*This article is as simple as possible (!) Summary on the working principles of physical systems used in quantum computer research, with the hope that there will be an infrastructure for friends who want to take advanced reading. Since we will talk about the working principles of the systems, we will enter other fields than quantum physics. Before you start, it is highly recommended to read what is quantum superposition, and what is quantum entanglement . Those interested in the theoretical information processing side of the business can read the mathematics of Quantum computers .*

Google's Sycamore chip

Quantum computer, by definition, is trying systems that perform computing operations **based on the basics of quantum physics** and thus assume computing power that conventional computers cannot reach. Quantum bits ( **qubits** ) is one of the physical working principle of quantum computer applications are generally subatomic particle **quantum superposition** flour and **quantum entanglement then** relies na. Thanks to the superposition feature, the amount of information we can encode to qubits increases **exponentially** . In classical processors, while the information is processed one by one (each possibility is tried separately), superposition and entanglement are ** parallel in** quantum computers.

**We are**able to manipulate

**at the same time**. This process, which we can call quantum parallelism, is different with the parallelism we use in conventional computers: the performance of classic supercomputers built on the parallel processor strategy is increasing linearly at best. Because the problem of classical parallelism is to be divided into small pieces and the parameter space is tried in different processors one by one again. A quantum computer with 32 qubits is

**theoretically**While it has 32 possibilities over 2, that is, about 4.3Gbit processing capacity, we can add 10 more qubits to the system (42 over 2) to 4.4Tbit capacity. A system of 300 qubits has the potential to offer processing power with more probability than the number of all atoms in the universe (predicted)! However, in order to use this power in real life,

**all qubits must be interconnected, qubit operations must function perfectly and**we have

**algorithms**that

**can use the system with 100% efficiency**. And the real world is not like a powder pink of course :) Of course, we can only reach the conclusion of one of these possibilities, especially when we want to read the quantum state, which we can call “output”, even if we can manipulate superposition and entanglements in parallel, because in the previous article As we mentioned, the quantum state collapses at the end of the measurement. As we will see later in the article, it is not easy to write a quantum computer algorithm. Things to calculate are no longer 0s, but phases, complex numbers, and quantum wave interference from them. This is one reason why quantum computers

**will rule together**instead of replacing classic computers .There is very little chance (not to mention the speed) of all the processes that the classical computer can do in the near and medium term by quantum computers.

**David DiVincenzo** , one of the famous theorists in the field, **suggested** in an article he wrote in 2000 that **5 main criteria** must be **met** in order to realize quantum computers :

**The physical properties of specific**together with kubit**scalable**system. This system can be a system such as photon qubits with vertical and horizontal polarization, an atom with two energy levels, a particle with two spin states.

The qubits in the system can

**be brought to**a certain (desired)**initial state,**such as | 000… 0⟩ . (The reason for | 0⟩ represents preference because it represents low energy and entropy).

**The ability of the Kubits to maintain their condition**and physical characteristics**consistently**for much longer than required for gate operations . (This is actually a paradox for all quantum systems because the desired situation is that the qubits react minimally to the thermal and electromagnetic effects from the environment, but also our qubits interact as strongly as possible with photons).

**Quantum gate operations**to enable us to apply algorithms on qubits.**Reading the**desired**qubits**at the end of the process .

**Since any two-state quantum system** can be used as a qubit, quantum computer research continues on many different physical platforms with different approaches and models. The model is seen as a bright future, quantum gates in the closest model to the classical computer logic (quantum gates) founded on **quantum circuit model** Although **I bilgis quantum-based measurements** and *"quantum annealing"* based on **adiabatic quantum bilgis I** present different approaches like. Most of the research in the industrial field is on the quantum circuit model.

The currently used quantum computer circuit algorithms are based on single-door and multi-door operations. The one-door operation manipulates a qubite, while the double-door operation manipulates two qubits. Let's take a look at some of these operations before moving on to physical systems, so let's keep in mind what we want to do with them while explaining the systems.

