Day 3 (June 25)

Recent advances in quantum annealing processors are opening up promising new directions for research. By integrating techniques such as multi-color annealing, which allows mid-anneal excitation of selected qubit subsets and measurements in arbitrary bases, we establish a pathway toward analog-digital quantum computing—an emerging paradigm that combines analog Hamiltonian dynamics with digital control—thereby enabling the quantum simulation of dynamical physical systems [1]. In this talk, I will present some experimental results that leverage these capabilities on a D-Wave Advantage2™ quantum processing unit. In particular, I will explore the emergence of disorder-induced quantum-localized phases by introducing controlled disorder into the system.
[1] arXiv:2603.15534

False vacuum decay (FVD) is a fundamental non-perturbative phenomenon in quantum field theory and statistical mechanics, typically viewed as a two-stage process of semiclassical nucleation followed by deterministic expansion. However, its complex dynamics and limited experimental accessibility make it challenging to study, leaving key questions about the nucleation, propagation, and interactions of true vacuum bubbles [1-3]. Building on studies in one-dimensional Ising chains [4], we investigate FVD in the two-dimensional quantum Ising model and identify a dynamical regime where nucleation and growth are intrinsically intertwined via local resonance conditions. Using a programmable quantum annealer with over 4000 qubits, we realize a metastable false vacuum where single-spin flips at a bubble interface become energy-conserving at a tunable resonance. This triggers a kinetically constrained expansion, where the energy gain of the true vacuum offsets the cost of domain-wall creation, resulting in fractal-like growth. Through a combination of experimental measurements, tensor-network simulations, and large-scale stochastic circuit modeling, we demonstrate that the true-vacuum wavefront propagates ballistically across all platforms, persisting even in the presence of dissipation and disorder. Furthermore, the interface exhibits sub-ballistic broadening consistent with the Kardar-Parisi-Zhang (KPZ) universality class, indicating that the coarse-grained dynamics are governed by interface fluctuations. Our results establish a resonance-driven kinetic regime of FVD that bypasses the standard nucleation-expansion separation, highlighting large-scale quantum simulation as a powerful tool for exploring non-equilibrium metastable dynamics relevant to quantum field theory and strongly correlated matter.

[1] G. Lagnese et al. False vacuum decay in quantum spin chains, Phys. Rev. B 104, L201106. (2021)

[2] A. Zenesini et al. False vacuum decay via bubble formation in ferromagnetic superfluids. Nat. Phys. 20, 558–563 (2024).

[3] A. Milsted et al. Collisions of False-Vacuum Bubble Walls in a Quantum Spin Chain, PRX Quantum 3, 02031. (2022)

[4] J. Vodeb et al. Stirring the false vacuum via interacting quantized bubbles on a 5,564-qubit quantum annealer, Nat. Phys. 21, 386–392 (2025)

Quantum annealing (QA) has emerged as a promising approach for solving complex combinatorial optimization problems. However, physical hardware continues to face limitations such as restricted qubit counts, environmental noise, and sparse connectivity. This research proposes the development of a simulator based on Simulated Quantum Annealing (SQA) that specifically incorporates the technical characteristics of D-Wave’s latest Zephyr architecture. By integrating Path Integral Monte Carlo (PIMC) methods with hardware-specific noise models such as Integrated Control Error (ICE) and clique embedding scaling laws, this framework enables the development of noise-reduction algorithms and the validation of hardware performance at scales beyond current physical devices.
https://arxiv.org/abs/2510.04594

We present Learning-Driven Annealing (LDA), a framework that links individual quantum annealing evolutions into a global solution strategy to mitigate hardware constraints such as short annealing times and control errors. Unlike other iterative methods, LDA does not adjust the annealing parameters (e.g., time or schedule), but instead learns about the problem structure to adaptively modify the problem Hamiltonian. By deforming the instantaneous energy spectrum, LDA suppresses first-order quantum phase transitions into high-energy local minima and guides the evolution toward low-energy regions of the Hilbert space.
We demonstrate the efficacy of LDA on 5580-qubit spin-glass instances and 28-bit factoring instances using the D-Wave Advantage 5.4 system. LDA outperforms other quantum and classical algorithms (e.g., reverse annealing, cyclic annealing, simulated annealing, Gurobi, Toshiba’s SBM, VeloxQ, and D-Wave hybrid) in both runtime and lowest energy, and represents a step toward practical quantum optimization, enabling NISQ devices to compete with classical solvers.

