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Week 4

[h1]The Hardware Aspect[/h1] [h2]The DiVicenzo Criteria[/h2] David DiVicenzo outlined minimum characteristics a technology must have in order to be a useful quantum machine. [ol] [li]A scalable physicasl system with well characteristed qubits [ul][li]Need the ability to create a set of qubits[/li][/ul] [/li] [li]The ability to initialise the state of the qubit to a simple fiducial gate [ul][li]Essentially allow a system to reset to a clean state[/li][/ul] [/li] [li]Long relevant decoherence times [ul][li]Need to be able to keep data in memory long enough to allow computation to happen[/li][/ul] [/li]it's just difficult to find someone to embed it at high quality [li]A universal set of quantum gatesDavid Wu [ul][li]Essentially allow it to complete any algorithm, so be able to rotate a single qubit to anywhere on the Bloch sphere[/li][/ul] [/li] [li]A qubit-specific measurment ability [ul][li]Need to be able to read the results[/li][/ul] [/li] [li]The ability to interconvert stationary and flying qubits [ul][li]In order to transfer data over long distances, we need to be able to convert from data held in something stationary (like a computer chip) to light (photons). [/li][/ul] [/li] [li]The ability to faithfully transmit flying qubits between specified locations. [ul][li]We also need to be able to move these photons between places with good accuracy.[/li][/ul] [/li] The first 5 criteria are known as [b]DiVincenzo's computation criteria[/b] and the last two as his [b]communication criteria[/b]. Practically however it should be noted that the machine should be useful and attractive to build. It would be useful for it to be as small as possible, for efficient space and uses as little energy as possible, so doesn't use too many resources. And it should not cost more than a good classical supercomputer (~$100 million), otherwise it wouldn't be an attractive piece of equipment for a company or organisation to have. [h2]Quantum Computing Systems[/h2] Photons and Ions can be used as Qubits, and a Quantum machine also needs some other fundamental device/component to control the states of these qubits. Similar to classical computers, quantum computers also would have a sort of memory where they would load data from, compute on it, then store it back. However where these quantum computers would differ significantly would be in [b]error corrections[/b]. [i]The memory in a quantum computer is more active than that of a classical computer, constant error correction is occurring.[/i] This is because there is no system presently stable enough to store data for lengthy periods of time without needing error correction. Unfortunately this makes the system slower overall, but not slow enough for it to be particularly problematic. The control of the quantum computer is done by a classical system part of it. Error correction, feedback and control at high speeds are what the classical component of a quantum machine does. However the qubits themselves are changing in real time, so the classical computer has to correct them at a similar if not the same pace. Currently the classical component would be fast enough to correct these changing qubits, however with a faster quantum machine clock frequency, it's likely that an even faster classical machine would be necessary, to do the error correction and such. [h2]Isotopic Engineering[/h2] Silicon 28 and 30 have zero nuclear spin, wherease Silicon 29 has 'one half' nuclear spin, the same as a single electron. If it is desired to use the nuclear spin of silicon as a qubit, we can, however if we are using electrons as qubits, or current or magnetic flux, then isotopes of non-zero nuclear spin can interfere with nuclear spin and cause decoherence. Decreasing nuclear spin would allow for Qubits to have a longer memory lifetime, and is critical for technologies such as quantum dots (discussed later). Isotopic engineering in itself separates isotopes from potentially non-useful ones, such as separating Silicon 29 out of Silicon 28 and 30. They are separated using a large centrifuge, and then purified into a single high quality crystal, which would be used in the building of a quantum computer and for quantum information. [h2]Photonic systems[/h2] An optical computer requires a source of single photons, and the ability to execute gates. The gates are performed using [i]beam splitters[/i] and devices that change the phase of a photon. To create a complete set of gates, [i]non-linear[/i] operations are needed, and the ability to measure the photons. A qubit can be telported from one side of a quantum computer to the other, and can contribute