11 Feb 2022

Post Quantum Cryptography - Quantum Computers

Author: TCC  /  Categories: Blogs

Quantum Computers – Part 2
Classical computers perform logical operations using a definite position of a physical state (i.e., using bits, which means operations on one of two positions 0 or 1). Unlike this model, quantum computers perform calculations based on the probability of an object's state before it is measured, which means they have the potential to process exponentially more data compared to classical computers. Instead of having a clear position, unmeasured quantum states occur in mixed superposition. This superposition can be entangled with those of other objects, meaning their final outcomes will be mathematically related. Special quantum computing algorithms are required to understand the complex mathematics behind the unsettled states of the entangled objects, in order to solve problems that would take a classical computer a very long (unpractical) time. Thus, one challenge is to design such algorithms that would potentially provide solutions to complex mathematical problems like fast searching, integer factorization or the discrete logarithm of long numbers. Moreover, this quantum computer has to solve them much faster than any classical computer, to make sense the investment, which is basically the concept of quantum supremacy.

Besides generating the algorithms mentioned above, another big problem lies ahead. Building a functional quantum computer requires holding an object in a superposition of states long enough to carry out various processes on them. Unfortunately, if there is unwanted interaction between a quantum computer and its environment (e.g., electric fields or anything that can record information about the qubits), this superposition loses its “in-between” state and becomes the usual bit used in classical computers. This problem is called decoherence, and results in premature “measurement” of the qubits, which forces/“collapses” them to classical bits (0 or 1). Therefore, devices need to be able to shield quantum states from decoherence, while still making them easy to read. The only solution to this problem is quantum error correction. This scheme encodes each qubit of the quantum computation into a collective state of physical qubits (e.g., thousands), which is not an easily achievable model. Unfortunately, without error correction, we cannot expect to scale beyond a few hundred qubits.

Moving one step further, to make use of any computer, we need to read its output. For quantum computers, by looking at the superposition of all equally possible states/answers, the rules of quantum mechanics say that we only see and read a random answer, which is not very useful. A superposition is a complex (real plus imaginary) linear combination in which multiple different states add together (see Part 1 of our blog). Thus, a qubit is a bit that has a complex number/amplitude attached to the possibility of being 0, and a different complex amplitude attached to the possibility of being 1. Simply put, the larger these amplitudes are, the larger the chance of seeing that outcome. The positive or negative contributions to an amplitude can interfere destructively and cancel each other out (i.e., the corresponding outcome is never observed), or they can interfere constructively and increase the likelihood of a given outcome. The goal in quantum computing is to devise an algorithm that coordinates the pattern of constructive and destructive interference such that for each wrong answer the contributions to the qubit amplitude cancel each other out, whereas for the right answer the contributions add up. By doing that, the right answer is obtained with a large probability when we read the superposition of states. The biggest problem in designing such an algorithm is not knowing the answer a priori.

Finally, like in any classical computer, we need to store, read and write all the qubits that are used by the quantum algorithms. Similar to classical random access memory, for building quantum computational and communication networks, it is desirable to have a random access quantum memory (RAQM) with the capability of storing many qubits, individual addressing of each qubit in the memory cell, and programmable read and write operations of a qubit from the memory cell to a qubit bus [1]. These read and write operations require implementation of a good quantum interface between the bus (typically carried by photonic pulses) and the memory qubits (built with atomic spin states). A good quantum interface should be able to map quantum states between the memory qubits and the bus qubits. We mentioned in Part 1 of our blog that entanglement is crucial to quantum computing. Therefore, entanglement sources and quantum memories are vital for quantum computers and networks. To this day, these devices primarily work at cryogenic temperatures or require cumbersome operating infrastructure, and have only been demonstrated in laboratory environments. The idea is to build quantum memories that operate at room temperature and store photons with high-efficiency and fidelity. Long storage times are also required, to support qubit synchronization over long-distance networks. There is active research for such a quantum memory that stores and releases single photons on-demand while preserving their quantum state at fidelity above 95%. It does not require extreme cooling or vacuum support infrastructure for operation, which is a key design consideration for real-world deployment and scaling [2].

At the end of this second part of our blog, we need to remember few things. First, quantum computers will not solve all types of mathematical problems. Second, building these computers is way more challenging that building classical computers. And third, a quantum computer that is big enough to outperform classical computers at practical applications (e.g., breaking a crypto algorithm) is probably many years ahead. Nevertheless, our mission is to be proactive. Thus, in the following blogs we will describe how quantum computing impacts Cryptography and how we plan to solve this future crisis by introducing new types of algorithms that are quantum safe.

Bibliography
[1] Wikipedia, Dec 2021. [Online]. Available:
https://en.wikipedia.org/wiki/Quantum_memory#Future_development.

[2] "PR Newswire," Nov 2021. [Online]. Available:
https://www.prnewswire.com/news-releases/qunnect-announces-sale-of-first-commercial-quantum-memory-301428820.html.

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