We introduce a quantum-echo Markov process to address an intrinsic limitation of classical Markov processes. Local update rules often fail to escape from local minima, whereas global updates reduce to random search. This observation highlights the importance of designing transition matrices that simultaneously control locality in both energy space and Hamming space. To this end, we employ quantum-echo dynamics, consisting of forward and backward unitary evolutions combined with a local operation. As the unitary dynamics, we consider both quantum-annealing (QA) and the quantum approximate optimization algorithm (QAOA). As a control parameter - either the annealing time or the QAOA circuit depth - is increased, the transitions become more nonlocal in Hamming space while remaining local in energy space. By expressing both types of locality in terms of out-of-time-ordered correlators, we clarify the underlying mechanisms. In QA, this behavior is explained by adiabaticity in QA, whereas in QAOA it arises from the emergence of a linear correlation between energy and Hamming weight in the eigenstates of an effective Hamiltonian. Based on these findings, we incorporate the quantum-echo Markov process into a basin-hopping algorithm and investigate its effectiveness across combinatorial optimization problems with diverse structural properties.

Quantum annealing (QA) is a promising approach for solving combinatorial optimization problems. However, it is known to exhibit unfair sampling, in which degenerate ground states are not sampled with equal probability even for sufficiently long annealing times. Fair sampling is important in applications such as solution diversity assessment and combinatorial counting, yet the characteristics of unfair sampling remains poorly understood, particularly in constrained combinatorial optimization problems. In this work, we investigate unfair sampling of QA in weighted graph bipartitioning problems (GBP), a representative constrained optimization problem. We study how the penalty coefficient in the penalty method affects sampling fairness. Through numerical simulations and experiments on the D-Wave Advantage2 system, we show that increasing the penalty coefficient reduces unfair sampling in a representative single instance, and that this qualitative behavior is also observed on actual hardware. A scaling analysis over randomly generated instances with up to 12 spins reveals that, while this trend does not hold universally, more than 70% of instances exhibit monotonically increasing sampling fairness as the penalty coefficient increases, even at the largest system size studied. These observations were also consistent with the theoretical predictions obtained from degenerate perturbation theory near the end of the annealing process. These results show that increasing the penalty coefficient improves sampling fairness, though at the cost of ground-state probability under practical annealing conditions, and call for a deeper theoretical understanding of unfair sampling in constrained optimization problems.
https://arxiv.org/abs/2604.11449

This study proposed a method to improve the performance of quantum annealing (QA)-based combinatorial optimization problem (COP) solvers using deep learning, with a particular focus on the training strategy.

QA has attracted research interest as a sampler and COP solver. However, due to hardware constraints, the size of tractable problems is limited. To address this issue, a recently proposed sampling-based solver for QA reformulates constrained COPs into a sampling problem using auxiliary variables. This approach reduces the number of qubits required to represent the problem and enables large-scale optimization.

The performance of this sampling-based COP solver depends on the choice of step sizes in its gradient-based updates, and their tuning is executed heuristically. In this study, to overcome this limitation, we consider a trainable sampling-based COP solver that optimizes its internal parameters from a dataset using a deep-learning technique called deep unfolding (DU). In this framework, the iterative updates of the solver are unfolded into a layered structure, and the step sizes are treated as trainable parameters. Furthermore, to enable backpropagation despite the nondifferentiability of the sampling process, a novel gradient estimation scheme is proposed.

