The World Needs Programmers

For these new kinds of [Quantum] computers. And such programmers have to be part scientists and part engineers.

They have to understand Quantum Physics, Quantum Mechanics, Quantum Chemistry, Quantum Electrodynamics, Quantum Computing...

...And The Art of Computer Programming [Donald Knuth]

2 Approaches

(i) Given a Problem design or use a Suitable Algorithm. [Programming/Algorithms]

(ii) Create a Algorithm First that can Solve Problems Given Later. [Designing The Right Kind of Quantum Computers With Foresight Of The Problems]

Topological Computing

Topological quantum computation aims to achieve its goal by using non-Abelian quantum phases of matter. Such phases allow for quantum information to be stored and manipulated in a nonlocal manner, which protects it from imperfections in the implemented protocols and from interactions with the environment.

Adiabatic Computing

Adiabatic quantum computation (AQC) is a form of quantum computing which relies on the adiabatic theorem to do calculations and is closely related to, and may be regarded as a subclass of, quantum annealing.

The term Adiabatic comes from the theory of thermodynamics. Adiabatic means ‘without changing the amount of heat’. There are several processes that one wants to conduct without changing the amount of heat. Usually, these processes are done very slowly. This guarantees that they will be reversible. Quantum computation is also a reversible process, and the above computation is carried out very slowly, hence the term adiabatic.

Quantum Annealing & Optimization

Quantum annealing (QA) is a metaheuristic for finding the global minimum of a given objective function over a given set of candidate solutions (candidate states), by a process using quantum fluctuations. Quantum annealing is used mainly for problems where the search space is discrete (combinatorial optimization problems) with many local minima; such as finding the ground state of a spin glass. It was formulated in its present form by T. Kadowaki and H. Nishimori in "Quantum annealing in the transverse Ising model"

Quantum Monte Carlo

(1) Diffusion Monte Carlo
(2) Variational Monte Carlo

Quantum Monte Carlo encompasses a large family of computational methods whose common aim is the study of complex quantum systems. One of the major goals of these approaches is to provide a reliable solution (or an accurate approximation) of the quantum many-body problem. The diverse flavor of quantum Monte Carlo approaches all share the common use of the Monte Carlo method to handle the multi-dimensional integrals that arise in the different formulations of the many-body problem. The quantum Monte Carlo methods allow for a direct treatment and description of complex many-body effects encoded in the wave function, going beyond mean field theory and offering an exact solution of the many-body problem in some circumstances. In particular, there exist numerically exact and polynomially-scaling algorithms to exactly study static properties of boson systems without geometrical frustration. For fermions, there exist very good approximations to their static properties and numerically exact exponentially scaling quantum Monte Carlo algorithms, but none that are both.

Quantum Walks & Search

Quantum walks are quantum analogues of classical random walks. In contrast to the classical random walk, where the walker occupies definite states and the randomness arises due to stochastic transitions between states, randomness arises in quantum walks through: (1) quantum superposition of states, (2) non-random, reversible unitary evolution and (3) collapse of the wavefunction due to state measurements.

As with classical random walks, quantum walks admit formulations in both discrete and continuous time.

The relevance of finite Markov chains (random walks in graphs) to searching was recognized from early on, and it is still a flourishing field.

Grover search, and in general amplitude amplification are well known quantum procedures which are provably faster than their classical counterpart.

Others...

Quantum Fourier Transforms

Quantum Physics

Quantum Chemistry

Materials

Analog Quantum Computers

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