# Unraveling the Latest Trends in Error Correction and Error Mitigation in Quantum Computers

Technology News | 2024-05-21

## The Key Technology of Quantum Computers: "Fault-Tolerant Quantum Computation"

In recent years, the advancement of quantum computers has been accelerating. Fujitsu, in collaboration with RIKEN, has started providing the first 64-qubit superconducting quantum computer by a Japanese company in 2023 [1]. We also plan to realize 256 qubits by 2025 and 1000 qubits after 2026. The successful realization of superconducting qubits using solid-state elements in 1999 [2] suggests that the number of qubits in quantum computers will increase exponentially in the coming years, marking a significant leap forward.

Various methods other than the superconducting method have been proposed for quantum computer hardware, and research and development for each method are rapidly progressing.

While it is true that increasing the number of qubits in a real machine is a recent trend, the tide is slowly changing. This is because there are two major challenges with current quantum computers:

① An innovation beyond the current approach is needed for large-scale quantum bits. ② There is a problem with quantum bit errors, which prevents long-term high-precision calculations.

First, let's discuss ①. In the case of superconducting quantum computers, a special refrigerator is used to cool down the quantum chips to extremely low temperatures, but there are constraints on the size of the refrigerator. There are ideas to parallelize multiple superconducting quantum computers for large-scale operations, but this leads to other difficult challenges, such as operating multiple quantum chips across refrigerators. An innovation beyond the current approach is needed for large-scale quantum bits, and it is not guaranteed that technological innovation will continue at the same pace once it starts, like a domino effect.

Next, for ②, quantum bits are affected by various external factors, causing errors. Currently, the operation accuracy of quantum bits has improved to over 99%, but there is a need to further increase this accuracy (for example, if you calculate 100 steps with 99% accuracy, the accuracy drops to about 37%).

Companies and academia researching and developing quantum computers are exploring ways to use quantum computers within a limited range of quantum bits, in addition to aiming to expand the number of quantum bits. Various types of quantum computers have been proposed, but no method has a roadmap that can reliably realize a large number of quantum bits.

Quantum computers are a dream technology that attracts high expectations from around the world, but the quantum computer community feels that a "winter era" may come for quantum computers. Recently, research and development of AI (Artificial Intelligence), which has finally begun to permeate business and general society due to the advent of Deep Learning and generative AI, has experienced several winter eras. Each time, the willingness to invest in research decreased, and activities towards commercialization declined. This is because the past AI (Artificial Intelligence) boom did not contribute to solving real-world problems or generate business as much as expected. To avoid repeating the same mistakes as AI (Artificial Intelligence), researchers of quantum computers aim to find social issues that can be solved early with quantum computers and establish them as businesses early.

The key here is the fault-tolerant quantum computation, which is a countermeasure for ②. If this is realized, it will be possible to perform large-scale practical calculations. As shown in the figure below, it is estimated that several million quantum bits are needed to realize a fault-tolerant quantum computer (FTQC) that can be used for practical problem solving [3].

The premise of several million quantum bits is an estimate that this number of quantum bits will be needed to realize quantum operations with several hundred to 1000 logical quantum bits protected from errors. Here, it is assumed that one logical quantum bit is composed of about 1000 quantum bits and that logical quantum operations are performed using the usual gate set introduced later. If the number of quantum bits required for error-correcting quantum computation can be reduced, as mentioned later, it may be possible to solve realistic problems with 10,000 quantum bits.

In this way, fault-tolerant quantum computation becomes important to solve realistic problems within a realistically small number of quantum bits.

In the following chapters, we will introduce the latest trends in error correction technology and error mitigation technology, which are attracting attention among research themes for the realization of future fault-tolerant quantum computers, based on the examples of Fujitsu's joint research.

## What is "Fault-Tolerant Quantum Computation"?

As mentioned earlier, quantum bits are affected by various factors such as surrounding heat, causing errors. Therefore, if you perform calculations for a long time, errors will accumulate, and it will not be possible to achieve/produce correct calculations.

To control the impact of these errors and realize accurate quantum calculations, Fujitsu is conducting joint research on error correction technology with Professor Fujii of Osaka University and on error mitigation technology with Professor Emerson of Keysight Technology/Waterloo University.

①Error Correction Technology

This is a technology for quantum computers to detect and correct errors that occur during computation. The basic idea of quantum error correction is to use multiple quantum bits redundantly to store the information of one quantum bit. This allows you to reconstruct the correct information from other quantum bits even if a single quantum bit receives an error.

For example, suppose you share one value with three quantum bits A, B, and C, and detect errors with two auxiliary quantum bits. Even if an error occurs in the B quantum bit, you can detect the occurrence of the error and correct B to the correct value by examining the correlation with the two auxiliary quantum bits linked to AB and BC, respectively. This is the basic idea of quantum error correction.

This mechanism is developed to use multiple quantum bits redundantly, which are called logical quantum bits. Fault-tolerant quantum computation is a quantum computation that can continue accurate calculations using these logical quantum bits while correcting errors that occur during computation on a quantum computer.

②Error Mitigation Technology

On the other hand, error mitigation technology aims to minimize the impact of errors, not to correct them. This is because it is thought that it will take some time to realize the error correction with sufficient accuracy, which requires a large number of quantum bits. In the future, we anticipate that it will be possible to apply error mitigation technology, which can increase the accuracy of calculations with fewer quantum bits at an earlier stage and lead to future fault-tolerant quantum computation. While it is important to suppress the occurrence of errors by improving hardware, the error mitigation technology mentioned here refers to software methods such as improving algorithms to minimize the impact of errors on calculation results. If the impact of errors can be reduced, it will be possible to perform calculations for longer steps.

