| Autor: |
Roeland Wiersema, Cunlu Zhou, Yvette de Sereville, Juan Felipe Carrasquilla, Yong Baek Kim, Henry Yuen |
| Jazyk: |
angličtina |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
PRX Quantum, Vol 1, Iss 2, p 020319 (2020) |
| Druh dokumentu: |
article |
| ISSN: |
2691-3399 |
| DOI: |
10.1103/PRXQuantum.1.020319 |
| Popis: |
Quantum variational algorithms are one of the most promising applications of near-term quantum computers; however, recent studies have demonstrated that unless the variational quantum circuits are configured in a problem-specific manner, optimization of such circuits will most likely fail. In this paper, we focus on a special family of quantum circuits called the Hamiltonian variational ansatz (HVA), which its takes inspiration from the quantum approximate optimization algorithm and adiabatic quantum computation. Through the study of its entanglement spectrum and energy-gradient statistics, we find that the HVA exhibits favorable structural properties such as mild or entirely absent barren plateaus and a restricted state space that eases their optimization in comparison to the well-studied “hardware-efficient ansatz.” We also numerically observe that the optimization landscape of the HVA becomes almost trap free, i.e., there are no suboptimal minima, when the ansatz is overparametrized. We observe a size-dependent “computational phase transition” as the number of layers in the HVA circuit is increased where the optimization crosses over from a hard to an easy region in terms of the quality of the approximations and the speed of convergence to a good solution. In contrast to the analogous transitions observed in the learning of random unitaries, which occur at a number of layers that grows exponentially with the number of qubits, our variational-quantum-eigensolver experiments suggest that the threshold to achieve the overparametrization phenomenon scales at most polynomially in the number of qubits for the transverse-field Ising and XXZ models. Lastly, as a demonstration of its entangling power and effectiveness, we show that the HVA can find accurate approximations to the ground states of a modified Haldane-Shastry Hamiltonian on a ring, which has long-range interactions and has a power-law entanglement scaling. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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