Classical step-size extrapolation reduces the maximum single-run circuit depth of a one-ancilla quantum ODE solver from O(1/ε) to O(polylog(1/ε)) without adding ancillae.
Randomly compiled quantum simulation with exponentially reduced circuit depths
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The quantum stochastic drift protocol, also known as qDRIFT, has become a popular algorithm for implementing time-evolution of quantum systems using randomised compiling. In this work we develop qFLO, a higher order randomised algorithm for time-evolution. To estimate an observable expectation value at time $T$ to precision $\epsilon$, we show it is sufficient to use circuit depths of $O(T^2\log(1/\epsilon))$ -- an exponential improvement over standard qDRIFT requirements with respect to $\epsilon$. The protocol achieves this using $O(1/\epsilon^2)$ repeated runs of the standard qDRIFT protocol combined with classical post-processing in the form of Richardson extrapolation. Notably, it requires no ancillary qubits or additional control gates making it especially promising for near-term quantum devices. Furthermore, it is well-conditioned and inherits many desirable properties of randomly compiled simulation methods, including circuit depths that do not explicitly depend on the number of terms in the Hamiltonian.
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quant-ph 3years
2026 3roles
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MLMC-qDRIFT couples multilevel qDRIFT estimators to achieve O(ε^{-2} log²(1/ε)) gate complexity for observable estimation instead of the standard O(ε^{-3}).
Continuous-time probabilistic angle interpolation enables Trotter-error-free stochastic quantum evolution, demonstrated on H3+ ground-state energy and sparse SYK out-of-time-ordered correlators via simulations and trapped-ion hardware.
citing papers explorer
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Circuit Depth Reduction of One-Ancilla Quantum Differential Equation Solver via Extrapolation
Classical step-size extrapolation reduces the maximum single-run circuit depth of a one-ancilla quantum ODE solver from O(1/ε) to O(polylog(1/ε)) without adding ancillae.
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MLMC-qDRIFT: Multilevel Variance Reduction for Randomized Quantum Hamiltonian Simulation
MLMC-qDRIFT couples multilevel qDRIFT estimators to achieve O(ε^{-2} log²(1/ε)) gate complexity for observable estimation instead of the standard O(ε^{-3}).
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Continuous-time evolution via probabilistic angle interpolation and its applications
Continuous-time probabilistic angle interpolation enables Trotter-error-free stochastic quantum evolution, demonstrated on H3+ ground-state energy and sparse SYK out-of-time-ordered correlators via simulations and trapped-ion hardware.