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Advanced Quantum Technologies

Cover Feature: Sampling Noise and Optimized Measurement Distribution in Imaginary‐Time Quantum Dynamics Simulations (Adv. Quantum Technol. 10/2026)

Feng Zhang, Niladri Gomes, Joshua Aftergood, Thomas Iadecola, Yong‐Xin Yao, Peter P. Orth

Published Oct 1, 2026• 0 citations
Publisher

Abstract

In article number e70418, Yong-Xin Yao and co-workers report a variational quantum circuit architecture for simulating quantum dynamics on quantum devices. Layered quantum gates process entangled qubits through fixed-depth circuits, converging via an optimization funnel toward a ground state. The spin-chain representations at the bottom illustrate imaginary-time evolution driving a spin model toward its lowest-energy configuration with optimized measurement distribution.

DOI
10.1002/qute.70515

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In article number e70418, Yong-Xin Yao and co-workers report a variational quantum circuit architecture for simulating quantum dynamics on quantum devices. Layered quantum gates process entangled qubits through fixed-depth circuits, converging via an optimization funnel toward a ground state. The spin-chain representations at the bottom illustrate imaginary-time evolution driving a spin model toward its lowest-energy configuration with optimized measurement distribution.
Variational quantum dynamics simulations (VQDS) provide a promising route to simulate real- and imaginary-time quantum dynamics on noisy intermediate-scale quantum devices using fixed-depth circuits. However, their practical performance is strongly limited by sampling noise arising from a finite number of circuit measurements. In this work, we systematically investigate the impact of sampling noise on VQDS, with a focus on ground-state preparation in one-dimensional Ising spin models using imaginary time evolution. We compare different regularization strategies for stabilizing the equations of motion and show that Tikhonov regularization provides robust performance in noisy imaginary-time evolution. We then benchmark measurement-distribution strategies that allocate shots by minimizing a cost function that characterizes the error in solving the equation of motion. Using noisy circuit simulations, we demonstrate that such optimized shot allocation can significantly improve state fidelity and reduce the total measurement cost by more than a factor of two compared to uniform shot distributions. We observe that the best results are found if a sufficiently large number of measurements is guaranteed for all circuits, suggesting that a finite fraction of shots should be distributed evenly. Our results provide practical guidelines for implementing measurement-efficient variational quantum dynamics and ground-state preparation on near-term quantum hardware.
Quantum computing encompasses a variety of computation models, including gate-based (GB), topological, quantum annealing, and measurement-based (MB). MB performs computation through single-qubit measurements on a highly entangled cluster state and is proposed to offer some practical advantages on near-term quantum hardware in terms of circuit depth. In this work, we propose MB-VQITE, which leverages the MB model for solving optimization problems using the variational quantum imaginary time evolution (VQITE) algorithm. We apply MB-VQITE to the molecular docking problem, which is relevant in pharmaceutical research. We perform direct comparisons between the MB and GB computing paradigms on IBM Cleveland quantum hardware and perform optimization procedures on noisy simulators. We find that MB-VQITE outperforms GB-VQITE on current quantum hardware by reducing circuit depth, thus decreasing noise to allow for smoother optimization.
The current generation of noisy intermediate-scale quantum computers introduces new opportunities to study quantum many-body systems.In this paper, we show that quantum circuits can provide a dramatically more efficient representation than current classical numerics of the quantum states generated under nonequilibrium quantum dynamics.For quantum circuits, we perform both real-and imaginary-time evolution using an optimization algorithm that is feasible on near-term quantum computers.We benchmark the algorithms by finding the ground state and simulating a global quench of the transverse-field Ising model with a longitudinal field on a classical computer.Furthermore, we implement (classically optimized) gates on a quantum processing unit and demonstrate that our algorithm effectively captures real-time evolution.
The current generation of noisy intermediate-scale quantum computers introduces new opportunities to study quantum many-body systems. In this paper, we show that quantum circuits can provide a dramatically more efficient representation than current classical numerics of the quantum states generated under nonequilibrium quantum dynamics. For quantum circuits, we perform both real- and imaginary-time evolution using an optimization algorithm that is feasible on near-term quantum computers. We benchmark the algorithms by finding the ground state and simulating a global quench of the transverse-field Ising model with a longitudinal field on a classical computer. Furthermore, we implement (classically optimized) gates on a quantum processing unit and demonstrate that our algorithm effectively captures real-time evolution.
Dynamical simulation of quantum many-body systems is a central task in quantum chemistry and requires efficient wavefunction representations. Although tensor-network and neural-network quantum states have achieved considerable success in ground-state calculations, entanglement growth hinders their application to quantum dynamics. Quantum computing may offer a route to quantum advantage, but algorithms such as Trotterization generally require fault-tolerant quantum computers, whereas near-term hardware supports only limited circuit sizes. Variational quantum simulation (VQS) instead represents the evolving state with a single shallow, fixed-size parameterized quantum circuit (PQC). Here, we introduce nonorthogonal variational quantum simulation (NOVQS), which applies linear combinations of parameterized quantum states to real- and imaginary-time evolutions. We design a shallow, hardware-friendly ansatz tailored to second-quantized electronic-structure Hamiltonians, together with resource-efficient protocols for measuring the matrices and vectors in the parameter equations of motion. Error analysis and resource estimation are also provided. Numerical simulations of hydrogen chains and the nitrogen molecule demonstrate that a collection of shallow, or even single-layer, PQCs can match or outperform a much deeper PQC in VQS. In particular, we identify a trade-off between circuit number and depth. NOVQS therefore provides a flexible route to enhancing wavefunction expressivity under circuit-depth constraints, making it a promising framework for quantum dynamics simulations on near-term quantum processors.
The imaginary-time evolution of quantum states is integral to various fields, ranging from natural sciences to classical optimization or machine learning. Since simulating quantum imaginary-time evolution generally requires storing an exponentially large wave function, quantum computers are emerging as a promising platform for this task. However, variational approaches, suitable for near-term quantum computers, struggle with a prohibitive number of measurements and impractical runtimes for relevant system sizes. Here, we suggest a stochastic approach to variational quantum imaginary-time evolution, which allows a significant reduction in runtimes. Our approach allows trading off invested resources and accuracy, which makes it also suitable for ground state preparation, where simulating the exact dynamics is not required. We demonstrate the efficiency of our algorithm in simulations and show a hardware experiment performing the imaginary-time evolution of the transverse field Ising model on 27 qubits.