Polynomial scaling of the quantum approximate optimization algorithm for ground-state preparation of the fully connected p -spin ferromagnet in a transverse field
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Polynomial scaling of the quantum approximate optimization algorithm for ground-state preparation of the fully connected p -spin ferromagnet in a transverse field. / Wauters, Matteo M.; Mbeng, Glen B.; Santoro, Giuseppe E.
I: Physical Review A, Bind 102, Nr. 6, 062404, 03.12.2020.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Polynomial scaling of the quantum approximate optimization algorithm for ground-state preparation of the fully connected p -spin ferromagnet in a transverse field
AU - Wauters, Matteo M.
AU - Mbeng, Glen B.
AU - Santoro, Giuseppe E.
N1 - Publisher Copyright: © 2020 American Physical Society.
PY - 2020/12/3
Y1 - 2020/12/3
N2 - We show that the quantum approximate optimization algorithm (QAOA) can construct, with polynomially scaling resources, the ground state of the fully connected p-spin Ising ferromagnet, a problem that notoriously poses severe difficulties to a vanilla quantum annealing (QA) approach due to the exponentially small gaps encountered at first-order phase transition for p≥3. For a target ground state at arbitrary transverse field, we find that an appropriate QAOA parameter initialization is necessary to achieve good performance of the algorithm when the number of variational parameters 2P is much smaller than the system size N because of the large number of suboptimal local minima. Instead, when P exceeds a critical value PN∗N, the structure of the parameter space simplifies, as all minima become degenerate. This allows achieving the ground state with perfect fidelity with a number of parameters scaling extensively with N and with resources scaling polynomially with N.
AB - We show that the quantum approximate optimization algorithm (QAOA) can construct, with polynomially scaling resources, the ground state of the fully connected p-spin Ising ferromagnet, a problem that notoriously poses severe difficulties to a vanilla quantum annealing (QA) approach due to the exponentially small gaps encountered at first-order phase transition for p≥3. For a target ground state at arbitrary transverse field, we find that an appropriate QAOA parameter initialization is necessary to achieve good performance of the algorithm when the number of variational parameters 2P is much smaller than the system size N because of the large number of suboptimal local minima. Instead, when P exceeds a critical value PN∗N, the structure of the parameter space simplifies, as all minima become degenerate. This allows achieving the ground state with perfect fidelity with a number of parameters scaling extensively with N and with resources scaling polynomially with N.
U2 - 10.1103/PhysRevA.102.062404
DO - 10.1103/PhysRevA.102.062404
M3 - Journal article
AN - SCOPUS:85097584685
VL - 102
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
SN - 1050-2947
IS - 6
M1 - 062404
ER -
ID: 270663106