Moreover, by utilizing error mitigation technology, it is also possible to reduce the number of quantum bits required for error correction. This is an important point as it is expected to accelerate the realization of fault-tolerant quantum computation.

## A New Quantum Computing Architecture Jointly Developed by Osaka University and Fujitsu

Through joint research on error correction by Osaka University and Fujitsu, it has been shown that it is possible to construct a quantum computer with 64 logical quantum bits, equivalent to about 100,000 times the highest performance of current computers, with only 10,000 quantum bits [4]. In other words, it is possible dramatically to accelerate the arrival of full-fledged quantum computers by realizing computational performance exceeding current computers with significantly fewer physical quantum bits than before.

Currently, it is said to be difficult to perform quantum calculations of more than about 50 quantum bits on a quantum simulator operating on a supercomputer. Therefore, if a quantum computer with 64 logical quantum bits can be constructed, it is expected to be able to demonstrate computational power far exceeding that of current supercomputers.

Let's turn to the new quantum computing architecture of Osaka University and Fujitsu in a bit more detail.

Quantum computation of a quantum computer is performed in steps by combining basic quantum gates in multiple stages. The basic quantum gate set includes CNOT gate, S gate, H gate, and T gate. Many of you may have heard of the names of NOT gate, AND gate, XOR gate, etc., which are the basic logic gate set of conventional computers. Indeed, the above basic quantum gate set of quantum computers corresponds to the basic logic gate set of conventional computers.

While CNOT gate, S gate, and H gate did not use many quantum bits, the operation of T gate has required a large number of quantum bits. Furthermore, when performing a quantum gate operation called "phase rotation" using basic quantum gates, it was necessary to perform the T gate many times in combination with other gates.

Osaka University and Fujitsu have been able to reduce the number of quantum bits required for arbitrary rotation to less than 1/10 of the conventional ones, by defining and introducing a new phase rotation gate instead of the T gate. This reduces the number of gate operations required for execution to about 1/20 of the conventional ones, and can suppress the quantum error probability of physical quantum bits to about 1/8, enabling extremely high-precision calculations.

With this research achievement, it is now possible to accelerate the realization of quantum computers that exceed the performance of current supercomputers.

## Error Mitigation Technology Jointly Developed by Keysight Technology and Fujitsu

Keysight Technology and Fujitsu have succeeded in obtaining a higher error mitigation effect even for types of noise that are difficult to remove individually by combining multiple error mitigation technologies. Here, we will introduce an overview of the effects of two error mitigation technologies and their combination.

- Randomized Compiling: This technology reduces the overall error rate by randomizing the type of quantum gate while maintaining the equivalence of the quantum circuit, thereby averaging the impact of errors. This prevents errors from specific gates from having a significant impact on the results. Randomized Compiling is particularly effective when noise is systematic or when errors are biased towards specific gate operations.
- Zero-Noise Extrapolation: This is a method of performing the same calculation multiple times at different noise levels and using the results to estimate the result in an ideal situation with no noise. This is a method to understand how noise affects the calculation results and to correct it.

In this section, we will introduce an example where the error rate under over-rotation noise was dramatically reduced by combining Randomized Compiling and Zero-Noise Extrapolation for the calculation of the ground state energy of VQE*1; H2 for quantum chemistry [5].

When only Randomized Compiling (RC) is applied, the error rate is slightly improved compared to before the application. On the other hand, when only Zero-Noise Extrapolation (ZNE) is applied, the error rate occurs significantly in the negative direction. However, when both are used in combination, it can be seen that the error rate is dramatically reduced.

One of the fields where the use of quantum computers is expected is the field of quantum chemistry. By simulating the behavior of complex molecules with a quantum computer, it is expected to reduce the experimental cost and development period necessary for the discovery of new materials and drug development. Being able to calculate the ground state energy with high accuracy contributes to the early application of quantum computers in the field of quantum chemistry.

Keysight Technology and Fujitsu expect the effect of Randomized Compiling among error mitigation technologies. This is because it exhibits effects from an error accuracy of about 1% (one error occurs for every 100 quantum bit operations), and the error mitigation effect dramatically increases as the error accuracy increases. The current error accuracy has achieved more than 1%, and it is in the stage of increasing the accuracy to 0.1%, 0.01%. At such stages, Randomized Compiling exhibits higher effects as the error accuracy increases.

*1 VQE (Variational Quantum Eigensolver): An algorithm for efficiently calculating the ground state energy using a quantum computer.

*2 Now Keysight Technologies Inc.

## Fault-Tolerant Quantum Computation Opens the Future of Quantum Computers

Quantum computers are currently attracting major attention from all over the world. The topic is often featured in the news, most frequently talking about the number of quantum bits in particular. It is true that easy-to-understand numbers are a major attention-grabber when covered in a short time.

However, researchers of quantum computers are not only looking at the number of quantum bits. An unseen innovation is needed to realize tens of thousands of quantum bits. Also, quantum computers are inherently very susceptible to noise.

To avoid the winter era of quantum computers, it is necessary to show at the earliest possible stage that practical problems can be solved with quantum computers. What is important for that is fault-tolerant quantum computation.

Researchers of quantum computers are innovating to make quantum bits realistic and fault-tolerant, so that quantum computers can be applied to practical problem solving at an early stage.