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A new study published in Science Advances presents a major step forward in the development of quantum algorithms that are more accurate, more efficient, and better suited to the capabilities of early quantum computers.
The research from Queen Mary University of London focuses on improving the way quantum computers calculate the fundamental properties of quantum systems—known as eigenstates. These calculations are essential for progress in fields such as chemistry, materials science, and physics, where understanding how particles behave at the quantum level can lead to breakthroughs ranging from new medicines to advanced materials.
Traditional quantum algorithms can be highly demanding: they often require deep, complex circuits and large numbers of qubits, making them difficult to run on today's noisy or early fault‑tolerant quantum hardware. The team behind this new work addresses these challenges by designing high‑precision algorithms that significantly reduce circuit depth and minimise the number of difficult controlled operations, making them far more practical for current and near‑future machines.
A key innovation explored in the study is the use of randomised linear-combination-of-unitaries technique for realising general quantum operations. This approach allows an efficient implementation of spectral filtering—a technique that allows the quantum computer to 'filter out' the information it needs with high precision. Combined with advanced ​quantum dynamics simulation methods, the approach lets researchers estimate properties like ground‑state or excited-state energy with near‑optimal efficiency, all while keeping hardware demands low.
The work offers rigorous theoretical guarantees and detailed analysis of how these algorithms perform, demonstrating advantages over existing methods. Crucially, the work provides concrete resource estimates for both noisy quantum devices and early fault-tolerant quantum devices. This offers a realistic roadmap for quantum usefulness. With quantum technologies progressing quickly, these findings bring the scientific community a step closer to real‑world quantum simulations that could transform multiple research fields.
This advancement highlights the growing impact of quantum algorithm research and its crucial role in unlocking the potential of emerging quantum hardware.
This work is led by Dr Jinzhao Sun at the School of Physical and Chemical Sciences at Queen Mary, in collaboration with academics at Imperial College, University of Cambridge, and University and Chicago.

www.science.org/doi/10.1126/sciadv.aeb1622