# Cryptography and Quantum world

Question: How likely is it that someone will build a working quantum computer with enough qubits to claim quantum superiority in cryptography in the next few years?

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Some reports tend to confirm that large companies are focusing on the development of qubits and the number of qubits in the current prototype quantum computer chip. Any quantum supremacy with a sufficient number of qubits requires some research and development work, including an integrated hardware approach with extensive conventional hardware so that the qubits can be controlled, programmed, and read out. The following points illuminate this discussion:

Firstly, every computer ever used, from the earliest computers to giant computers, is a "Turing machine" and therefore comparable to each other. All computers designed and built-in recent decades are simply larger and smaller versions of each other. In this respect, a quantum computer is not simply an evolved Turing machine, but a new form of machine. A quantum computer can be used as a conventional computer, but not vice versa. Conventional Turing machines are not comparable to quantum computers. The execution of certain cryptographic algorithms could have a different complexity and timing execution on quantum computers than on conventional machines.

Secondly, the most powerful quantum computers currently have a limited number of accessible qubits (127 in IBM's most recent generation, denoted as "Quantum System One", and the last announced 54 in Google's Sycamore processor). We also know that some ramps from large companies like IBM include a roadmap for quantum computing, with the goal of having a system with 1000 qubits by 2023 (there is no practical evidence that they could do it). In cryptanalysis, for example, the number of qubits needed to crack 2024-RSA is 4,098. More precisely, to crack RSA with a 2,048-bit key requires 4,098 logical qubits, which means that 8 million physical qubits are needed. This calculation takes about 30 hours. These estimates can vary significantly depending on the quantum error correction assumption. A single logical qubit is assumed to be backed up by thousands of physical qubits. So it looks like the integrated hardware approach is not yet sufficient or will not be sufficient for years to come. This leaves a lot of room as to what we can currently do with the computing power available to us. As companies continue to increase the number of qubits, they are trying to focus on Turing machines and use what we currently have in accessible qubits.

Based on the above claims and the accessible and announced information, I believe that a partially functioning cryptography quantum computer will be accessible and interesting for research and development in the near future. In the best-case scenario, we will learn in eight to twenty years (depending on the progress of development) if someone has the ability to build a working quantum computer with enough qubits to assert the superiority of quantum cryptography.

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Respond: Based on the above, it is unlikely that anyone will build a working quantum computer with enough qubits to claim quantum supremacy in cryptography in the next few years.

Date: April, 2022.