**How does it work?**

**Single qubit operations:** We call the operations performed on a qubit one qubit operations. If we think of Kubiti as a **3D vector** in a sphere (Bloch sphere), the operations made **are about turning the vector around the axes** . Thus, we can position the qubit at any point on the surface of the sphere.

*Hadamard Gate:* Puts the applied qubite **into a superposition** . If we put the resulting superposition back into operation H, we will return to the original qub. It is an unprecedented operation in classical computers.

An important point of this operation is **the** change of the **phase** of the superposition depending on the condition of the qubit entering the process . This phase difference leads to quantum wave interference. I would like to mention a little more detail here because its effect is very important. To understand the quantum wave interference, let's do a simple optical experiment:

The F photon passes through a semi-permeable mirror at point A. This semi-permeable mirror **acts as** a **Hadamard operation** and puts the photon into a superposition. After passing A, the photon proceeds on the X path with a 50% probability, while 50% probability proceeds on the Y path. On the X and Y roads, there are mirrors that reflect fully, and then we put a semi-permeable mirror in the junction again. Considering the classical methods, we say that after the second semi-permeable mirror, the photon falls on the D1 sensor and the D2 sensor falls on a 50% probability. But **when** we really do the experiment, the **D2 sensor always** signals! When we perform the hadamard operation again to the superpositioned qub, **different phases destroy each other because of the wave interference.**and back to what we started.

The meaning of this for quantum computers is to try the possible ways of solving the problem (function) **in multiple layers in parallel** and to present the solution in a **single layer** . One of the most important issues for researchers who write the algorithm is to put as many qubits into parallel processes in multiple layers and obtain the result of the process with as few variables as possible.

*Pauli-X gate:* Rotates the Kubit about *x* around the *x-* axis. NOT gate equivalent on classic computers. Converts | 0⟩ to | 1⟩, | 1⟩ to | 0⟩.

*Pauli-Y gate:* Rotates the Kubit about etrafında around the *y-* axis, so a phase is added to the X gate. Converts | 0⟩ → *i to* | 1⟩, | 1⟩ → *-i* | 0⟩.

*Pauli-Z gate:* Rotates the Kubit about *z* around the *z-* axis. | 0⟩ → | 0⟩, | 1⟩ → *i* | 1⟩

*Phase gates:* There are other gate operations such as S, T, R and NOT, which change the phase of

the | 1⟩ qubit just like the Z gate does.

**Two and multiple qubit operations** : As the name suggests, it is attempted for gate operations that process multiple qubits. We provide entanglement between Kubitler with the help of these operations.

*C-NOT gate: In* this operation we have a control and a target qubit. If our control qubit is | 0⟩, the target qubit does not change. If the **control qub is | 1⟩, we apply the Pauli-X gate to the control qub,** that is, we convert | 0⟩ to | 1⟩, | 1⟩ to | 0⟩.

There are also versions of the same operation with the Pauli-Y, Pauli-Z and C-Phase gate applied.

*SWAP gate:* This operation replaces two qubits. Varieties such as √SWAP and √ *i* SWAP are frequently used in superconducting circuits.

*Toffoli gate* : **Triple qubit** operation , also known as CCNOT gate . If the status of the two control kubs

is | 1⟩, the Pauli-X gate is applied to the third kub.

Apart from these operations, there are more complex operations such as XX, YY, ZZ, Deutsch gates.

**Entangling the qubits: We** can envision our qubits by performing **Hadamard and CNOT** operations in order of 2 qubits . Assuming that we have two qubits in the case of | 0⟩:

The initial state of | 00⟩ becomes | 00⟩ + | 10⟩ with the H gate applied to the first qub. But this is not a Bell situation . By applying the CNOT operation, we make the system one of the **entangled Bell states** .

We can now switch to physical systems.

How is it done?

Now that we know what we want to do, we can look at how we can do it now. As I mentioned before, quantum computer research on different systems continues.

