Hi all,
This week Mattia Chiurco will talk about “Optimizing Quantum Time Dynamics with Classical Support”. See below for the abstract.
The talk will take place on Thursday at 11:00 in HIT E 41.1.
Best,
Ladina
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Title:
Optimizing Quantum Time Dynamics with Classical Support
Abstract:
Quantum time evolution is fundamental for simulating many-body systems in quantum chemistry and condensed matter physics. Trotter–Suzuki decomposition approximates the full evolution operator with deep circuits that often exceed near-term hardware coherence times. Variational quantum time evolution (VarQTE) leverages McLachlan’s variational principle to derive an ordinary differential equation for a parameterized circuit that approximates evolution on a given input state using much shallower circuits. However, computing the quantum geometric tensor and the energy gradient at each time step to solve this ODE incurs considerable measurement overhead, scaling poorly with the number of variational parameters.
In this work, we introduce and benchmark three classical methods to alleviate this bottleneck in a hybrid quantum-classical pipeline by performing the majority of QGT and gradient calculations classically and focusing quantum resources on classically intractable subroutines, such as state sampling.
First, we employ lightcone truncation, simulating only the relevant causal subcircuits so that each variational quantity depends on just a small subset of qubits, enabling efficient evaluation for shallow-depth ansätze on the order of a hundred qubits.
Next, we apply a Pauli propagation algorithm to extend our reach to deeper circuits at the cost of increased computational complexity. Finally, we implement a lightcone‐aware overlap procedure within the matrix product state framework to evaluate the QGT and the energy gradient by restricting tensor contractions to the causal subspace, enabling simulation of systems with lightcone sizes beyond the reach of statevector methods.
To assess the expressive power of VarQTE, we compare to second order Suzuki–Trotter dynamics across transverse-field Ising and isotropic Heisenberg Hamiltonians on one- and two-dimensional lattices. We quantify compressibility factors and demonstrate that a moderate number of variational layers can effectively emulate numerous Trotter steps with comparable accuracy. We also investigate adaptive ansatz expansion protocols, including layer freezing, and identify trade-offs between parameter growth and lightcone spread.
Furthermore, we benchmark VarQTE against approximate quantum compiling (AQC). The comparison reveals that VarQTE matches the performance of AQC for 1D systems. However, for higher dimensional systems the integration of AQC becomes increasingly complex, and VarQTE becomes the more amenable routine.
Finally, we demonstrate that our VarQTE pipeline can be used to generate a subspace expansion protocol which in turn can be integrated into a spectral estimation application via sample-based Krylov quantum diagonalization (SKQD) on 12- and 52-qubit Kagome lattices.
Our results chart a pathway toward efficient variational dynamics and spectral estimation on near-term quantum computers platforms