Hardware efficient method shifts quantum workload to classical side
Hardware-Friendly Estimation of LCU-Based Expectation Values via Quantum-to-Classical Workload Shifting
Emerging Technologies
Summary
Estimating values from quantum systems usually requires complicated quantum hardware and many steps, which are hard for current quantum devices. The authors propose a new method called HERMES that moves much of the difficult work from quantum machines to classical computers. This approach avoids extra helper qubits and complex quantum gates, using simpler measurements and classical calculations instead. It performs well on simulations of small molecules and is more noise-resistant than traditional methods, although it needs more classical computing power.
What this means in practice
- •For quantum algorithm developers: Estimate quantum observable values efficiently on near-term devices without ancilla qubits or complex gates by shifting computations to classical post-processing.
- •For quantum chemistry software teams: Simulate ground-state energies of molecules on noisy intermediate-scale quantum hardware using measurement-efficient methods that tolerate noise better than standard LCU approaches.
Authors
Hari Hara Suthan Chittoor, Thirumalai Manimaran
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 $μ= \mathrm{Tr}(OAρA^{\dagger})/\mathrm{Tr}(AρA^{\dagger})$ 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 $\mathrm{H}_2$ and $\mathrm{LiH}$ 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 $\mathrm{LiH}$ simulation infeasible for the baseline, at the cost of classical overhead growing with the number of Pauli terms in $A$.