Superconducting circuits, trapped ions, neutral atoms, quantum dots, silicon chips with phosphor atoms implanted are some of them. Even though it has not been demonstrated experimentally, Majorana topological qubits are one of the candidates. But as of now, superconducting circuits and trapped ions lead the race ahead. So we will focus on these two systems.

**Trapped Ions:** Although companies such as IBM, Google, Microsoft and Rigetti are making their investments in superconducting circuits, the first **natural candidate to** come to mind for quantum computing is the **only atomic systems** . Trapped ions are a system that has been studied academically in these single atom systems for a long time and its performance is accepted. Since the **energy levels of** atoms **are discrete** and their **transition energies are different** , we can code these levels as | 0⟩ and | 1⟩. We call the energy difference between the energy level | 0⟩ and the energy of | 1 geçiş, and **at the frequency corresponding to the difference between** these **energy levels.**With a working laser we can raise the atom (electron) to | 1⟩. As the same electron drops from | 1⟩ to | 0⟩, it releases a photon with the same frequency.

Left: Nucleus (center) and discrete electron orbits.Medium: Energy levels that electrons can pass.Right: Display of qubite levels suitable for quantum computer processes, selected from the energy levels of the calcium atom.

It is of course not easy to keep the atoms under control and produce technology with them. The most used method in research is Paul ion trap, which brought **Wolfgang Paul the** 1989 Nobel Prize for Physics. This method is a four-pole trapping that creates an electric field with **DC and AC potentials** applied to the electrodes on both ends and in the middle of the device . Since the trapping is done with an electric field, it is necessary to use ions instead of neutral atoms. In a high vacuum environment (an environment where 100 trillion times less molecules are present than normal room conditions), a metal, such as Calcium, is heated to temperatures higher than 1000 Kelvin, and some atom **becomes gaseous** in the vacuum chamber . These neutral atoms **are shot with high energy electrons.** we turn it into ions and after a while they become imprisoned in traps.

With the AC potential applied at several MHz on the X and Y axes, the ions seem to be sitting on a **saddle** . Trapping on the Z axis is provided with DC potential. But the trapping ions provided by the electric field do not immobilize the ions sufficiently.

We can make the trapped ions even more immobile using **laser cooling techniques** . Atoms absorb photons or emit photons when we send laser beams to atoms, whose frequency corresponds to the transition frequency. Using the absorption and emission effects, **we can control the momentum of the ion, ie its velocity. **Laser beams sent from different and opposite directions thus reduce the speed of the ion and make it more stable. In addition, by using lasers, electrons **are** reduced to **the lowest vibration levels** by means of various optical pumping methods and the ion **is** brought **to minimum energy** .

It may not be easy to determine which energy levels are to be used as | 0⟩ and | 1⟩. When choosing between **dozens of atomic levels** , many parameters should be taken into consideration and experimental problems should be solved and processes should be optimized. However, after that, our trapped ions become ready for quantum computer processes.

David Wineland's trapped ion lab, which received the 2012 Nobel Prize in Physics.The optical table required for laser cooling techniques and qubit operations is at the front and the trapping equipment is at the back.

In order to implement operations where the condition of a qubit, such as the CNOT gate, in trapped ions determines the operation to be performed on the other qub, we have to use **quantum vibration levels as** well as the levels corresponding to the | 0⟩ and | 1⟩ states . As I mentioned above, all ions in the chain are attracted to the lowest energy levels at first. But if we want to circulate the two ions in the chain, we must somehow interact **with** these two ions that **have no physical contact between them** . At this point we are using vibration modes. While the atomic energy levels to be used as the | 0⟩ and | 1⟩ states are selected, the atomic vibration energy levels to be used for this process are also selected. What we want to do is this: when we send a laser pulse to the X ion at a certain frequency,**In the case of | 0⟩, there will be** no **interaction** between **the** laser and the ion . If it is **| 1⟩,** the laser will raise the electron to **a higher level of vibration** . The electron that reaches the upper vibration level **will affect other ions in the** chain due to **Coulomb force** . Immediately after, we will send a laser pulse to the Y ion at a preselected frequency. The laser will **interact** with the Y ion in the **case of the** coulomb force , **but not when it** is **not**. Thus, we can apply the CNOT gate by assigning the X ion as the control qub and the Y ion as the target qubit. At the end of the process, we take the X ion back to the lowest vibration level and continue the algorithm from where it left off. At the end of the algorithm, we send laser pulses to all ions to measure. All superpositions collapse into a random state, and we read the ions in the binary state as binary, 0 or 1. Therefore, the less superpositioned ions at the end of the algorithm, the better overall.

