Emory Physicists Show Beginners How to Factor 15 with a remote quantum computer: A complete guide for beginners

Quantum computing, a rapidly growing field, has the potential to revolutionize internet security protocols with applications like Shor’s factoring algorithm. However, understanding and implementing this algorithm can be challenging due to its complexity. Researchers from Emory University have presented an experimental implementation of Shor’s algorithm in a beginner-friendly manner using IBM quantum processors.

This experiment can be performed as part of a quantum computing course and can help satisfy the need for bachelor’s degree programs and curricular materials for quantum information science and engineering. The potential of Shor’s algorithm to invalidate current internet security protocols highlights the need for new protocols that can withstand quantum computer attacks.

What is Quantum Computing, and Why is it Important?

Quantum computing is a rapidly growing field that has gained significant attention, especially after the 2022 Nobel Prize in Physics was awarded for advancements in this area. One of the most significant applications of quantum computing is Shor’s factoring algorithm, which has the potential to revolutionize internet security protocols currently in use. However, understanding and implementing Shor’s algorithm can be challenging for non-specialists due to the complexity of the subject matter and the lack of comprehensive educational materials.

Quantum computing operates on the fundamental unit known as a qubit. Unlike a classical bit, which can be either 0 or 1, a qubit can exist in a superposition, meaning it can be both 0 and 1 at the same time. This property allows quantum computers to process information at a much faster rate than classical computers. However, understanding and manipulating qubits require a solid understanding of complex numbers, summation notation, eigenvalues, and eigenvectors.

How Can Quantum Computing be Made Accessible to Beginners?

In a recent study conducted by Jed Brody and Kristen Gram from the Department of Physics at Emory University, an experimental implementation of Shor’s factoring algorithm was presented in a beginner-friendly manner. The researchers used IBM quantum processors, which are remotely accessible online for free, to factor 15 using a 7-qubit processor. The experiment was reproducible, although four other quantum processors exhibited excessive error.

The researchers aimed to provide a convenient standalone reference that would allow instructors and students to run Shor’s algorithm on real quantum processors. This experiment can be performed as part of a quantum computing unit or in a quantum computing course. It can also help satisfy the urgent need for bachelor’s degree programs, courses, and curricular materials for quantum information science and engineering.

What is Shor’s Algorithm, and How Does it Work?

Shor’s algorithm is a quantum algorithm for integer factorization. It was developed by Peter Shor in 1994 and has the potential to break many of the cryptographic systems in use today. The algorithm works by transforming the factoring problem into the problem of finding the period of a function, which can be efficiently solved on a quantum computer.

In the study by Brody and Gram, the researchers introduced the quantum Fourier transform and inverse quantum Fourier transform, which are key components of Shor’s algorithm. They then used the inverse quantum Fourier transform to perform quantum phase estimation, which estimates the eigenvalues of operators. Finally, they defined a problem called order finding and solved it with quantum phase estimation. This process demonstrated how Shor’s algorithm uses order finding to factor a number.

What are the Implications of Quantum Computing for Internet Security?

The potential of Shor’s algorithm to invalidate internet security protocols currently in widespread use is significant. Most internet security protocols rely on the difficulty of factoring large numbers into primes. However, Shor’s algorithm can factor these numbers efficiently, potentially breaking these security protocols.

This highlights the need for new security protocols that can withstand attacks from quantum computers. It also underscores the importance of understanding and implementing Shor’s algorithm, as it will play a crucial role in the development of these new protocols.

How Can Quantum Computing Education be Improved?

Despite the importance of quantum computing, there is a lack of comprehensive educational materials suitable for beginners. Research papers are often too complex for non-specialists to understand, and textbooks often lack complete details about implementing algorithms like Shor’s.

The experiment conducted by Brody and Gram is a step towards addressing this issue. By providing a beginner-friendly guide to implementing Shor’s algorithm, they have made a significant contribution to quantum computing education. However, more needs to be done to make quantum computing more accessible to students and educators. This includes developing more beginner-friendly materials, offering more courses on quantum computing, and integrating quantum computing into existing science and engineering programs.