The transition from Noisy Intermediate-Scale Quantum (NISQ) computing to Fault-Tolerant Quantum Computing (FTQC) represents a significant milestone in quantum technology. Within this transition period, a new algorithm called Quantum Zeno Monte Carlo (QZMC) has emerged as a promising solution for addressing the challenges of early error-corrected quantum computers.
QZMC is designed as a classical-quantum hybrid algorithm that demonstrates remarkable resilience to both device noise and Trotter errors, while maintaining polynomial computational complexity for gapped systems. This algorithm enables the computation of both static and dynamic physical properties without requiring initial state overlap or variational parameters, which results in reduced quantum circuit depth.
Traditional quantum computing approaches face significant hurdles. Finding Hamiltonian eigenstates and their properties is crucial for applications like material design and quantum machine learning, but requires initial states sufficiently close to target eigenstates to achieve polynomial quantum time solutions with fully fault-tolerant systems. During the NISQ era, quantum algorithms have prioritized noise resilience, leading to ansatz-based approaches that lack provable polynomial complexity.
The recent development of 48 logical qubit devices signals the beginning of error-corrected quantum computing, potentially bridging the gap between NISQ and FTQC eras. These early error-corrected quantum computers can handle longer quantum circuits than their NISQ predecessors and execute algorithms with polynomial complexity. However, they still face device noise due to limited error correction capabilities, meaning algorithms designed for the FTQC era may not be suitable.
The QZMC algorithm addresses these limitations by offering noise resilience while maintaining polynomial quantum time costs. The researchers validated its noise resilience by implementing it on IBM’s NISQ devices for systems with up to 12 qubits. Numerical demonstrations on a noiseless quantum computer simulator confirmed its resilience to Trotter errors and polynomial computational scaling. Notably, QZMC’s resilience to Trotter errors allows for computing eigenstate properties with shallower circuits compared to recent phase estimation techniques.
This development represents a significant step toward achieving quantum advantage with early error-corrected quantum computers, potentially accelerating practical quantum computing applications.
Reference: Han, M., Park, H. & Choi, S. Quantum Zeno Monte Carlo for computing observables. npj Quantum Inf 11, 46 (2025). doi:10.1038/s41534-025-01002-3