One of the advantages of these systems over other systems is that each ion can **be** easily controlled **individually** with lasers and two qubit operations can be performed **between any two ions** . But as the ion chain gets longer, signal noise and *crosstalk* increase. As the consistency of the quantum states of ions started to take shorter, the speed and reliability of the operation decreases. There are several recommended methods to solve these problems. One single chain, instead of **a 2-dimensional mesh** designed and kubit operations when we want to make two different chains with ions ions that **electric fields with the help of** "common area" is defined as the place **to move**and to carry out the process in this area with two ions side by side. This approach also allows for operation-specific areas such as "memory", "interaction", "measurement" and "loading" on the chip. The disadvantage is that the traps become more **complicated** and the quantum computer speed is limited by the ion transport rate. Another proposed method is to perform the ionic entanglement operation in a *remote* location, as in *classical* quantum optics experiments, instead of using on-chip door operations . This method is based on simply sending a laser pulse to two ions and measuring the photons released from the ions not on the chip but in another location. It is possible to circulate more than two ions with this method, but from the trapped ions in current systems**Since the efficiency of collecting the released photons is** very low, the process speed of creating entanglement is quite low.

**Superconducting circuits: In** recent years, news about the quantum computer have been about the development of such systems, as large companies have invested in superconducting circuits. Using electronic circuits as quantum computer hardware is very attractive for many reasons. Some of these are state-of-the-art **lithography techniques** , our ability to circuit in a few nanometer sizes, the suitability of **microwave control systems** , and the **operating speed** at the nanosecond level . In fact, circuit systems and classical electric flow are not the **first candidates to come to mind** to make quantum systems . Because electronic circuits **macro systems**and they are not systems where quantum effects can be seen directly. Because there are too many electrons in the electric current and electrons constantly collide with each other and with the matter of matter with the effect of the ambient temperature. In quantum information systems, we want single particles to be very well under control. So we have to make such an electronic circuit so that the system behaves like **an artificial single atom** , let's see quantum effects instead of macro effects. And let's mimic **different atomic levels** of **energy ranges** so that we have | 0⟩ and | 1⟩ states in the system.

Although researchers use different qubit models and circuit designs, physical systems are based on circuits using the superconductor **Cooper electron pairs** and **Josephson effect,** which brought the Nobel Prize in Physics 1972 and 1973 respectively . Superconducting materials are tested for substances that do not resist electron flow under a certain temperature (usually at very low temperatures, such as 1 K). Superconducting circuits are critical to **protect the quantum states of** qubits . In superconducting materials, the charge is carried by **electron pairs** called Cooper pairs **instead of single electrons** . Cooper pairs **electron phonon interactions**They match with: a negatively charged electron attracts positively charged ions in a material lattice and **a shift occurs in the lattice** . This shift **affects another electron** that **is** far enough away from the electron-electron impulse caused by the Coulomb effect . The bond between the electron that causes the slip in the lattice and the electron affected by the slip is formed by the help of phonones, and a pair is formed that effectively acts **as a single particle** . The **Cooper pair,** which is at very low temperatures , does not **show scattering while** defecting the defects in a normal electron material , so electron flow occurs **as if the** material has **no resistance** .