Although learning the internal parameters accelerates convergence, applying QA directly to the training process is impractical. This is because training requires a large number of repeated quantum annealer calls, resulting in prohibitively high computational cost. To address this issue, we further propose classical-quantum transfer learning, in which parameters are trained using classical samplers and then transferred to the solver with QA.

The results of numerical experiments demonstrate that the proposed approach improves both the convergence speed and execution time of the QA-based solver, highlighting its effectiveness as a practical strategy for enhancing quantum optimization.

Mixed-integer optimization, while offering flexible descriptions of real-world decision-making problems by combining integer and continuous variables, becomes computationally intensive as the problem scales. For large-scale mixed-integer quadratic programming problems (MIQP), a framework has been proposed that combines Benders decomposition with a quantum-classical hybrid solver to achieve faster processing than commercial exact solvers [1]. In this study, we aim to clarify, as a phase diagram, the critical conditions under which the difficulties corresponding to the dependence of the number of iterations, cuts, and initial conditions of the Benders decomposition become apparent, using a statistical mechanics replica method for the target MIQP. By comparing the critical boundary obtained from the derived saddle point equation with overlaps in numerical experiments, we theoretically organize the regions where the hybrid solution method is effective and where it becomes difficult.
[1] Yoshihara Takuma and Masayuki Ohzeki. "Accelerating Extended Benders Decomposition with Quantum-Classical Hybrid Solver." Journal of the Physical Society of Japan 95.3 (2026)

In this study, we propose a hybrid ADMM framework for binary optimization problems with nonlinear objective functions. In the proposed method, the discrete subproblem is solved by simulated annealing (SA), and we show that this approach reduces computation time by approximately a factor of 30 compared with an ADMM variant that solves the discrete part with Gurobi, while maintaining solution quality close to the exact solution.

In this framework, the original problem is decomposed by the alternating direction method of multipliers (ADMM)[1] into relatively tractable continuous-variable subproblems and a difficult discrete-variable subproblem. To evaluate the effectiveness of the proposed method, we consider randomly generated optimization problems with binary variables and nonconvex nonlinear objective functions, and compare an ADMM method using SA for the discrete subproblem with an ADMM method using Gurobi. The results also confirm stable convergence up to problem size N=100. Furthermore, because the penalty parameters strongly affect the optimization results, we compare two automatic tuning methods. We show that spectral radius analysis (SRA)[2] yields smaller optimality gaps over a wider range of initial values than residual balancing (RD)[3], demonstrating greater robustness in discrete and nonconvex settings.

These results indicate that annealing-based hybrid ADMM is an effective approach for difficult optimization problems involving discrete variables and nonlinear objective functions. Our proposed method is also a promising technology for resource allocation in wireless communications. Future work includes replacing SA with quantum annealing and extending the evaluation to larger-scale problems.

[1]Gabay, Daniel, and Bertrand Mercier. "A dual algorithm for the solution of nonlinear variational problems via finite element approximation." Computers & mathematics with applications 2.1 (1976): 17-40.

[2]Mccann, Michael T., and Brendt Wohlberg. "Robust and simple ADMM penalty parameter selection." IEEE Open Journal of Signal Processing5 (2024): 402-420.

[3] Boyd, Stephen, et al. "Distributed optimization and statistical learning via the alternating direction method of multipliers." Foundations and Trends® in Machine learning3.1 (2011): 1-122.

Significant machine learning progress has been realized in the past decade---from performing simple classification tasks to the advent of large language models. The accelerated adoption of deep neural networks can be partly accredited to the computational efficiency and accessibility of graphical processing units (GPUs). This success has resulted in an increased demand for compute-resource alternatives to GPUs. With the maturation of annealing quantum computing, research is being realized to place annealing quantum processing units (QPUs) as viable technology for machine learning applications. In this talk, I will present a practical approach to exploiting the sampling efficiency of annealing QPUs for performing neural network computations in discriminative modelling tasks. This demonstration consists of a series of experiments involving scalable models with varying degrees of contribution from annealing QPUs.