TY - JOUR
T1 - Expressibility of the alternating layered ansatz for quantum computation
AU - Nakaji, Kouhei
AU - Yamamoto, Naoki
N1 - Funding Information:
Although our results are limited to the case ℓ = 2, 3, we have numerically observed that the ALT acquires even higher expressibility when making ℓ bigger. Therefore, we conjecture that the above conclusion still holds for ALT with ℓ ≥ 4. The rigorous proof is left for future work. Acknowledgement: This work is supported by the MEXT Quantum Leap Flagship Program Grant Number JPMXS0118067285.
Publisher Copyright:
© 2021 Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften. All right reserved.
PY - 2021
Y1 - 2021
N2 - The hybrid quantum-classical algorithm is actively examined as a technique applicable even to intermediate-scale quantum computers. To execute this algorithm, the hardware efficient ansatz is often used, thanks to its implementability and expressibility; however, this ansatz has a critical issue in its trainability in the sense that it generically suffers from the so-called gradient vanishing problem. This issue can be resolved by limiting the circuit to the class of shallow alternating layered ansatz. However, even though the high trainability of this ansatz is proved, it is still unclear whether it has rich expressibility in state generation. In this paper, with a proper definition of the expressibility found in the literature, we show that the shallow alternating layered ansatz has almost the same level of expressibility as that of hardware efficient ansatz. Hence the expressibility and the trainability can coexist, giving a new designing method for quantum circuits in the intermediate-scale quantum computing era.
AB - The hybrid quantum-classical algorithm is actively examined as a technique applicable even to intermediate-scale quantum computers. To execute this algorithm, the hardware efficient ansatz is often used, thanks to its implementability and expressibility; however, this ansatz has a critical issue in its trainability in the sense that it generically suffers from the so-called gradient vanishing problem. This issue can be resolved by limiting the circuit to the class of shallow alternating layered ansatz. However, even though the high trainability of this ansatz is proved, it is still unclear whether it has rich expressibility in state generation. In this paper, with a proper definition of the expressibility found in the literature, we show that the shallow alternating layered ansatz has almost the same level of expressibility as that of hardware efficient ansatz. Hence the expressibility and the trainability can coexist, giving a new designing method for quantum circuits in the intermediate-scale quantum computing era.
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U2 - 10.22331/q-2021-04-19-434
DO - 10.22331/q-2021-04-19-434
M3 - Article
AN - SCOPUS:85105315461
SN - 2521-327X
VL - 5
JO - Quantum
JF - Quantum
ER -