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Tachyum Prodigy Solutions for Post-Quantum Cryptography

  • Jan 21, 2025 Date of publishing
  • 9 Pages

Quantum computing is quickly emerging as an exciting new leading-edge technology that is moving from theory to practical applications. Quantum computing is being driven by certain applications that aren’t addressed well with classical computers which include problems that involve exponential scaling. Two examples of this type of problem are optimization and chemistry.

An example optimization problem taken from daily life is the possible seating configurations around a table for a meeting in a conference room. If the meeting has four participants the number of possible seating configurations is 4! or 24. If you increase the number of participants to eight, the number of possible seating configurations increases to 40,320, and if you hold a meeting with 10 people seated around the conference room table, the number grows to 3,628,800. This is an example of a problem that scales exponentially, making it difficult and impractical for a classical computer to solve in an exhaustive way as the number becomes very large. Classical computers solve these problems by approximation.

Chemistry is another area where quantum computers are showing a lot of promise. Simulating molecular clusters is very challenging for classical computers since the simulations need to account for every electron-electron repulsion and every attraction of each electron to the nuclei, so currently even the largest supercomputers can only simulate very small molecular clusters.

There are fundamental differences between classical computing and quantum computing that allow quantum computers to address the above types of problems much more efficiently than classical computers. First of all, classical computers use bits that are either in the “0” or “1” state, so everything is a series of 0s and 1s, and the capacity of a classical computer increases linearly with the number of bits. Quantum computers use qubits instead of bits, which have very unique characteristics that don’t exist with classical computers.

A qubit can represent a 0 or 1 like a classical bit, but you can also apply quantum rules to it, which include some very interesting properties. One property is superposition. Quantum superposition is the ability of a quantum system to act as if it is in multiple states at the same time until it is measured. One qubit can represent not just 0 or 1, but a superposition of 0 and 1. In addition, complex superpositions can exist, so 2 qubits can be in a superposition of four states, three qubits in a superposition of eight states, etc. What this means is that the power of quantum computers increases exponentially with the number of qubits.

Another property is entanglement. Entangled qubits allow changing the state of one qubit to immediately change the state of the entangled qubit, so the states of entangled qubits cannot be described independently of each other. Quantum computers utilize superposition and entanglement to solve problems that are difficult if not impossible for classical computers such as the problems described above.

Quantum computing is still in the early stages, but is growing and maturing quickly. In 2019 Google announced the largest quantum computer at that time with 54 qubits, and as of late 2024 IBM’s Condor was considered to be the largest with 1121 qubits. Another critical area of research in addition to the number of qubits is developing reliable ECC protection, as the qubits in current systems are quite noisy. Incorporating reliable, scalable ECC will be a key area of focus as quantum computers continue to mature. At this point quantum computers are at the academic level for limited applications.