Speaker
Description
Simulating the real-time dynamics of quantum systems is a key application of quantum computing. Variational quantum simulation (VQS) attempts to overcome the resource-intensive requirements of methods such as Trotterization by using a variational quantum circuit, controlled by $m$ parameters, to simulate the time evolution.
However, so far, VQS and all its variants suffer from at least one of the four following drawbacks:
($i$) $O(m^2)$ complexity due to estimation of the quantum geometric tensor;
($ii$) implementation of the Hadamard test for the imaginary gradient;
($iii$) NP-hardness of optimization of the variational ansatz;
($iv$) Trotter step errors.
VQS suffers from ($i$, $ii$), while variants such as projected variational quantum dynamics (p-VQD) or variational fast forwarding, from ($iii$, $iv$).
These restrictions have hampered the study and experimental implementations of real-time evolution in noisy quantum computers.
Here, we propose the geometry-aware variational quantum simulator (GVQS) as the first near-term, real-time simulation method that avoids all four drawbacks.
We achieve this by relying on a geometry-aware amplitude encoder and methods based on exact geodesic transport (EGT).
In particular, GVQS removes the restrictions of VQS by using an analytic quantum geometric tensor, removing ($i$), and making use of our special ansatz structure to directly estimate the imaginary gradient, removing ($ii$).
As a further result, we significantly enhance the performance of p-VQD by integrating the EGT optimizer.
We demonstrate GVQS on the fixed-particle-number, two-mode Bose-Hubbard Hamiltonian, observing superior performance over p-VQD.
Our methods open up simulation of quantum evolution as a promising application of noisy quantum computers.
| Topic | Quantum variational circuits and their applications |
|---|---|
| Additional Topic | Quantum algorithms for machine learning applications |