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Hardware-efficient ansatz without barren plateaus in any depth
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Hardware-efficient ansatz without barren plateaus in any depth
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Variational quantum circuits have recently gained much interest due to their relevance in real-world applications, such as combinatorial optimizations, quantum simulations, and modeling a probability distribution. Despite their huge potential, the practical usefulness of those circuits beyond tens of qubits is largely questioned. One of the major problems is the so-called barren plateaus phenomenon. Quantum circuits with a random structure often have a flat cost-function landscape and thus cannot be trained efficiently. In this paper, we propose two novel parameter conditions in which the hardware-efficient ansatz (HEA) is free from barren plateaus for arbitrary circuit depths. In the first condition, the HEA approximates to a time-evolution operator generated by a local Hamiltonian. Utilizing a recent result by [Park and Killoran, Quantum 8, 1239 (2024)], we prove a constant lower bound of gradient magnitudes in any depth both for local and global observables. On the other hand, the HEA is within the many-body localized (MBL) phase in the second parameter condition. We argue that the HEA in this phase has a large gradient component for a local observable using a phenomenological model for the MBL system. By initializing the parameters of the HEA using these conditions, we show that our findings offer better overall performance in solving many-body Hamiltonians. Our results indicate that barren plateaus are not an issue when initial parameters are smartly chosen, and other factors, such as local minima or the expressivity of the circuit, are more crucial.
Forward citations
Cited by 7 Pith papers
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Exponentially many initializations to avoid barren plateaus
A first-moment operator diagnostic reveals exponentially many inequivalent initialization distributions avoid barren plateaus in variational quantum algorithms, with numerics indicating distinct attained minima.
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Adding non-unitary gadgets to variational quantum circuits can create an illusion of trainability — the cost varies, but most parameters remain exponentially hard to train.
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Challenges in Barren Plateau Mitigation with Dynamic Parameterized Quantum Circuits
Dynamic parameterized quantum circuits still leave a significant fraction of parameters untrainable despite cost anti-concentration, implying BP mitigation via DPQCs is at least as hard as designing BP-free unitaries.
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Variational Thermal State Preparation on Digital Quantum Processors Assisted by Matrix Product States
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Beyond Logical Circuits: Hardware-Aware Analysis of Expressibility and Trainability in Variational Quantum Algorithms
Hardware transpilation of parameterized quantum circuits produces ansatz-dependent shifts in expressibility (up to 125%) and trainability (up to 25%), altering the expected trade-off between them.
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