Hao-Kai Zhang

New work to give a solution to the long-standing dilemma between trainability and expressibility of quantum circuits. scirate.com/arxiv/2406.118…. "Predicting quantum learnability from landscape fluctuation". Joint with @zhkphys and Chenghong. 1/5

*Here are the two theorems for your convenience, which utilize a geometrical concept of ``path'' on the circuit:

Here is our new arXiv paper! We prove the absence of barren plateaus in a new class of circuits---finite (or logarithmic) local-depth circuits, a circuit version of tensor network states. Hope you enjoy it! arxiv.org/abs/2311.01393

We validate our analytical results with extensive numerical simulations and demonstrate the effectiveness of variational training using the generalized toric code model. [6/6]

This fact suggests that long-range entangled ground states, such as topologically ordered states, are in general possible to be prepared efficiently on quantum devices via variational methods. [5]

These circuits are allowed to be deep in the conventional definition of circuit depth so that they can generate long-range entanglement, but their local depths are finite, i.e., there is only a finite number of non-commuting gates acting on individual qubits. [4]

Based on our unified framework, we prove the absence of barren plateaus in training finite local-depth circuits for the ground states of local Hamiltonians. [3]

However, deep circuits are generally untrainable due to the barren plateau phenomenon. In this work, we give a general lower bound on the variance of circuit gradients for arbitrary quantum circuits composed of local 2-designs. [2]

Ground state preparation is classically intractable for general Hamiltonians. On quantum devices, shallow parameterized circuits can be effectively trained to obtain short-range entangled states under the paradigm of variational quantum eigensolver. [1]

Here goes our new work today! arxiv.org/abs/2205.05056 We show a new scaling theorem for generic variational quantum algorithms beyond vanishing gradients! Joint work with our interns @zhkphys @chengkai_z, and Geng @BaiduResearch