[Paper Review] Reviewing a Paper on Executing Shor's Algorithm with a Tabletop-Size Optical Quantum Computer

Yuichiro Minato

2024/10/25 04:58

Out of pure curiosity, I came across this article:

A Taiwanese Research Team Develops a Desktop-Sized Quantum Computer

A research team from National Tsing Hua University in Taiwan has developed the world’s smallest quantum computer using a single photon. This desktop PC-sized device operates at room temperature and can perform calculations, including prime factorization. They succeeded in compressing information into 32 dimensions within a single photon, overcoming traditional quantum computer challenges. The technology has potential applications in various fields, including drug development and information security.

I’m not registered for the official journal source, so I’ll refer to the non-peer-reviewed ArXiv version instead:
https://arxiv.org/abs/2408.08138

Traditional quantum computers typically use multiple qubits to take advantage of superposition and entanglement for computation. In this case, however, they execute Shor's algorithm for cryptography by storing extensive information within a single photon.

First, let’s briefly review Shor’s algorithm, the algorithm used in this research. Shor’s algorithm is one of the most sophisticated algorithms aimed at prime factorization. For more detailed information, you can check the following overview:

A Beginner’s Guide to Shor’s Algorithm for Breaking Encryption with Quantum Computers

Shor's algorithm addresses the problem of finding the order ( r ) of any pair of coprime integers ( a ) and ( N ), where ( 1 \leq r < N ). The process involves three main steps:

Preparing a superposition state
Performing modular arithmetic with a logical circuit
Using a quantum Fourier transform (QFT) to extract the quantum state in bits

Most of the quantum circuit operation occurs in step 2, while the QFT is primarily a pre-processing step to extract the results.

In this case, the computation involves factoring the number 15, which uses 5 qubits. Factoring 15 allows for a relatively simple quantum circuit, making it manageable. Below is the circuit from the paper.

Source: https://arxiv.org/pdf/2408.08138

Being able to perform 5-qubit calculations on a desktop is quite impressive.

There are various methods of computation using light. From the quantum circuit, you can see that it performs the same calculations as qubit-based quantum computers. Here, however, they utilize a single photon as the quantum unit for the computation, which makes the hardware setup intriguing.

The paper also includes a simplified schematic.

Source: https://arxiv.org/pdf/2408.08138

I don’t know much about photonics myself, but superposition is essential for executing Shor’s algorithm. To create the initial superposition state, they use a technique called time-bin encoding, where a single photon’s pulse generation time is divided into 32 segments. Since ( 32 = 2^5 ), each time bin is assigned a superposition state corresponding to the quantum state, allowing computation.

In a typical quantum setup, you would prepare 5 qubits, each in a superposition state, creating the 32 possible quantum states. Here, the fewer qubits are compensated by time division, which likely wouldn’t work for larger calculations.

As for computation, since quantum information is stored in these time bins, discrete time bins need to be processed. They achieve this by utilizing time delays. After polarization with a polarizer, only the polarized pulses are delayed to interfere with unpolarized subsequent pulses. This interference, when further polarized, adjusts the amplitude, allowing them to manipulate the quantum state for calculations. Computation between times is mostly adjacent, but non-adjacent interference is also possible.

In this photon-based quantum computer, a gate is placed at the beginning of the light waveguide to operate on the time bins. As a result, with a single photon, it’s possible to store 5 qubits worth of quantum states over time, enabling extensive computation.

It’s fascinating to see the variety of computational methods in the world. That’s all for now.