Quantum Computing. Melanie Swan

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      The normal speed-up in quantum computing compared to classical computing is due to the superposition of 0s and 1s, in that the quantum circuit can process 0s and 1s at the same time. This provides massive parallelism by being able to process all of the problem inputs at the same time. Photonics allows an additional speed-up to the regular speed-up of quantum computing. In photonic quantum computing, superposition can be used not only for problem inputs but also for processing gates (Procopio et al., 2015). Time can be accelerated by superpositioning the processing gates. Standard quantum architectures have fixed gate arrangements, whereas photonic quantum architectures allow the gate order to be superimposed as well. This means that when computations are executed, they run through circuits that are themselves superpositioned. The potential computational benefit of the superposition of optical quantum circuits is an exponential advantage over classical algorithms and a linear advantage over regular quantum algorithms.

3.3.7 Neutral atoms, diamond defects, quantum dots, and nuclear magnetic resonance

      Overall, there are many methods for generating qubits and computing with them (Table 3.3). In addition to the four main approaches (superconducting circuits, ion traps, Majorana fermions, and photonics), four additional approaches are discussed briefly. These include neutral atoms, diamond defects (nitrogen-vacancy defect centers), quantum dots, and nuclear magnetic resonance (NMR).

      3.3.7.1Neutral atoms

      An early-stage approach to quantum computing is neutral atoms. Neutral atoms are regular uncharged atoms with balanced numbers of protons and electrons, as opposed to ions that are charged because they have had an electron stripped away from them or added to them. Qubits are produced by exciting neutral atoms trapped in optical lattices or optical arrays, and qubits are controlled in computation by another set of lasers. The neutral atoms are trapped in space with lasers. An optical lattice is made with interfering laser beams from multiple directions to hold the atoms in wells (an egg carton-shaped structure). Another method is holding the atoms in an array with optical tweezers. Unlike ions (which have strong interactions and repel each other), neutral atoms can be held in close confinement with each other and manipulated in computation. Atoms such as cesium and rubidium are excited into Rydberg states from which they can be manipulated to perform computation (Saffman, 2016). Researchers have been able to accurately program a two-rubidium atom logic gate 97% of the time with the neutral atoms approach (Levine et al., 2018), as compared to 99% fidelity with superconducting qubits. A 3D array of 72 neutral atoms has also been demonstrated (Barredo et al., 2018).

Table 3.3. Qubit types by formation and control parameters.

Qubit type	Qubit formation (DiVincenzo criterion #1)	Qubit control for computation (DiVincenzo criteria #2–5)
1.Superconducting circuits	Electrical circuit with oscillating current	Electromagnetic fields and microwave pulses
2.Trapped ions	Ion (atom stripped of one electron)	Ions stored in electromagnetic traps and manipulated with lasers
3.Majorana fermions	Topological superconductors	Electrically controlled along non-Abelian “braiding” path
4.Photonic circuits	Single photons (or squeezed states) in silicon waveguides	Marshalled cluster state of multidimensional entangled qubits
5.Neutral atoms	Electronic states of atoms trapped by laser-formed optical lattice	Controlled by lasers
6.Quantum dots	Electron spins in a semiconductor nanostructure	Microwave pulses
7.Diamond center defects	Defect has an effective spin; the two levels of the spin define a qubit	Microwave fields and lasers

      Source: Adapted from McMahon (2018).

      3.3.7.2Diamond defects (nitrogen-vacancy defect centers)

      An interesting approach, although one that may have scalability challenges for commercial deployment, is diamond center defects. Imperfections in the crystal lattice within diamonds are commonplace and have been exploited for a variety of uses from crystallography to the development of novel quantum devices. Defects may be the result of natural lattice irregularities or artificially introduced impurities. For quantum computing, impurities are introduced by implanting ions to make nitrogen-vacancy photonic centers. A nitrogen vacancy can be created in a diamond crystal by knocking out a carbon atom and replacing it with a nitrogen atom and also by knocking out a neighboring carbon atom so that there is a vacant spot. The nitrogen vacancy produces the so-called Farbe center (color center), which is a defect in a crystal lattice that is occupied by an unpaired electron. The unpaired electron creates an effective spin which can be manipulated as a qubit. The nitrogen-vacancy defect center is attractive for quantum computing because it produces a robust quantum state that can be initialized, manipulated, and measured with high fidelity at room temperature (Haque & Sumaiya, 2017).

      3.3.7.3Quantum dots

      Another early-stage approach, in the form of a semiconductor concept, is quantum dots (quantum dots are nanoparticles of semiconducting material) (Loss & DiVincenzo, 1998). In this method, electrically controlled quantum dots that can be used as qubits are created from electron spins trapped in a semiconductor nanostructure, and then electrical pulses are used to control them for computation. A semiconductor-based structure is fabricated that is similar to that of classical processors. Metal electrodes are patterned on the semiconductor layer so that electrostatic fields can be made from the wires to trap single electrons. The spin degrees of freedom of the electrons are used as qubits. Within the semiconductor nanostructure, there are small silicon chambers that keep the electron in place long enough to hybridize its charge and spin and manipulate the electron spin–orbit interactions for computation (Petta et al., 2005). The coherence interactions typically last longer in silicon than in other materials, but can be difficult to control. There has been some improvement in controlling qubit decoherence in quantum dot computing models (Kloeffel & Loss, 2013).

      3.3.7.4Nuclear magnetic resonance

      Nuclear magnetic resonance (NMR) is one of the first approaches to quantum computing, but is seen as being difficult to scale for commercial purposes. NMR uses the same technology that is used in medical imaging. The physics principle is that since atoms have spin and electrical charge, they may be controlled through the application of an external magnetic field. In 2001, IBM demonstrated the first experimental realization of quantum computing, using NMR (Vandersypen et al., 2001). A 7-qubit circuit performed the simplest instance of Shor’s factoring algorithm by factoring the number 15 (into its prime factors of 3 and 5).

References

      Barredo, D., Lienhard, V., Leseleuc, S. et al. (2018). Synthetic three-dimensional atomic structures assembled atom by atom. Nature 561:79–82.

      Bednorz, J.G. & Muller, K.A. (1986). Possible high TC superconductivity in the Ba-La-Cu-O system. Zeit. Phys. B. 64(2):189–93.

      Bennett, C.H. & DiVincenzo, D.P. (2000). Quantum information and computation. Nature 404:247–55.

      Chen, L., Jordan, S., Liu, Y.-K. et al. (2016). Report on post-quantum cryptography. NIST Interagency Report 8105.

      Deutsch, D. (1985). Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. Roy. Soc. Lond. A. 400(1818):97–117.

      DiVincenzo, D.P. (2000). The physical implementation of quantum computation. Fortschrit. Phys. 48(9–11):771–83.

      Drozdov, A.P., Eremets, M.I., Troyan, I.A. et al. (2015). Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system. Nature 525(7567):73–6.

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