Quantum computing is the area of study focused on developing computer technology based on the principles of quantum theory.

Tens of billions of public and private capital are being invested in quantum technologies. Countries around the world have realized that quantum technologies can be a huge disruptor of existing businesses, they have collectively invested $24 billion in quantum research and applications in 2021.

**A comparison of classical and quantum computing**

**classical computing** it is based, at its ultimate level, on the principles expressed by Boolean algebra. The data must be processed in an exclusive binary state at any time or what we call bits. While the time each transistor or capacitor needs to be at 0 or 1 before changing state can now be measured in billionths of a second, there is still a limit to how quickly these devices can change state.

As we move towards smaller and faster circuits, we begin to reach the physical limits of materials and the threshold for the classical laws of physics to apply. Beyond this, the quantum world takes over, in a quantum computer, various elementary particles such as electrons or photons can be used either with their *position *either *Polarization *acting as a representation of 0 and/or 1.** **Each of these particles is known as a quantum bit, or *qubit*, the nature and behavior of these particles form the basis of quantum computing. Classical computers use transistors as the physical building blocks of logic, while quantum computers can use trapped ions, superconducting loops, quantum dots, or vacancies in a diamond.

**Physical vs Logical Qubits**

When we talk about error-correcting quantum computers, we talk about physical and logical qubits. Physical qubits are the physical qubits in quantum computers, while logical qubits are groups of physical qubits that we use as a single qubit in our computation to combat noise and improve error correction.

To illustrate this, let’s consider an example of a quantum computer with 100 qubits. Let’s say this computer is prone to noise, to remedy this we can use multiple qubits to form a more stable single qubit. We might decide that we need 10 physical qubits to form an acceptable logical qubit. In this case, we would say that our quantum computer has 100 physical qubits which we use as 10 logical qubits.

It is important to distinguish between physical and logical qubits. There are many estimates about how many qubits we will need to perform certain calculations, but some of these estimates talk about logical qubits and others talk about physical qubits. For example: to break the RSA cryptography we would need thousands of logical qubits but millions of physical qubits.

Another thing to note, in a classical computer, the computing power increases linearly with the number of transistors and the clock speed, while in a quantum computer, the computing power increases exponentially with the addition of each logical qubit.

**Quantum superposition and entanglement**

The two most relevant aspects of quantum physics are the principles of *overlap *Y *tangle*.

**Overlap**: Think of a qubit as an electron in a magnetic field. The spin of the electron can be aligned with the field, known as the spin-up state, or opposite the field, known as the spin-down state. According to quantum law, the particle enters a superposition of states, in which it behaves as if it were in both states simultaneously. Each qubit used could take on a superposition of 0 and 1. Where a 2-bit register in an ordinary computer can store only one of four binary configurations (00, 01, 10, or 11) at any given time, a 2-bit register The register in a quantum computer can store all four numbers simultaneously, because each qubit represents two values. If more qubits are added, the increased capacity expands exponentially.

**entanglers**t: Particles that have interacted at some point retain a type of connection and can become entangled with each other in pairs, in a process known as correlation. Knowing the spin state of an entangled particle, up or down, lets you know that its partner’s spin is in the opposite direction. Quantum entanglement allows qubits that are separated by incredible distances to interact with each other instantly (not limited to the speed of light). No matter how great the distance between the correlated particles, they will remain entangled as long as they are isolated. Taken together, quantum superposition and entanglement create vastly improved computing power.

**Quantum computers fall into four categories:**

- Emulator/Quantum Simulator
- quantum annealing
- Noisy Intermediate Scale Quantum (NISQ)
- Universal quantum computer, which may be a cryptographically relevant quantum computer (CRQC)

**Emulator/Quantum Simulator**

These are classical computers that you can buy today that simulate quantum algorithms. They make it easy to test and debug a quantum algorithm that may one day run on a universal quantum computer (UQC). Since they don’t use any quantum hardware, they aren’t faster than standard computers.

**quantum annealing**

A special-purpose quantum computer designed to run only combinatorial optimization problems, not general-purpose computation or cryptography problems. While they have more physical Qubits than any other system today, they are not organized as gate-based logical qubits. Currently this is a commercial technology in search of a viable future market.

**Noisy Intermediate Scale Quantum Computers (NISQ).**

Think of these as *prototypes* of a universal quantum computer, with several orders of magnitude fewer bits. They currently have between 50 and 100 qubits, limited gate depths, and short coherence times. As there are several orders of magnitude of Qubits, NISQ computers cannot perform any useful computations, however they are a necessary phase in learning, especially to drive total system and software learning in parallel to hardware development. Think of them as the training wheels for future universal quantum computers.

**Universal Quantum Computers / Cryptographically Relevant Quantum Computers (CRQC)***)*

This is the ultimate goal. If you could build a fault-tolerant universal quantum computer (i.e. millions of error-corrected physical qubits resulting in thousands of logical qubits), you could run quantum algorithms in cryptography, search and optimization, quantum system simulations, and problem solvers. linear equations.

**Post-quantum/quantum resistant codes**

The new cryptographic systems would be secure against conventional and quantum computers and could interoperate with existing communication protocols and networks. The symmetric key algorithms of the Commercial National Security Algorithm Suite (CNSA) were selected to be safe for use by national security systems, even if a CRQC is developed. Cryptographic schemes that are believed by the commercial industry to be quantum secure include** **cryptography based on lattices, hash trees, multivariate equations and elliptic curves of supersingular isogeny.

**Difficulties with quantum computers**

• **Interference** – During the computation phase of a quantum computation, the slightest disturbance in a quantum system (for example, a stray photon or wave of EM radiation) causes the quantum computation to collapse, a process known as *decoherence*. A quantum computer must be totally isolated from all external interference during the calculation phase.

• **correction bug** – Given the nature of quantum computing, error correction is ultracritical: even a single error in a calculation can cause the validity of the entire calculation to collapse.

• **Output Compliance** – Closely related to the previous two, retrieving output data after a quantum computation has completed risks corrupting the data.** **