Quantum Computers Cut Measurement Costs with New Method

Researchers are developing new methods to efficiently find the ground state of quantum systems, a crucial task for utilising quantum computers and a key subroutine for many algorithms. Jona Erle from the Mathematical Institute, University of Oxford, Quantum Motion, and Moderna, working with Balint Koczor from the Mathematical Institute, University of Oxford, present a novel approach called the Shadow Enhanced Greedy Quantum Eigensolver (SEGQE). This framework significantly reduces the need for costly logical measurements by employing classical shadows to rapidly evaluate the impact of potential quantum gates. Their work establishes rigorous bounds on computational cost and demonstrates, through numerical testing on transverse-field Ising models and random Hamiltonians, that SEGQE scales favourably with system size, offering a promising measurement-efficient strategy for early-stage quantum computing architectures. Imagine sculpting a perfect miniature from a block of stone, refining it with each careful strike. To achieve similar precision with quantum systems is immensely challenging. Yet a new method dramatically reduces the number of operations needed to find a system’s lowest energy state. This advance offers a practical path toward utilising near-term quantum computers for complex calculations. Scientists are increasingly focused on preparing high-fidelity ground states as a central task within quantum computing, with applications extending to quantum chemistry, quantum optimisation, and quantum machine learning. Highly expressive circuits can suffer from barren plateaus, regions where gradients become exponentially small, while simpler circuits may lack the necessary accuracy to approximate the target state effectively. These trainability issues are often compounded by poor local minima during optimisation, demanding a substantial measurement budget for practical applications. Resource minimisation is particularly critical in the early stages of fault-tolerant quantum computing, where logical measurements remain a costly operation. As a result, researchers have begun exploring alternative state-preparation strategies that maintain flexibility, avoid expensive gradient estimation. Maximise information gained from each quantum measurement. Classical shadows, a technique for estimating multiple expectation values from a limited number of measurements — are proving to be a valuable tool in this endeavour. At each step uses classical shadows to evaluate the potential energy reduction achieved by adding candidate gates. The gate predicted to yield the largest decrease in energy is then appended to the circuit, progressively refining the state towards the ground state. At the heart of SEGQE’s efficiency is its ability to evaluate a large set of candidate gate additions in parallel using classical post-processing, resulting in a per-iteration sample complexity that scales logarithmically with the number of gates considered. Here, the design of SEGQE offloads computationally intensive searches to classical hardware, enabling efficient parallelisation and utilisation of high-performance computing resources. While the circuit depth increases with each added gate, the per-iteration measurement cost grows only mildly with system size, and the information extracted per quantum shot retains the asymptotic optimality guarantees of classical shadows. This makes SEGQE particularly well-suited for early fault-tolerant regimes, where deeper circuits are feasible but logical measurement rates are limited, offering a promising approach for initial state preparation in applications like fault-tolerant phase estimation. In turn, at iteration one, The project team obtained a per-iteration sample complexity exhibiting logarithmic dependence on the number of candidate gates. Meanwhile, this logarithmic scaling is vital because it means the computational cost increases slowly as the number of possible quantum gate choices grows, making the method practical for larger systems. Initially, the algorithm begins with an identity circuit. Iteratively builds upon it to approximate the ground state of a given Hamiltonian. At the same time, at each iteration, the current circuit is applied to an initial state, potentially incorporating prior classical information, to produce a new quantum state. Then, a collection of classical shadows are recorded, obtained through uniformly random local Pauli measurements performed on the quantum state — the core of SEGQE lies in its classical post-processing stage. Where these shadows are used to estimate the energy reduction induced by a large set of candidate local gates. For each gate within a set of K gates. It calculates the energy difference between the current state and the state after applying the gate. In turn, this calculation involves decomposing each Pauli term in the Hamiltonian with respect to the qubit support of the unitary gate — for efficient evaluation of the energy difference using the classical shadows. Once estimated, the algorithm identifies the gate that minimizes the energy and updates the circuit accordingly, and to accurately estimate these energy differences, The project leverages the properties of Pauli operators. Meanwhile, this form an orthonormal basis on the relevant operator space. By expanding the transformed Pauli operators in terms of this basis, the energy difference can be expressed as a linear combination of expectation values, which are estimated using the classical shadows. Instead of directly evaluating the expectation values on the quantum computer, these values are computed entirely classically, reducing the demand for quantum resources. At the same time, the procedure continues until either a predefined circuit depth is reached or no candidate gate yields an energy reduction exceeding a predefined threshold. By employing classical shadows and focusing on local gates, SEGQE aims to minimise the measurement budget while maximising the utilisation of classical computational power. Making it well-suited for early fault-tolerant quantum computing architectures. This approach contrasts with methods requiring deeper circuits or faster logical measurement rates, offering a promising path towards efficient ground-state preparation. Reducing quantum verification needs through intelligent sampling with SEGQE Scientists developing quantum algorithms face a persistent challenge: the sheer number of measurements needed to verify results. For years, achieving practical quantum advantage has been hampered by this demand. As early quantum devices possess limited qubit counts and are prone to errors. Leveraging classical calculations to assess the impact of each step before committing to a quantum measurement. As a problem’s complexity increases, traditional methods struggle to scale efficiently. This effort demonstrates a logarithmic relationship between the number of candidate gates and the required samples, a promising sign for tackling larger systems. The algorithm’s performance relies on accurately estimating energy reductions using classical shadows, a technique that introduces its own approximations. By focusing on greedy optimisation, the method prioritises immediate gains, potentially overlooking paths that might yield better long-term solutions. Benchmarks have been conducted on transverse-field Ising models and random Hamiltonians, and these show encouraging results. To extend these findings to a wider range of physical systems and Hamiltonian structures will be essential. A key area for future work lies in combining SEGQE with other state-preparation techniques. Rather than viewing it as a standalone solution, integrating it into a broader quantum computation set of tools could unlock even greater efficiencies. The next step may involve exploring adaptive shadow techniques, where the classical sampling strategy itself is refined based on the evolving quantum state. For the broader effort to build useful quantum computers, this effort represents a step towards bridging the gap between theoretical potential and practical realisation — unlike many algorithms that remain distant prospects, SEGQE is designed with the limitations of near-term hardware in mind. Previous approaches demanded ever-increasing resources, this method offers a pathway to extract meaningful results from existing devices, and since the algorithm’s efficiency stems from clever use of classical computation, it could buy valuable time as quantum hardware continues to mature. Researchers to explore more complex problems sooner than previously thought. 👉 More information 🗞 A Shadow Enhanced Greedy Quantum Eigensolver 🧠 ArXiv: https://arxiv.org/abs/2602.17615 Tags: