Computers 2 Electric Boogaloo : The Need for Quantum Computers and Their Current State

The quinntessential components of a computer are its main volatile memory storage, arithmetic unit, and control unit. Communication between them occurs through a transistor that is the simplest form of data processing in a computer, it can be either on or off (1 or 0 respectively). Combinations of several bits can represent complex information. Transistors are combined using logic to make very complex modules. For instance, the AND gate sends the output 1 if both of its conditions are true and a 0 all other times. Combinations of logic gates form meaningful modules such as for adding. From adding we get to multiplying and from there we can do anything. All operations are simpler than first grade math such as adding one and/or zero or multiplying the two.

Figure 1: Logic Gates for multiplication through iterated addition, two cycles out of eight have passed

Moore’s Law states that the number of transistors in a dense integrated circuit doubles about every two years. This might be reaching its limits as right now a single transistor on a computer chip is reaching the size of an atom and this is starting to become a problem. Logical gates which either allow or constrict the flow of electricity or electrons stop serving as gates the smaller they get. The typical size of transistor is around 13 nano-meter which is around 14,000 times smaller than the diameter of a hair strand. As gates are shrinking to the size of a few nano-meters, electrons can simply transfer themselves over the blocked passage through quantum tunneling. Thus Moore’s Law is going to stop being true in a few decades and soon enough we will reach peak processing speed that is physically possible in classic computing.

Figure 2: Moore’s Law in action. Progression of nonvolatile memory storage

This is why we need quantum computers. If we are to go past the possible processing speed per unit area we need to be able to use quantum tunneling to our advantage. Quantum computers have qubits which can be set to both the two values 0 and 1 simultaneously through superposition. A qubit can be any two level quantum system such as spin and a magnetic field, or a single photon. 0 and 1 are the systems possible states, like a photons horizontal or vertical polarization. You can converge the two simultaneous values of a qubit by sending the photon that represents your qubit through a filter. The qubit has to decide whether it is either vertically or horizontally polarized. so as long as its unobserved it is both 0 and 1 but only in measuring does it collapse into a single state allowing more value storage. For instance, a classical bit can store only 1 of 2 possible values a qubit can store both of the 2 possible values at once and 4 bits can store 1 of the 8 possible values 4 qubits can store all 4 values at once. For equivalence from bits to qubits,  2 qubits can store 4 normal bits of information and 2 bits can store 4 states so 2 qubits can store 8 normal bits of information. On the one hand, something like 300 bits which barely represents 37.5 bytes which can store the sentence “Hey my name is Anas, nice to meet you”. On the other hand, 300 qubits can store more bits than there are particles in the universe

Entanglement (through a process called spooky action) is when a close connection makes each of the qubits reach to change in in others state instantaneously, no matter how far they are apart. This means by observing a single qubit you can observe properties of its partner by inference. Chinese scientists have used spooky action to change the spin of a quantum particle 1,200 km apart.

A normal logic gate gets a simple set of inputs and produces one definite output, a quantum gate manipulates an input of super positions, rotates them, and produces another set of super positions as its output.If we use quantum gates and superposition as well as entanglement this allows one operation or measurement to simultaneously measure all probabilities for all other similar results, allowing a typical measurement which takes 128 cycles a quantum computer can do in 7 cycles.

Figure 3: Standard brute force method of private key decryption of SHA256 from public key. Classical bits are used. Logic gate courtesy of Singh

Conclusions

While quantum computers may not replace our computer, they will replace any database searching machine, which (as efficient as it may be) might have to search every single one of its entries, quantum computer algorithms need only the square root of that time which for larger databases is game changing. So, instead of Google presenting you all the information you want in from a million data entries only takes 1000 tests instead of a million

As of now, a public key encodes messages only you can decode with your private key. Public keys can be used to calculate your private key using maths that a normal computer compute in a reasonable amount of time, but a quantum computer might be able to do in the square root of that time, through brute forcing trial and error. However, a computer can send another computer a stream of qubits which are entangled with the qubits in the senders computer. The sent qubits each have a single pair that cannot be replicated without further spooky action. The sender can manipulate the sent qubits 60 times per second or at a rate of 60Hz to change the key 60 times per second making the time taken to mathematically decode a private key to an encrypted message have to be calculated 60 times per second, which as of now no quantum computer could ever be able to achieve. Making all qubit encryption undecodable.

References

Gibney, E. (2014). QUANTUM COMPUTER QUEST. Nature, 516(7529), 24-26.

Johnson, G. (2004). A shortcut through time : The path to the quantum computer (1st Vintage Books ed.). New York: Vintage Books.

Mermin, N. (2016). Quantum computer science : An introduction. Cambridge, UK ; New York: Cambridge University Press.

Singh, Simon (1999) ‘The Code Book – The Science of Secrecy from Ancient Egypt to Quantum Cryptography’, The Fourth Estate, London