Chapter 3 : Implementation

The theory of quantum computing has always been surrounded by lots of hype and intrigue. It is true that quantum computers, which operate at very cold temperatures, are the intended solution to problems that would take classical machines a lifetime. Since we have already explained the theoretical approach and the structure of its basic algorithms, the remaining question is : How to build a quantum computer ?

The central premise of this chapter is directed to the architectural analysis of these supercomputers. It's extremely difficult to build these large-scale machines because of the delicacy of quantum phenomena in nature which are only studied at very small isolated physical systems like atoms and photons. The storage of binary information is carried out in a single unit of quantum data called qubit, according to many methods. In fact, they can be stored in the polarization of a photon for example, or in the energy states of atom.

A- Qubits: Building Blocks of Quantum Computers :

First of all, let's start by how the qubits are physically made. Figure x shows us a schematic illustration of the basic building block of a quantum computer: The superconducting qubit which can be considered as a "quantum transistor" (also called a SQUID, Superconducting QUantum Interference Device).

figure x: Schematic of a superconducting qubit.

As a matter of fact, this structure supports the quantum effects like electron waves allowing the main qubit behavior. This is basically due to the properties of the material from which a qubit is made. The large circle in the scheme is made from niobium, a very rare metal, while classical transistors are made from silicon. Once the temperature of this metal decreases until it's cooled down, it becomes what we call a superconductor, and it starts to demonstrate quantum mechanical properties.

Using voltages, a conventional transistor, , the fundamental unit of classical computers, provides you with two different binary states. The superconducting qubit structure instead provides you with two states as small magnetic fields, which either point up or down.

Schematic of qubit states

B- Quantum Hardware Implementation Methods

Building quantum computers represents a tempting challenge to computer engineers and applied physicists. While their implementation is still under development , some few qubits-based small quantum machines have been satisfyingly built and well tested .

There are many different implementation methodologies of quantum hardware. In this part, we consider five which proved long term implementation capacities: NMR, ion traps , all optical , super conducting and quantum dots. And we will also consider their strengths and weaknesses to create a clear comparison between their differences and similarities.

I. NMR

In 1997, Nuclear Magnetic Resonance (NMR) technique appeared as the most promising technology in the context of quantum computation hardware. Since then, all quantum algorithms have been demonstrated by NMR. This technique is based on the use of molecules and their spin states. The molecules are perceived as qubits and they make the building units of larger systems which must be in a state of thermal equilibrium. Mathematically speaking, this state is represented by the density matrix :

where H is the Hamiltonian matrix of an individual molecule and

where k is the Boltzmann constant and T the temperature.

These are three techniques of NMR:

1) Solution NMR:

In a solution NMR, the qubit is designated by the spin of the atomic nucleus that processes once it gets into a magnetic field. It is addressed by frequency which changes depending on the atoms' position in the carefully planned molecule the solution NMR deals with. I this regard, a liquid solution holds many copies of this entity and each is an independently-running quantum computer.

Strengths and Weaknesses of Solution NMR.

2) All-Silicon NMR

This technique uses the properties of 29Si to build quantum computers. The qubits are stored in the nuclear spin( with a value of 1/2 ) and are put horizontally in a line across a micromechanical bridge of spin 0 nuclei. A passable signal requires 10^5 copies for measurement. "Readout is done via magnetic resonance force microscopy (MRFM), reading oscillations of the bridge. Unitization is done via electrons hose spins are set with polarized light. Operations are done via microwave radiation directed at the device."

Strengths and Weaknesses of All-Silicon NMR

figure x : Schematic of All-Silicon NMR

3) Kane Solid State NMR

A solid-state quantum computer is made entirely of semiconductor Silicon with great scalability being built on Very-large-scale integration ( VLSI ) technology for control. This system was first proposed by Kane in 1998 and was studied afterwards by engineers like Oskin , Copsey et al, who suggested moving qubits long distance using teleportation for error correction. In a solid state NMR system , separated phosphorus atom is inserted in a silicon substrate. In the spin of this atomic nucleus ,the qubit is held and interacts with other near qubits by electrons paired with the nuclei via superfine interactions .

Strengths and Weaknesses of Kane Solid State NMR

II. Ion Trap

In this scalable system , the storage of qubits occurs in the energy level of separated ions. Large system of interconnected traps is the result of ion trap experiments performed on few ions in one trap. In practice , ions are placed in magnetic fields so they could move around to make them reach operation areas to bring them together, as shown in the figure below. We apply laser pulses on the multi-qubit gates made ion chains to deliver fluorescence considered as a 1 or not so to deliver a 0 to accomplish the readout.

Strengths and Weaknesses of Kane Solid State NMR

A six-zone trap capable of moving individual ions.

III. All-Optical

There are two categories of All-optical systems , Linear Optics Quantum Computation (LOQC ) where measurement is the only nonlinear property , and those depending on many nonlinear effects to execute the gates. Experts have considered the fact that light sources are capable of producing definite numbers of photons in a precise period of time with measurement -based gates and high quality single photon indicators.

Strengths and Weaknesses of Kane Solid State NMR

Strengths Weaknesses

Well-understood physics and easy fabrication. Photon losses; for nonlinear systems, weak nonlinear effects give poor gate quality; high resource requirements for probabilistic gates.

IV. Super conducting

There are three kinds of super conducting devices: those using charge , flux or phase to represent quantum bits. This technology uses classical electron-beam lithography - the practice of scanning a focused beam of electrons to draw custom shapes on a surface covered with an electron-sensitive film - and shadow evaporation method , also called Niemeyer -Dolan technique, to create nanometer-sized structures .

Strengths and Weaknesses of Super conducting

Strengths Weaknesses

Very fast gates, advanced experimental demonstration, straightforward fabrication. Low coherence time relative to measurement time, sensitivity to background charge fluctuations and local magnetic fields.

V. Quantum Dot

In the context of quantum information processing , a "quantum dot" is created by the gathering of electrons in a small location. This is generated by the variation of the electrical potential of a two-dimension electronic gas formed by the detained electrons in the boundary layer that separates two materials. The spin ,the energy levels of electron confined in a quantum dot or the number of electrons can entirely define the qubit . A couple of quantum dots can be used a dual-rail where the left one represents a logical 0 and the other is a 1.

Strengths and Weaknesses of Quantum Dot

Conclusion

In this section of this report , a brief explanation of quantum computers hardware implementation methods was given along with the strengths and weaknesses of each method.

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