[RBRC Seminar] Quantum Circuit Optimization using Differentiable Tensor Network States

by David Rogerson

Thursday 12 Dec 2024, 12:30 → 14:30 US/Eastern

2-160 (https://bnl.zoomgov.com/j/1600983728?pwd=RAD7OLcqre7Ycsp6JfFp6HAnpyLxex.1)

Noisy intermediate scale quantum computing shows promising in simulating models of strongly interacting quantum systems, like discretized quantum field theories. To minimize the effect of short coherence times and noisy gates, shallow circuits are required. Classical algorithms based on Matrix Product States (MPS) on the other hand allow a noiseless simulation but are restricted to states with low-entanglement. These are usually ground-states of local low-dimensional systems and prohibit long time quench dynamics.

As a step to combine the benefits of both approaches we present a tensor network based quantum circuit optimizer running on classical hardware https://arxiv.org/abs/2408.12583. The algorithm is able to find shallow quantum circuit representations of MPS with fidelities of over 99%. These circuits are ready to be ported on quantum hardware and can be used for example as an non-trivial initial state for the time evolution on quantum hardware.  The optimizer combines MPS based TEBD and automatic differentiation with the ADAM optimizer on charge conserving unitary manifolds.

The examples we consider are three lattice 1+1D field theories: The transverse field Ising model using qubits, The 3-states Potts model using qutrits and the massive Schwinger model using a staggered fermion representation. For all these 3 models the algorithm finds system size independent shallow circuits which prepare the groundstate for system sizes up to L = 100. Deeper circuits in the order of the system size allows to optimize circuits for the first 10 exited eigenstates for L = 24.