Speedup of the quantum adiabatic algorithm using delocalization catalysis

Cao, Chenfeng; Xue, Jian; Shannon, Nic; Joynt, Robert

doi:10.1103/physrevresearch.3.013092

Cited by 8 publications

(7 citation statements)

References 35 publications

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“… 27 – 30 . Combining it with the idea of the reference Hamiltonian 31 – 33 leads to new protocol. The latter calls for using a control parameter (e.g., a longitudinal magnetic field) which is collinear with a local Bloch sphere direction of the individual qubits.…”

Section: Introductionmentioning

confidence: 99%

“…Iterative version of optimization, which runs along a closed cycle in the space of parameters, turns to be efficient and has already appeared in the literature, see e.g., refs. 27-30. Combining it with the idea of the reference Hamiltonian [31][32][33] leads to new protocol. The latter calls for using a control parameter (e.g., a longitudinal magnetic field) which is collinear with a local Bloch sphere direction of the individual qubits.…”

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confidence: 99%

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Many-body localization enables iterative quantum optimization

2022

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Many discrete optimization problems are exponentially hard due to the underlying glassy landscape. This means that the optimization cost exhibits multiple local minima separated by an extensive number of switched discrete variables. Quantum computation was coined to overcome this predicament, but so far had only a limited progress. Here we suggest a quantum approximate optimization algorithm which is based on a repetitive cycling around the tricritical point of the many-body localization (MBL) transition. Each cycle includes quantum melting of the glassy state through a first order transition with a subsequent reentrance through the second order MBL transition. Keeping the reentrance path sufficiently close to the tricritical point separating the first and second order transitions, allows one to systematically improve optimization outcomes. The running time of this algorithm scales algebraically with the system size and the required precision. The corresponding exponents are related to critical indexes of the continuous MBL transition.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Many-body localization enables iterative quantum optimization

2022

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“…In the case of CQA, a ground state for the driver Hamiltonian can be more difficult to prepare and so annealing protocols are often generalized beyond a two Hamiltonian interpolation. To overcome this barrier, we consider annealing protocols involving three Hamiltonians, a form for annealing schedules often seen when exploiting ‘catalysts’ 29 – 31 : with , , and . In “ Special drivers for CQA solvers tackling CFD ” section we show how to explicitly construct the driver Hamiltonian for this approach and in “ Implementing CQA protocols for CFD with special drivers ” describe a general CQA protocol using an interpolation of an initial Hamiltonian, the driver Hamiltonian, and a final Hamiltonian.…”

Section: Constrained Quantum Annealing Approachmentioning

confidence: 99%

Quantum annealing with special drivers for circuit fault diagnostics

Leipold

Spedalieri

2022

Sci Rep

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We present a very general construction for quantum annealing protocols to solve Combinational Circuit Fault Diagnosis problems that restricts the evolution to the space of valid diagnoses. This is accomplished by using special local drivers that induce a transition graph on the space of feasible configurations that is regular and instance independent for each given circuit topology. Analysis of small instances shows that the energy gap has a generic form, and that the minimum gap occurs in the last third of the evolution. We used these features to construct an improved annealing schedule and benchmarked its performance through closed system simulations. We found that degeneracy can help the performance of quantum annealing, especially for instances with a higher number of faults in their minimum fault diagnosis. This contrasts with the performance of classical approaches based on brute force search that are used in industry for large scale circuits.

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“…For the Max-1-3-SAT + problem instance, we calculate the infidelity in levels [4,8,16,24,32,40,48,56,64] with QAOA and record the level at which the inequality IF ≤ 0.1 is first satisfied. If IF is still larger than 0.1 in level 64, we record the final level as 64.…”

Section: Quantum Costmentioning

confidence: 99%

“…NISQ devices such as Sycamore [2] and Zuchongzhi [3] have demonstrated a quantum advantage on the random circuit sampling problem, but this is still a long way from realizing an advantage in practical applications. This suggests a focus on the development of quantum optimization algorithms, such as the quantum adiabatic algorithm(QAA) [4][5][6][7][8], the quantum approximate optimization algorithm (QAOA) [9,10], and the variational quantum algorithm (VQA) [11][12][13][14][15]. In these approaches an outer classical optimizer is employed to train the parameterized quantum circuits.…”

Section: Introductionmentioning

confidence: 99%

Solution of SAT Problems with the Adaptive-Bias Quantum Approximate Optimization Algorithm

Yu¹,

Cao²,

Wang³

et al. 2022

Preprint

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The quantum approximate optimization algorithm (QAOA) is a promising method for solving certain classical combinatorial optimization problems on near-term quantum devices. When employing the QAOA to 3-SAT and Max-3-SAT problems, the quantum cost exhibits an easy-hard-easy or easy-hard pattern respectively as the clause density is changed, just as classical solvers do. We show by numerical simulations and analytical arguments that the adaptive-bias QAOA (ab-QAOA) does not show the easy-hard or easy-hard-easy transition, at least up to 10 variables. For this problem size, the ab-QAOA can solve the hard-region 3-SAT and Max-3-SAT problems at level 4 and level 8 respectively with near perfect fidelity. For the QAOA, level 24 and level 64 do not suffice for a solution. We argue that the improvement comes from a more targeted and more limited generation of entanglement during the time evolution. In the ab-QAOA local fields are used to guide the evolution, which suggests that classical optimization is not necessary. We demonstrate that this is the case: an optimization-free ab-QAOA can solve the hard-region problems effectively, though not as effectively as the ab-QAOA itself. Our work paves the way for realizing quantum advantages for optimization problems on NISQ devices.

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Speedup of the quantum adiabatic algorithm using delocalization catalysis

Cited by 8 publications

References 35 publications

Many-body localization enables iterative quantum optimization

Many-body localization enables iterative quantum optimization

Quantum annealing with special drivers for circuit fault diagnostics

Solution of SAT Problems with the Adaptive-Bias Quantum Approximate Optimization Algorithm

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