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Randomly Compiled Quantum Simulation with Exponentially Reduced Circuit Depths
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Randomly Compiled Quantum Simulation with Exponentially Reduced Circuit Depths
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.
Forward citations
Cited by 6 Pith papers
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Optimal Lower Bounds for Hamiltonian Simulation
There exist simple weighted-local Hamiltonians for which quantum simulation requires Ω(min over K of (Kt + t²λ_K²/ε)) gates — exactly matching the composite qDRIFT algorithm's cost.
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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 achieves O(ε^{-2} log²(1/ε)) gate complexity for observable estimation in quantum dynamics by using coupled multilevel qDRIFT estimators with variance decay across levels.
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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 tra...
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Circuit-Efficient Randomized Quantum Simulation of Non-Unitary Dynamics with Observable-Driven and Symmetry-Aware Designs
A randomized compilation of LCHS for non-unitary dynamics, with an observable-driven variant and a symmetry-aware sampler, claims reduced ancilla and circuit depth at the cost of more repetitions.
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