to gate operations, both linear and non-linear. The aforementioned beam splitters are also used to construct these gates, and with those, you can make a basic quantum machine. But having that many gates is not space efficient, so [b]waveguide chips[/b] have been made, which do essentially the same thing. But despite this, a machine with millions of gates would be very larger, and many of the processes may be through the same set of gates. To combat this, [b]time-domain multiplexing[/b] has been developed, which essentially loops the output back through it many, many times. A major challenge for optical computation is the amount of errors, when a photon may randomly go in a different direction due to some external interaction. To combat this, the machines would have redundancy of information. so if some is lost, you may still have the original data to correct the error. As such, you could also just use a large number of photons to represent a single logical qubit, which would intrinsically incorporate quantum error correction. But to use this properly, it is necessary to count the exact number of photons, which will be done using a [i]superconducting photon number resolving detector[/i]. [h2]Quantum Dots[/h2] We can create [i]artificial atoms[/i] known as [b]Quantum Dots[/b] by manipulating electrical fields to create material barriers to the movement of electrons. [h3]Real Atoms[/h3] The nucleus of an atom creates an electrical potential centered around itself that attracts the electrons, with the lowest energy at the center. But the electrons don't simply fall into the nucleus, and instead have certain distances from it. It turns out that the electrons can only take certain energy levels that correspond to standing waves around the nucleus. The position of the electrons is a quantum probability amplitude, rather than a single fixed point, known as an [i]orbital[/i]. The shape and size of these orbitals depends on the strength of the electrical potential created by the nucleus. [h3]Artificial Atoms[/h3] We have very limited ability to influence real atoms, so if we confine a number of electrons in a manner similar to how they would be in atomic orbitals, we can create artificial atoms known as [i]Quantum Dots[/i]. We confine the electrons using a combination of the material structure and electrical fields created using voltages. An electron wont normally move past the physical edge of the device. With a junction made of certain types of materials, it takes substantial energy to cross the boundary. When a positive voltage is applied to a wire, it attracts electrons, and conversely a negative charge repels electrons. Using these characteristics carefully, we can confine an electron tightly in either a disk-shaped area or a small volume. Quantum dots are either [b]self-assembled[/b], or [b]gate-defined[/b]. Self-assembled ones are made of materials that clump together. In one approach, small amounts of a certain type of semiconductor are grown on top of a substrate (chip surface) of another type of semiconductor, and differences in the spacing between the atoms cause the new material to bead up, like water on a good rain jacket. In the vertical direction, our electron will then be confined to the boundary where the materials meet, and horizontally, it will be limited to the disk-shaped footprint of the dot. [b]Gate-defined[/b] quantum dots are made like computer chips, with microscopic wires laid on top of a material such as silicon using a process known as [i]photolithography[/i]. But there is an additional twist: different layers of material are deposited before the wires are created on top. The electrons are then confined in the vertical dimension by the material boundary, and in the horizontal directions by electrical fields created by voltage on the wires. [h3]Qubits[/h3] Because spin is a magnetic effet, we need to use magnetic fields to control it, and to define what 'up' and 'down', i.e the 2 distinct states, are. In some designs, the spin can be controlled optically using lasers pulses. Changing the spin of an electron requires careful control of the magnetic fields, which are generally slow, and are difficult to use to target a single quantum dot. To get around this, some designs propose the use of multiple dots to represent a qubit. For example, if there are 2 electrons making up the qubit, the qubit can be defined as the difference in the state of the 2 electrons. Using some of these alternative designs, we can exclude the need to modify the magnetic field. and instead control the exchange of electrons between two dots to execute single-qubit and two-qubit gates. [h3]Strengths and Weaknesses[/h3] Some