Abstract
We benchmark the accuracy of a variational quantum eigensolver based on a finite-depth quantum circuit encoding ground state of local Hamiltonians. We show that in gapped phases, the accuracy improves exponentially with the depth of the circuit. When trying to encode the ground state of conformally invariant Hamiltonians, we observe two regimes. A finite-depth regime, where the accuracy improves slowly with the number of layers, and a finite-size regime where it improves again exponentially. The cross-over between the two regimes happens at a critical number of layers whose value increases linearly with the size of the system. We discuss the implication of these observations in the context of comparing different variational ansatz and their effectiveness in describing critical ground states.
Highlights
Future large-scale fault-tolerant quantum computers will allow to simulate quantum systems made by a large number of constituents, providing important insight on their properties [1,2,3]
We have analyzed the performance of a finite-depth quantum circuit in order to encode the ground state of local Hamiltonians
Beyond that number of layers, the precision improves again exponentially, and the variational quantum eigensolver (VQE) provides a faithful representation of pseudo-critical ground states
Summary
Future large-scale fault-tolerant quantum computers will allow to simulate quantum systems made by a large number of constituents, providing important insight on their properties [1,2,3]. The general philosophy of a VQA is to define a parametrized quantum circuit whose architecture is dictated by the type and size of the quantum device that is available, and that depends on a set of classical parameters, e.g. the angles of single-qubit gates encoding a rotation. These parameters can be optimized using quantum-classical optimization loops, by extremizing a cost function. We discuss how the tension between the finite speed of propagation of the correlations consequence of Lieb-Robinson bounds and the growth of entanglement in critical systems is responsible of the linear scaling with the size of the system of the critical number of layers l∗(n) that determines the location of the cross-over between the two regimes
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