Here is another detail that I would like to mention in terms of physical integrity. Electrons are normally in a group of particles called **fermions** . Since two fermion particles, electrons **cannot be in the same quantum state at the same time** , different atoms, molecules and substances in the periodic table can be formed. Another group of particles **bosons** the same case at the same time quantum **can find** . This is how we can produce lasers with photons that are members of the Bozon family. Although electrons are fermions in the Cooper pair, when they become pairs (since the sum of the spins is no longer a fractional number) **they become bosons** . So all Cooper pairs**they can collapse collectively to the lowest energy level** . Condensate all pairs to a single state, reducing the degree of freedoms of the pairs to two: the number of pairs in the superconductor island and the superconducting phase of the condensation. Thus, we can write the entire superconductor island with a single wave function.

Although superconducting materials show quantum effects, they are not sufficient to use as a quantum computer. At this point, **Josephson effect** comes into play. At the time, 22-year-old Brian Josephson was looking for the answer to the question of what happens if two superconducting islands weakly interfere, for example, if an insulating layer of 2 to 3 nanometer thin divides the islands. If we look at the classical physics logic, since the electrons are not enough, they should bounce off the insulating material as if they hit the wall and stay on their own island. But that's not the case, Cooper couples ** tunnel** through the insulating barrier ! Moreover, this

**To observe, it is sufficient to have a superconducting phase difference between the two islands, there is no need to apply electrical potential. Because the wave functions of two superconducting islands, which are very close to each other, overlap each other and electrons can flow through the material which is normally very high without any resistance.**

*super current*When we apply DC potential to the system, we begin to see AC current due to the increase in phase difference. The Josephson joint acts as an **inductor** and the **joint starts acting like an oscillator** ! Moreover, it is a **non-linear** oscillator since its inductance depends on the amount of super current . Thus, we obtain a system whose energy ranges are not equal and thus we can assign | 0 | and | 1⟩ states. When a capacitor is added to the system, we have an LC circuit.

If we place a normal inductor in a superconducting circuit, the circuit energy ranges turn into an equal harmonic oscillator.The Josephson joint acts as a nonlinear inductor.Source,

So how do we use this superconductor Josephson joint as a qubit. Although there are many different qubit structures, there are three main types of architecture: **load, phase and flux qubits.**

*The* energy level determines the **number of Cooper pairs** on the superconductor island in the *load quad* Therefore, a small superconductor island is connected to a superconductor reservoir with the Josephon joint in these qubits, also called the *Cooper pair box* . We determine the number of Cooper pairs in the superconductor island with the Josephson joint on one side and the capacitor plate on the other side, **with the voltage we apply** , **we can put the system into a super position if we want** . We can use *single electron transistor (SET)* to make measurements .

*The* principle of the *phase qubit is* a little different. In this architecture, we connect the Josephson joint directly to the DC current source and we can use the system as a qubit with microwave signals that **will resonate with the energy levels at** the **local minimum levels** of the system.

*We* put one normal inductor in the *flux qubit* i circuit next to the Josephson joint. We have a **two-well asymmetric potential** system based on phase difference . Since the flux through the Josephon joint can also pass in quanta, the **amount of magnetic flux** applied **is half the flux in the Josephson joint, and the** system potential becomes symmetrical and the **flux goes to the superposition so that it can go to both sides of the circuit** . We can also accept this as the sub-energy levels of wells to enter the superposition. Thus **, we have** a qubit **depending on the direction of the flux** . D-Wave Although their systems use flux qubits, they use adiabatic quantum computing model instead of gate operations strategy.

Apart from these three main qubit architectures, Transmon, Fluxonium, Xmon, Quantronium, Gatemon etc. There are many other hybrid architectures, such as. Transmon qubit is a variant of the load qubit, Xmon and Gatemon are different versions of the Transmon qubit. IBM and Google teams are using Transmon qubit. A capacitor connected in parallel to the two Josephson joints in the **Transmon qubit** increases the Josephson energy of the system, **reducing** the **noise** created by the loads . It also enhances the effective interaction of the qubit with microwave photons. Thus, **more efficient door operations** can be done.