of the designs can be used with photons as well, so would be useful for communications, especially for exchange-oriented designs, as the gate execution speeds are very high, so performance when the system is scaled up would be great - which is of course, and additional incentive for development further in the field of [i]silicon photolithography[/i]. The greatest weakness of these are that the memory lifetime tends to be very short, as it is hurt by many different interactions on the quantum level, leading to decoherence. Furthermore the dots require temperatures near absolute zero, so the setup would be very difficuult. Finally, while it is theoretically possible to put many quantum dots on a single chip, the wires necessary to control them clutter the arrangement, and finding an architecture for many qubits using quantum dots has proven to be very challenging. [h2]Superconducing Systems[/h2] To make a small quantum information processing system using superconducting qubits, you'd need to put several superconducting qubits in an array, and then control them to manipulate the quantum state to demonstrate simple information processing. As precise control is paramount, microwave pulses on a timescale of 10 to 100 nanoseconds are used to implement single qubit and dual qubit quantum gates. The superconducting chip itself is createdusing optical and electron beam lithography. Similar to Quantum dots, this technique has difficulties due to wiring, as there is just very little space for input/output wires in the two-dimensional array that would be used in a simple quantum information processor. [h2]NV Diamonds[/h2] [img src='https://res.cloudinary.com/deylrqt2d/image/upload/v1543158838/large_hero_94dff419-444a-4823-b191-98aafa51323f_rt1s0x.jpg'] Many materials are atoms arranged in a regular crystal. When an atom is missing, or is replaced with a different kind, that uniform arrangement is broken. The change in the number of protons in the nucleus there alters the amount of attraction that electrons feel, so a single electron can be trapped there. Because the energy levels change, the wavelength, or color, of the light absorbed and emitted changes, leading to the name color center. For quantum computing, replacing a single carbon atom in diamond with a nitrogen atom creates a useful color center. [h3]Qubits[/h3] The ground state of an NV centre is known as a [i]spin triplet[/i], as there are 3 states, +1, 0 and -1, two of which are used to make a qubit. The states of the qubits can be controlled by pulses of microwave radiation, just as with various other technologies. NV centers also emit photons that're in the visible light range, which opens the possibility of entangling them over some distance, if they are made to emit a photon at the same time. Diamond made of natural carbon includes some amount (about 1% ) of an isotope of carbon, 13- C that has a spin in its nucleus. If a 13-C atom is near our NV center, we can exchange the state of the NV center with the nucleus, and have two qubits instead of one. The nuclear qubit is slow to react to external forces, and so it has a long lifetime. [h3]Strengths and Weaknesses[/h3] A great advantage is that the NV Diamond method can potentially work at room temperature, and they emit visible photons, which are easier to detect and capture. This also makes them attractive candidates in the creation of quantum networks. The biggest drawback is how difficult it is to make them, so researchers have to find naturally occurring ones, or fire atoms at a piece of diamond at high energy, creating defects in the lattice, though it is still very hard to place them accurately. [h2]Ion Trap[/h2] (Invented by Wolfgang Paul, not Pauli). Atoms are normally in molecules and as such need to be isolated. One such method is the [b]Linear Paul trap[/b]. [h3]Linear Paul trap[/h3] The trap is placed in a vacuum chamber (generally tens of centimeters across, though researchers are working on much smaller chambers) with fewer atoms per cubic meter than the vacuum of outer space at the altitude of the International Space Station. This kind of trap can hold more than one ion, spaced a few microns apart in a line, where the standing waves create stationary points. Up to fourteen atoms have been trapped in this fashion and used as qubits. The ions can be controlled by pulses of laser light fired in from outside the chamber, through a window. Different wavelengths of light are used for different purposes, such as keeping the atoms cool, executing single- qubit gates, or measuring the ions. A common way to measure the qubit is to use fluorescence, causing the atom to absorb a photon and re-emit