Hardware-Friendly Estimation of LCU-Based Expectation Values via Quantum-to-Classical Workload Shifting
Abstract
Estimating the expectation value of an observable O for a quantum state evolved under a general, possibly non-unitary, operator A is a fundamental task in quantum simulation, chemistry, and variational algorithms. Existing linear-combination-of-unitaries (LCU) approaches implement A on hardware, requiring ancilla qubits, controlled unitaries and, in randomized variants, fresh circuit executions for every Monte Carlo sample. These costs are prohibitive on NISQ and early fault-tolerant devices. We propose HERMES (Hardware-Efficient Reusable Measurements for Estimating LCU-based expectation valueS), which moves the processing of A entirely to the classical domain. Expanding A and O in the Pauli basis and sampling pairs of Pauli terms classically, HERMES rewrites μ= Tr(OAρA†)/Tr(AρA†) as a ratio of weighted sums of Pauli expectation values on the unmodified state ρ, with no ancillas, controlled unitaries, or quantum implementation of A. A two-level measurement reduction scheme (Pauli deduplication and commuting-group partitioning) bounds the number of distinct measurement settings independently of the sample count, unlike randomized LCU methods whose circuit executions grow linearly with it. On ground-state energy estimation of H2 and LiH via imaginary-time evolution, HERMES matches or beats Pauli single-ancilla LCU baseline using shallow circuits with no two-qubit gates beyond state preparation under qubit-wise commuting grouping. It is also more robust to noise and completes a noisy LiH simulation infeasible for the baseline, at the cost of classical overhead growing with the number of Pauli terms in A.
Related
- Hybrid Quantum and Classical Workload Management with Graph-based Scheduling
- Efficient expectation value estimation for quantum circuits via extended stabilizer frameworks and adaptive variance estimation
- New directions in dynamical expectation estimation
- Resource Assessment of Classical and Quantum Hardware for Post-Quench Dynamics
- Reducing quantum and classical resources for quantum-centric supercomputing workloads on near-term hardware
BibTeX
@misc{chittoor2026hardwarefriendly,
title = {{Hardware-Friendly Estimation of LCU-Based Expectation Values via Quantum-to-Classical Workload Shifting}},
author = {Hari Hara Suthan Chittoor and Thirumalai Manimaran},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32841},
eprint = {2610.32841},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32841},
}
RIS
TY - UNPB
TI - Hardware-Friendly Estimation of LCU-Based Expectation Values via Quantum-to-Classical Workload Shifting
AU - Hari Hara Suthan Chittoor
AU - Thirumalai Manimaran
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32841
UR - https://arxiv.org/abs/2610.32841
AB - Estimating the expectation value of an observable O for a quantum state evolved under a general, possibly non-unitary, operator A is a fundamental task in quantum simulation, chemistry, and variational algorithms. Existing linear-combination-of-unitaries (LCU) approaches implement A on hardware, requiring ancilla qubits, controlled unitaries and, in randomized variants, fresh circuit executions for every Monte Carlo sample. These costs are prohibitive on NISQ and early fault-tolerant devices. We propose HERMES (Hardware-Efficient Reusable Measurements for Estimating LCU-based expectation valueS), which moves the processing of A entirely to the classical domain. Expanding A and O in the Pauli basis and sampling pairs of Pauli terms classically, HERMES rewrites μ= Tr(OAρA^†)/Tr(AρA^†) as a ratio of weighted sums of Pauli expectation values on the unmodified state ρ, with no ancillas, controlled unitaries, or quantum implementation of A. A two-level measurement reduction scheme (Pauli deduplication and commuting-group partitioning) bounds the number of distinct measurement settings independently of the sample count, unlike randomized LCU methods whose circuit executions grow linearly with it. On ground-state energy estimation of H_2 and LiH via imaginary-time evolution, HERMES matches or beats Pauli single-ancilla LCU baseline using shallow circuits with no two-qubit gates beyond state preparation under qubit-wise commuting grouping. It is also more robust to noise and completes a noisy LiH simulation infeasible for the baseline, at the cost of classical overhead growing with the number of Pauli terms in A.
ER -