Exponentially Reduced Circuit Depths Using Trotter Error Mitigation

Journal Article · Tue Aug 12 00:00:00 EDT 2025 · PRX Quantum

DOI:https://doi.org/10.1103/kw39-yxq5· OSTI ID:3006232

Watson, James D. ^[1]; Watkins, Jacob ^[2]

---

1. National Inst. of Standards and Technology (NIST), Gaithersburg, MD (United States); Univ. of Maryland, College Park, MD (United States)
2. Michigan State Univ., East Lansing, MI (United States); JP Morgan Chase (United States)

Product formulas are a popular class of digital quantum simulation algorithms due to their conceptual simplicity, low overhead, and performance, which often exceeds theoretical expectations. Recently, Richardson extrapolation and polynomial interpolation have been proposed to mitigate the Trotter error incurred by the use of these formulas. This work provides a rigorous, general analysis of these techniques for computing time-evolved observables, simplifying the interpolation algorithm in the process, and shows that extrapolation generically improves the performance of product formulas for this task. We demonstrate that, to achieve error 𝜖 in a simulation of time 𝑇 using a 𝑝 ⁢th-order product formula with extrapolation, circuit depths of 𝑂⁡(𝑇^1+1/𝑝 ⁢polylog (1/𝜖)) are sufficient—an exponential improvement in the precision over product formulas alone. Furthermore, we prove that these algorithms achieve commutator scaling, and improve the 𝑇 complexity for the interpolation algorithm. By relaxing the requirement of performing exact Chebyshev interpolation, our simplified algorithm eliminates the need for fractional implementations of Trotter steps, reducing computational overhead. Finally, we show these techniques can be combined with the classical shadows method to estimate many time-evolved local observables. Taken together, our findings provide the strongest evidence yet for the utility of Trotter error-mitigation techniques in algorithmic applications.

• Research Organization: Michigan State Univ., East Lansing, MI (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Nuclear Physics (NP)
• Grant/Contract Number: SC0023658
• Other Award/Contract Number: DGE-1848739; PHY-2310620; OMA-2120757
• OSTI ID: 3006232
• Journal Information: PRX Quantum, Journal Name: PRX Quantum Journal Issue: 3 Vol. 6; ISSN 2691-3399
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

quantum algorithms & computation
quantum simulation