## Quantum Computers

Quantum computers have the potential to revolutionize computer science. They use quantum mechanical properties to perform calculations and are many times faster than conventional computers.

Quantum computers have the potential to revolutionize computer science. They use quantum mechanical properties to perform calculations and are many times faster than conventional computers. A uniform concept for the realization of quantum computers has not established itself to date, and there are also no efficient algorithms yet (Beach et al. 2004). It is a highly specialized topic.

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#### 1.1 Qubits

A qubit, short for quantum bit, is a quantum mechanical two-level system, such as the two spin states of an electron or the vertical and horizontal polarization of a photon. The difference between a qubit and a classical bit has to do with the states in complex vector space permitted by quantum mechanics. This difference allows qubits to store exponentially more information than traditional bits (DiVincenzo 2000). In this context, nonadiabatic holonomic quantum computing is becoming more and more interesting due to its robustness with regard to control errors (Xu et al. 2015).

#### 1.2 Quantum Circuits

Quantum circuits consist of a collection of quantum gates that perform elementary calculations. This normally produces heat, and quantum systems are very sensitive to heat. Reversible logic shows great potential here, because it can be used to perform calculations where practically no heat is generated (Lin et al. 2015a; Thakral et al.).

Nearest neighbor quantum circuit: In some applications, such as quantum circuits, only adjacent qubits can interact with each other. To bring the two qubits to each other, swap gates are used (Xu et al. 2016a).

#### 1.3 Spin

Spin is the torque associated with quanta. It is specified as a multiple of the reduced Planck constant (Encyclopædia Britannica).

Nitrogen-vacancy center in diamonds: The nitrogen-vacancy center is an atomic defect in the crystal lattice of diamonds. It is optically active and has an electron spin in the ground state. The spin can be used as a qubit and a field sensor (Neumann 2012).

#### 1.4 Entanglement

Entanglement describes a state of multiple quanta that cannot be characterized as a product of the individual quanta. Entangled states are common in quantum mechanics, but cannot be measured by classical methods (Wu et al. 2016b).

Hyper-entanglement: Hyper-entanglement, the entanglement of a quantum system in multiple degrees of freedom, can improve the channel capacity and security of quantum communication over long distances (Bao-Cang and Fu-Guo 2015).

Rydberg blockade: The Rydberg blockade is an atom-atom interaction that can be used to create quantum circuits (Gonçalves and Marcassa 2016; Zhang et al. 2012).

#### 1.5 Security With Quantum Computers

Quantum computers offer a high degree of security, since data transmission cannot be manipulated or intercepted with current means.

- Quantum image processing: In image processing, there are some applications, such as the use of watermarks, which are virtually unsolvable with classical computing systems. Since quantum computers theoretically have a much higher computational speed, some of these problems could be solved with their help (Beach et al. 2004).
- Blind Quantum Computing: With Blind Quantum Computation, the user can submit calculations to a server that is not trusted. The algorithms and data remain hidden and can neither be intercepted nor manipulated (Perez-Delgado and Fitzsimons 2015; Takeuchi et al. 2016).

#### 1.6 Algorithms For Quantum Computers

Classic algorithms cannot simply be adopted for quantum computers because the system architectures are fundamentally different. The development of efficient quantum algorithms is thus a current field of research.

- Quantum Walk: Quantum Walk is a theoretical model for the temporal development of discrete quantum systems and is used for the development of algorithms (Luo and Xue 2015).
- Quantum-inspired particle swarm optimization: Classic particle swarm optimization solves continuous optimization problems. More efficient classical algorithms are inspired by the parallel characteristics of quantum computation (Huang et al. 2015b; Zouache et al. 2016).

#### 1.7 Error Tolerance Of Quantum Computers

Quantum states are difficult to control, often causing errors. The susceptibility of quantum gates to heat is a particular problem. Error rate of quantum gates: Quantum gates perform the elementary operations of a quantum computer and should have the lowest possible error rate. Notable advances have been made in recent years in this area (Sanders et al. 2016).

#### 1.8 Topological Quantum Computers

Topological quantum computers are a type of quantum computer that is robust with regard to decoherence (Shi et al. 2016).

Majorana Fermions: Majorana Fermions are elementary particles that are their own antiparticles. They have a potential application in error-tolerant topological quantum computing (Yang and Jian-Hong 2015).

#### 1.9 Quantencomputer in der Optik

Since photons are also used in quantum computers, some actions can also be performed using classical optics (Leverrier and Garcia-Patron 2015).

Boson sampling: During Boson sampling, a quantum computer achieves a much higher speed than a classical computer. Boson sampling is a scientific research issue. Its most important feature is that this issue can be solved with the current technology of nonlinear optics and does not require a complete quantum computer (Huh et al. 2015; Leverrier and Garcia-Patron 2015).