the other one in a predictable way. This happens even if they are separated by very long distances.
- Einstein called spooky ‘action at a distance’.
Interference – Quantum interference states that elementary particles (Qubits) can not only be in more than one place at any given time (through superposition), but that an individual particle, such as a photon (light particles) can cross its own trajectory and interfere with the direction of its path.

The bit is the fundamental unit of a classical computer.
- Its value is 1 if a corresponding transistor is on and 0 if the transistor is off.
- The transistor can be in one of two states at a time – on or off – so a bit can have one of two values at a time, 0 or 1.
In the Qubits, instead of being either 1 or 0, the information is encoded in a superposition: say, 45% 0 plus 55% 1.
This is entirely unlike the two separate states of 0 and 1 and is the third kind of state.
One qubit can encode two states. Five qubits can encode 32 states. A computer with N qubits can encode 2N states – whereas a computer with N transistors can only encode 2 × N states.
So a qubit-based computer can access more states than a transistor-based computer, and thus access more computational pathways and solutions to more complex problems.
It’s typically a particle like an electron.

What are Transmons:

In quantum computing, and more specifically in superconducting quantum computing, a transmon is a type of superconducting charge qubit that was designed to have reduced sensitivity to charge noise.
Google and IBM have been known to use transmons, where pairs of bound electrons oscillate between two superconductors to designate the two states.

Potential Applications For Quantum Computing

National Mission on Quantum Technology and Applications (NMQTA)

Union Budget 2020-21 proposed to spend Rs 8,000 crore on the newly launched NMQTA.
In 2018, the Department of Science & Technology unveiled a programme called Quantum-Enabled Science & Technology (QuEST) and committed to investing Rs. 80 crore over the next three years to accelerate research.
The mission seeks to develop quantum computing linked technologies amidst the second quantum revolution and make India the world’s third-biggest nation in the sector after the US and China.