Quantum computer

Quantum computers can use quantum-mechanical phenomena such as superposition and entanglement to perform computation. These are able to solve certain computational problems, such as integer factorization, of which underlies RSA (Rivest–Shamir–Adleman) encryption, for example, an order of magnitude faster than a traditional computer could.

Binary code represents information as either a 0 or 1, and these traditional von Neumann architecture computers are better at serial processing. Quantum computers are better at parallel processing because they use qubits, which are simultaneously both 0 and 1. Qubits are formed by the quantum states of particles, for example, the spin state of individual electrons. This superposition of states allows a quantum computer to test every possible combination of qubits at the same time. A thousand qubit system could test $2^{1000}$ potential solutions in the blink of an eye, thus vastly outperforming a conventional computer even with parallel processing across thousands of CPUs. To get a sense for the magnitude of $2^{1000}$ (which is approximately $10^{301}$ ), note that there are only about $10^{80}$ atoms in the visible universe.

Time crystals are used to stabilize qubits. They are resistant to entropy and can be used for quantum memory. A time crystal was recently observed by Google.

Applications suited to a high degree of parallelism:

Quantum entanglement and modelling for quantum teleportation systems.
Computational chemistry, for example a new drug R&D program is trial and error, iterative, time-consuming and expensive.
Particle physics workflows such as needed for colliders; quantum chromodynamics and quantum physics.
Molecular modeling such as in chemical reactions that are quantum in nature, forming entangled quantum superposition states.
Global weather prediction and modelling. 30 percent of world GDP is directly or indirectly affected by weather, impacting food production, transportation and trade. Another benefit is giving ourselves time to take cover from disasters.
Artificial Intelligence and Machine Learning, based on calculating the probabilities for many possible choices.
Cybersecurity and cryptography. New quantum-resistant cryptography methods would be needed that would resist quantum computers able to crack the old prime factorization methods.
Financial Modelling and stock markets. Randomness inherent to quantum computers is congruent to the stochastic nature of financial markets. Investors often wish to evaluate the distribution of outcomes under an extremely large number of scenarios.
Combinatorics and set theory
Chaos Theory
Simulating the electronic structure of a small molecule

Although no current quantum computers are powerful enough to do so against any real implementations, a vulnerability for traditional encryption such as that used in cryptocurrency, and the most popular cryptographic algorithm, as of 2022, AES, is that quantum computers will be able to crack them. Math problems, like the ones encrypting our sensitive data today, that, for certain algorithms, would take a traditional supercomputer millions of years to solve could be solved by theoretical future quantum computers in downwards of 48 hours. In a cryptographic attack known as "capture now, decrypt later", people and governments are harvesting encrypted data today to, in theory, decrypt later with quantum computers. In the near future once quantum computers are mainstream, they will be used to breach our current non-resistant cryptographic defenses.

Two ways of circumventing this problem would be to create traditional encryption algorithms that are quantum resistant, Post-quantum cryptography, or adopt quantum encryption algorithms, Quantum cryptography, that would be impossible for traditional or quantum computers to crack. Quantropi claims to be one of the world's first companies to offer the latter method with their non-photonic quantum key distribution that works over the cloud - so clients are able to use existing infrastructure and the internet to encrypt their sensitive information into quantum states of entropy. Quantropi’s QEEP symmetric encryption ensures "uncertainty" to attackers, rendering data uninterpretable forever. They also provide a quantum-secure layer to AES encryption.

A quantum computer using nanotechnology is a moleculartronic computer.

Quantum Supremacy[]

if you can state a computational problem that is computationally expensive for a classical computer using all known algorithms and techniques, but that is much easier and less computationally expensive for a quantum computer, and you can demonstrate a vast speed-up in computational time using a quantum computer, then Quantum Supremacy will have been achieved. This has been achieved since 2019.

Current fastest quantum processors that have achieved quantum supremacy:

Google's Sycamore processor - 53 qubits
China's photonic Jiuzhang - 53 qubits
China's Zuchongzhi processor - 66 qubits (link)
2021: IBM's Eagle chip has 127 qubits
2023: IBM's Osprey Processor has 433 qubits
IBM Condor at 1121 qubits released in 2023
Atom Computing at 1180 qubits in October 2023

Quantum Advantage[]

Quantum Advantage would be achieving Quantum Supremacy for a problem that’s actually relevant to the real world, such as the double slit experiment in the Heisenberg Uncertainty Principle.

The quantum supremacy and quantum advantage definitions have become blurred and almost synonymous. Current preference is for quantum advantage, since "supremacy" has a negative connotation.