Read on Twitter
Ideally, for VQAs, we'd like to use ansätze that are highly expressive and trainable.
Here we present a fundamental relationship between these key properties.
The more expressive the ansatz the flatter its landscape i.e. you can't have both.
@kunal_phy @MvsCerezo @ColesQuantum
Here we present a fundamental relationship between these key properties.
The more expressive the ansatz the flatter its landscape i.e. you can't have both.
@kunal_phy @MvsCerezo @ColesQuantum
Our results extend the original barren plateau result (which is restricted to ansätze that form 2-designs) to arbitrary ansätze.
This extension should prove useful because many standard ansätze are approximate rather than exact 2-designs.
Check out: https://arxiv.org/pdf/2101.02138.pdf
This extension should prove useful because many standard ansätze are approximate rather than exact 2-designs.
Check out: https://arxiv.org/pdf/2101.02138.pdf
This schematic summarises our results.
Inexpressive ansätze can solve certain problems but not others. Inexpressive ansätze may or may not have trainability issues.
Highly expressive can solve most problems. But they have small gradients and therefore trainability issues.
Inexpressive ansätze can solve certain problems but not others. Inexpressive ansätze may or may not have trainability issues.
Highly expressive can solve most problems. But they have small gradients and therefore trainability issues.
Our numerics suggest that reducing the expressibility of an ansatz may be used avoid barren plateaus.
Strongly correlating parameters and/or initialising close to the solution (and then restricting the ansatz to exploring that region) seem especially effective techniques.
Strongly correlating parameters and/or initialising close to the solution (and then restricting the ansatz to exploring that region) seem especially effective techniques.