it so that we can see the ion by the light it emits. [h2]Surface Traps[/h2] This is much better, as it can allow for more qubits to be captured. A [b]surface trap[/b] uses many small electrodes, tens or hundreds of microns across. Each electrode can be individually controlled to create a small electromagnetic field nearby. Set in a line, we can push and pull individual ions that are suspended in the electromagnetic field above the surface of the trap (hence the name). We can move the atoms around, bringing them together or separating them as we wish. The electrodes can be arranged so that the ions can be moved along paths in two dimensions, allowing qubits to interact with each other. [h3]Strengths and Weaknesses[/h3] These ions are suspended in vacuums, so have lifetimes of up to a minute (very long), they are also very high fidelity, as the gates are by lasers, in a vacuum, so very little interference indeed. But they are very large and so very spatially inefficient, furthemore moving them also takes a comparatively long time, in comparison to solid state drives (SSDs). However, the fact that they are of such high fidelity means that the advantages may offset the disadvantages, which are mentioned above. [h2]Quantum Machines of Today[/h2] [img src='https://res.cloudinary.com/deylrqt2d/image/upload/v1543162225/Screenshot-2018-11-25-16_10_12_th8y6h.png'] [h1]Quantum Error Correction (QEC)[/h1] The simplest approach is to simply repeat information, so rather than sending say, 0, send 00 or 000. Better to send 000 however, because if the reciever get 01 or 10, they won't know if the intended message was 0 or 1, but sending three repetitions clears that up, as 110 was probably supposed to be 1 and 010 was probably supposed to be 0. [img src='https://res.cloudinary.com/deylrqt2d/image/upload/v1543164358/Screenshot-2018-11-25-16_45_19_jsjzjp.png'] [h2]Quantum Errors[/h2] Of course, classical information is binary, so the only errors that can occur are bit flips: a 0 becomes a 1, or a 1 becomes a 0. But qubits are more complex, having both a value (0 or 1) that can be in superposition and a phase that can be any angle. Measuring a state, as we have seen, can cause a superposition state to collapse, either completely or partially. We will use the effect to force all errors to behave like either a bit flip (a rotation about the X axis), or a phase flip (a phase rotation about the Z axis). To describe a quantum error correcting code, often we use the notation [b] [[n,k,d]][/b] , where n is the number of physical qubits in a block, k is the number of logical qubits that the block encodes, and d is the code distance. In current classical computer systems, error correcting codes are used for storing data on hard disks or transmitting data across a network, but its uncommon to keep the data encoded in an error correction code while performing a computation. In quantum systems, however, the error rates are so high that we want to keep the data encoded while performing the computation. Managing the errors as we operate on more than one logical qubit in a block is tricky, so codes encoding only a single logical qubit ( k=1 ) are common, with an important exception we will discuss later. Error correcting codes depend on the ability to extract information about errors. Next, we will delve into the mechanism used in quantum codes. [h2]Parity[/h2] Error correcting codes generally identify errors by calculating the parity of a set of bits. [b]Parity tells us whether the number of ones in a set of bits is even or odd[/b]; the parity of 001 and 111 is 1, while the parity of 000, 110, and 101 is 0. Parity can be calculated by taking the XOR (exclusive OR) of the set of bits. Extracting parity without destroying the superposition is the tricky part of QEC. The CNOT can help. Odd number of 1's = 1, even number of 1's = 0. (Remember 0 is even). [img src='https://res.cloudinary.com/deylrqt2d/image/upload/v1543180451/Screenshot-2018-11-25-21_13_50_y7t3dl.png'] [img src='https://res.cloudinary.com/deylrqt2d/image/upload/v1543180371/Screenshot-2018-11-25-21_12_33_ieawme.png'] [h2]Quantum codes[/h2] Lets examine its error protection properties: if a single bit is flipped, we have a state such as 101, and the parity extraction will find parity 1 on the first two qubits and also on the second two qubits. Since a good state has parity 0, we know that both pairs have a bit flip error, and its easy to see that this implies that it must be the middle qubit is in error. We can easily correct it by flipping the middle qubit again. [img src='https://res.cloudinary.com/deylrqt2d/image/upload/v1543182600/Screenshot-2018-11-25-21_49_47_rd8jd5.png']