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Exponentially Accurate Open Quantum Simulation via Randomized Dissipation with Minimal Ancilla

Jumpei Kato1,2,3,*,†, Kaito Wada3,*,‡, Kosuke Ito4,2,§, and Naoki Yamamoto2,5,∥

  • *J. K. and K. W. contributed equally to this work.
  • †Contact author: jumpei_kato@keio.jp
  • ‡Contact author: wkai1013keio840@keio.jp
  • §Contact author: kosuke.ito@quantum.keio.ac.jp
  • ∥Contact author: yamamoto@appi.keio.ac.jp
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PRX Quantum 7, 033046 – Published 4 September, 2026

DOI: https://doi.org/10.1103/91yq-swlv

Abstract

Simulating open quantum systems is an essential technique for understanding complex physical phenomena and advancing quantum technologies. Some quantum algorithms simulate Lindblad dynamics exponentially accurately, i.e., they achieve logarithmically short circuit depth in terms of accuracy, but they need to coherently encode all possible jump operators with a large ancilla consumption. Minimizing the gate and ancilla counts while achieving such a logarithmic scaling in accuracy remains an important challenge. In this work, we present two randomized quantum algorithms for simulating general Lindblad dynamics with multiple jump operators aimed at an observable estimation that achieves a circuit depth with not only logarithmic scaling in accuracy but also either partial or complete independence from the parameters specifying the Lindbladian. This is based on a novel random circuit compilation method that leverages dissipative processes with only a single jump operator, leading to the proposed methods using minimal ancilla qubits—4+⌈log2M⌉ in the first case and seven in the other, where each single jump operator has at most M Pauli strings. In addition, we numerically demonstrate the practical advantage over existing approaches by providing a detailed analysis of the required gate and ancilla counts. This work represents a significant step toward making open quantum system simulations more feasible on early fault-tolerant quantum computing devices.

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Popular Summary

Quantum computation offers a promising approach for simulating the dynamics of open quantum systems. Previous quantum algorithms for simulating the Lindblad equation achieve nearly optimal gate scaling in terms of simulation time and accuracy. However, these algorithms need to encode all possible dissipative processes in a quantum circuit simultaneously. This results in a large number of gates and ancilla qubits, making them challenging for early fault-tolerant devices. In this work, we develop a randomized algorithm that avoids encoding all dissipative processes at once. It randomly compiles the Hamiltonian dynamics and dissipations, while enabling highly accurate observable estimation with only a minimal number of additional qubits. This randomness also enables efficient simulation of complicated Lindbladians with many terms. Our results include fault-tolerant resource estimates of gate and qubit counts for practical many-body problems. These estimates show that our algorithm can make classically challenging simulations more practical on early fault-tolerant quantum computers.

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PRX Quantum 7, 033046– Published 4 September, 2026
  • Received 14 March 2025
  • Revised 2 December 2025
  • Accepted 20 May 2026
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