HOUSTON – (Sept. 3, 2025) – Quantum computers promise enormous computational power, but the nature of quantum states makes computation and data inherently "noisy." Rice University computer scientists have developed algorithms that account for noise that is not just random but malicious. Their work could help make quantum computers more accurate and dependable.
In a conventional computer, information is stored in bits ⎯ a 0 or a 1 ⎯ and can be read directly. In a quantum computer, information is stored in a quantum state, which entails a multiplicity of co-existing probabilities irreducible to any single value. Each time a quantum state is measured, this multiplicity collapses into a single, random outcome.
"According to the laws of quantum mechanics, observing a quantum state often 'destroys' it, resulting in a random measurement that only reveals partial information about that state," said Yuhan Liu, a Rice postdoctoral researcher and the lead author on a paper accepted to the Institute of Electrical and Electronics Engineers' flagship conference Symposium on Foundations of Computer Science, where it will be presented in December. "Quantum state learning studies how to accurately translate quantum information by using multiple copies of the quantum state."
Quantum state learning is sometimes also called quantum state tomography: Just as a medical scan pieces together cross sections to reconstruct an organ in three dimensions, tomography in quantum computing uses multiple copies of a quantum state to reconstruct it. The method is critical for benchmarking quantum hardware, validating quantum algorithms and ensuring the reliability of quantum technologies.
Quantum devices are currently in a stage of development dubbed NISQ for "noisy intermediate-scale quantum," meaning they tend to be error prone: Tiny disturbances in the environment where a quantum device is located, unexpected disruptions at the physical hardware level or other calibration issues can easily corrupt quantum systems, introducing measurement errors. This means that for quantum state learning, handling quantum noise is one of the biggest challenges.
"Scientists have tried to find different ways to model this noise," said Nai-Hui Chia , assistant professor of computer science at Rice and co-corresponding author on the study.
Many models assume noise occurs randomly or uniformly, but the Rice team introduced a more robust and realistic framework that considers not just random error but also the possibility of targeted interference.
"Our model is strong in the sense that it also considers nonphysical and potentially malicious factors that may affect the system," Chia said. "Our goal here was to see if we could design a good algorithm to certify devices or do other tasks such that we would be secure against a deliberate attack by an adversary."
The team introduced and investigated this new framework, showing it could deliver optimal results provided a "sufficiently large" number of copies of a quantum state. The researchers also mapped the criteria for both peak performance and failure.
"We wanted to understand the fundamental limits: What is the maximum level of corruption the algorithm can endure, beyond which there would be no hope to learn the information accurately?" Liu said. "These questions are very important both in theory and in practice."
The answer brings both good news and bad.
"The bad news is that for some states, learning under adversarial noise is nearly impossible," Liu said. "An adversary only needs to change an exponentially small fraction of the states or measurements to totally fool any learning algorithm."
But this happens only for states that "look like pure noise," which would be useless for computation anyway.
"The good news is that for a large class of well-structured states that are frequently used in many quantum algorithms, it is possible to achieve reasonably good accuracy, even when the noise is added maliciously," Liu said.
While it was designed to deal with a problem in quantum computing, the new adversarially robust framework relied heavily on nonquantum statistical and algorithmic tools. For Liu, the work builds on the insight that while some problems may look like quantum problems, "when you dig inside, the core difficulty relies on techniques from classical statistics and algorithms."
Maryam Aliakbarpour , a Rice computer scientist who studies learning theory ⎯ i.e. how machine learning works as a computational process ⎯ contributed guidance and expertise on the classical side of the research.
"I design algorithms that solve statistical problems under realistic constraints, and some of the things I consider in my work were directly relevant here," said Aliakbarpour, Rice's Michael B. Yuen and Sandra A. Tsai Assistant Professor in the Department of Computer Science. "This problem was a true collaboration."
To move past the NISQ stage, quantum technology will have to continue to improve strategies for effectively handling noise. One avenue for doing so is to fine-tune the underlying physical systems that host quantum states.
Promising new discoveries in two-dimensional materials are edging closer to "quieter" and more stable quantum hardware, and Rice researchers are at the forefront of this exploration: Just a few examples of recent advances include wrinkles with stable electron spin texture , strategic 2D metal layers that stage phonon interference and carefully tuned 3D structures known as optical cavities that coax exotic quantum behaviors into being.
Another front for tackling the issue is at the software level: Quantum algorithms that are attuned to the complex and delicate nature of quantum states are critical for advancing quantum computing. The new adversarially robust framework developed by Aliakbarpour, Chia and Liu, together with Vladimir Braverman, an adjunct professor of computer science at Rice, offers a creative algorithmic approach to dealing with quantum computers' noisiness.
The research was supported by the National Science Foundation (2528780, 2243659, 2339116), the U.S. Office of Naval Research (N00014-23-1-2737), the Department of Energy (DE-SC0024301) and Rice. The content herein is solely the responsibility of the authors and does not necessarily represent the official views of the funding organizations and institutions.
