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Quantum-Corner: Quantum Computing

What is quantum Computing?

A quantum computer is essentially a programmable calculator, similar to the present (digital) computers and the (analog) computers from the past. But what makes them so different?

A digital computer stores its intermediate calculation results in an electronic circuit, called "register". The smallest logical circuit in a register can store a single bit ("0" or "1") via a low or high voltage. All bits together in a register represent a binary number of many bits. Registers of 64 bits ore more are quite common.
Each instruction changes the content of that register, and after a few instructions, the intermediate result will be stored somewhere in memory to free the register for another calculation.

An analog computer (from the past), represents arbitrary numbers as arbitrary voltages. During calculation, this voltage is changed via all kinds of analog electronic circuits to obtain the desired result.

A quantum computer combines both principles with quantum mechanic circuits. It has also a register, and the smallest logical quantum circuit in such a register is called a qubit. The quantum mechanical "state" in a single qubit can represent two (complex) numbers (with some restrictions), and two of those qubits can represent four numbers, etc. However, if all those qubits cooperate with each other in a quantum mechanical manner (entanglement) then a register of N qubits can hold 2N numbers. This count increases quite rapidly, since a single register of 10 qubits represent 1024 (complex) numbers simultaneously, and 20 qubits over a million.

Each time a quantum mechanical instruction operates on such a register, the combined quantum state changes. It has the effect that such instruction operates on all 2N numbers simultaneously. However, if you want to readout the contents of such a register after several calculation steps, you can only ask a qubit once if it is in a certain state. And the result of that measurement is only "yes" or "no" regarding the probability you guessed it right. Thereafter, the quantum mechanical state is changed ("collapsed"), so you had only one possibility to do that right. In order words, a quantum computer with N qubits can perform intermediate calculations with 2N numbers, but the end result remain restricted to N bits.

To get an idea about the huge potential of this: a quantum register with 20 qubits can be simulated well on a laptop, because it involves "only" a million numbers. To simulate a register of 40 qubit, you need a huge super computer to store a few Terra bytes of memory. And to implement 50 qubit on a digital computer is considered as impossible. In 2019, a quantum computer of thatr size has been demonstrated, and an important milestone will be the creation of a kilo-qubit quantum computer

This quantum concept allows for a new category of algorithms, and the most beautiful ones are still do be invented. But the expectation is that the use of quantum computing for solving problems can offer a break through in various research directions.

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