I would like to mention one more circuit element that allows us to perform two qubit operations with superconducting circuits and to measure in many qubit types. **The transmission line resonators (transmission line resonator)** this circuit element that we call **cavity quantum electrodynamics** (cavity quantum electrodynamics) is working with its principles. Buckets are an experimental setup commonly used in lasers and single atom systems. This mechanism, which we can think of as **a one-dimensional system with mirrors on both sides** , is a structure that contains only the electromagnetic field whose **frequency is proportional** to the **distance between the mirrors** . The fact that one of the mirrors is very permeable **allows photons to come in and out of the cavity.**. In this way, lasers can emit light out in a single dimension like a line.

But the main interesting feature of the cavities is **their interaction with single atoms** . If we trap a photon inside a **burrow, the frequency of the burrow changes according to the energy level of** the **atom** in **the burrow. **In other words, if the atom has a state of | 0⟩, the frequency of the cavity is 5GHz, and when we turn the atom to | 1⟩, the frequency of the cavity becomes 5.x GHz. The name of the bucket we mentioned in the superconductor circuits is the transmission line resonant. By measuring the reflection of the signal sent to the tinnitus connected to the superconducting qubits, we can understand whether the qubite is in the state | 0⟩ or | 1⟩. In order to do two qubit operations, we put the matching ring between the qubits.

Two transmon qubit circuits.Kubits are connected to separate resonances for separate gate operations for measurement.Source

The mapping resonant functions as a quantum bus between two qubits. **It** is very critical here **that** we **can control the frequencies of the transmon qubits separately with the flux we apply,** because we need to be able to adjust whether the frequencies of the qubits are separate with each other and also with the jiggle. The desired situation **is different with frequency resonators frequency of qubits** that according to the electromagnetic cavity *interleaved regimen* also be a system. In this regime, where the interaction of Kubit çınlaç is less, **if the qubit frequencies are equal, the path of virtual photons in the stimulation cavity in a qubit**affects the other with. After setting the kubites to | 00⟩ first, we send a signal

*that*does not have the same frequency as the kubite so that it does not absorb one of the qubits . Thanks to the AC Stark effect (changing the atomic energy levels of the electromagnetic field), we can transfer the quantum state of one qubit to the other qubi by synchronizing the frequency of the qubit it is sent to in its signal over a period of signal length. Thus, we have implemented two qubit operations, which we call √iSWAP gate.

As you can see, when we want to do two qubite operations with superconductive qubits, there must already be specially designed quantum busses between the qubits. There must be 45 buses in a 10-qubit circuit. This is not yet preferred as it makes the circuit very complex, open to crosstalk and large in size. Qubits are mostly connected only to the closest qubits.

Connection comparison of trapped ions with a 5-qubit superconducting circuit.In superconducting circuits, the qubit is connected to the nearest qub with a physical data path, whereas trapped ions do not require physical connection, so all qubits can be connected to each other.

The ideal operating temperature of the superconducting circuits is about 0.015 Kelvin (space gap 2.73 Kelvin, room temperature 300 Kelvin). Devices called dilution coolers are used for this cooling process. In addition, there is a need for cables that can operate very efficiently at different microwave frequencies, and to control and read all these signals, and very sensitive electronic equipment.

IBMQ cooler open state.The superconducting circuit containing the Kubits is placed in the lower section at 15mK and wiring is done.

**To summarize:** Superconducting circuits are based on a small, established technology that is not difficult to manufacture. But circuits that need to be cooled are open to noise and error. Although the two-door operations are very fast at the nano-second level, they require physical buses that cause the circuit to grow. In trapped ion systems, qubits can be connected to all other qubits. Door operations are slow but more efficient. The noise problem is much less in these systems, but it is a big problem that all the laser and optical equipment are reduced.