Variational Quantum Simulation: A Case Study for Understanding Warm Starts

PRX Quantum, Journal Year: 2025, Volume and Issue: 6(1)

Published: Jan. 23, 2025

The barren plateau phenomenon, characterized by loss gradients that vanish exponentially with system size, poses a challenge to scaling variational quantum algorithms. Here we explore the potential of warm starts, whereby one initializes closer solution in hope enjoying larger variances. Focusing on an iterative method for learning shorter-depth circuits conduct case study elucidate and limitations starts. We start proving algorithm will exhibit substantial (at worst vanishing polynomially size) small region around initializations at each time step. Convexity guarantees these regions are then established, suggesting trainability polynomial-size steps. However, our highlights scenarios where good minimum shifts outside guarantees. Our analysis leaves open question whether such minima jumps necessitate optimization across landscapes or there exist gradient flows, i.e., fertile valleys away from gradients, allow training. While main focus is this simulation, end discussing how results work other settings. Published American Physical Society 2025

Language: Английский

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Barren plateaus swamped with traps

Physical review. A/Physical review, A, Journal Year: 2025, Volume and Issue: 111(1)

Published: Jan. 27, 2025

Language: Английский

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Barren plateaus in variational quantum computing

Nature Reviews Physics, Journal Year: 2025, Volume and Issue: unknown

Published: March 26, 2025

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Equivalence of cost concentration and gradient vanishing for quantum circuits: an elementary proof in the Riemannian formulation

Quantum Science and Technology, Journal Year: 2024, Volume and Issue: 9(4), P. 045039 - 045039

Published: Aug. 15, 2024

Abstract The optimization of quantum circuits can be hampered by a decay average gradient amplitudes with increasing system size. When the is exponential, this called barren plateau problem. Considering explicit circuit parametrizations (in terms rotation angles), it has been shown in Arrasmith et al (2022 Quantum Sci. Technol. 7 045015) that plateaus are equivalent to an exponential variance cost-function differences. We show issue particularly simple (parametrization-free) Riemannian formulation such problems and obtain tighter bound for variance. An elementary derivation shows single-gate cost function strictly equal half gradient, where we sample variable gates according uniform Haar measure. total variances its then both bounded from above sum and, conversely, above. So, decays gradients variations go hand hand, cannot resolved avoiding gradient-based favor gradient-free methods.

Language: Английский

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Expressivity of deterministic quantum computation with one qubit

Physical review. A/Physical review, A, Journal Year: 2025, Volume and Issue: 111(2)

Published: Feb. 18, 2025

Language: Английский

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Efficient particle-conserving symmetric quantum circuits

Physical review. A/Physical review, A, Journal Year: 2025, Volume and Issue: 111(2)

Published: Feb. 25, 2025

The variational quantum simulation technique on gate-based processors can be made more efficient if symmetries of the Hamiltonian system interest are factored into design construction underlying parameterized circuits (PQC) needed by technique. In first part this work, we present an easy and practical approach that used to construct symmetric circuits. method directly adapted for any symmetry, though in work focus explicitly examples Z2, Z3, particle number conservation. We show how gates respects aforementioned symmetries. second part, numerical analysis particle-conserving gates. simulation, example, eigensolver (VQE), PQC parameterized. Since there often many possible inequivalent parametrizations, it is not immediately obvious which gate parametrization would most general a wide range Hamiltonians respect symmetry. streamline our Hamiltonians. numerically analyze efficiency different parametrizations studying two examples, namely, physics problem learning ground state Heisenberg spin chains, artificial random arbitary states sampled within conserved subspace. Published American Physical Society 2025

Language: Английский

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A coherent approach to quantum-classical optimization

Communications Physics, Journal Year: 2025, Volume and Issue: 8(1)

Published: May 12, 2025

Abstract Hybrid quantum-classical optimization techniques, which incorporate the pre-optimization of Variational Quantum Algorithms using Tensor Networks, have been shown to allow for reduction quantum computational resources. In particular case large problems, commonly found in real-world use cases, this strategy is almost mandatory reduce otherwise unfathomable execution costs and improve quality results. We identify coherence entropy as a crucial metric determining suitability states effective initialization candidates. Our findings are validated through extensive numerical tests Approximate Optimization Algorithm, we find that optimal pure Gibbs states. Further, these results explained with inclusion simple notion expressivity adapted classical problems. Based on finding, propose protocol significantly improves effectiveness subroutine.

Language: Английский

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Enhanced Generalization of Variational Quantum Learning Under Reduced-Domain Initialization

Published: July 24, 2023

Trainability and generalization are two key issues in quantum machine learning on the basis of variational algorithms. It has been demonstrated [1] that with reduced-domain initialization strategy, trainability parameters can be greatly enhanced for complex objectives general deep circuits. In this paper, we further explore under initialization. We theoretically derive upper bound error demonstrate enhancement as compared to usual parameter methods. Thus, our results clearly show push boundary applicability toward practical applications.

Language: Английский

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Efficiently Solving the Max-cut Problem via a Quantum Qubit Rotation Algorithm

Published: July 24, 2023

Optimizing parameterized quantum circuits promises efficient use of near-term devices to achieve potential advantage. However, there is a notorious tradeoff between the expressibility and trainability parameter ansatz. We find that in combinatorial optimization problems, since solutions are described by bit strings, one can trade expressiveness ansatz for high train ability. To be specific, focusing on max-cut problem we introduce simple yet algorithm named Quantum Qubit Rotation Algorithm (QQRA). The comprised with single-qubit rotation gates implementing each qubit. angles trained free barren plateaus. It demonstrated approximation ratio QQRA close 1 complete graphs. illustrate effectiveness QQRA, compare it well known approximate classical Goemans- Williamson algorithm.

Language: Английский

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