arXiv subjects

Haomu Yuan

Publications and source records attributed to Haomu Yuan.

8 recordsLinked to original sources

arXiv2026

Towards Exponential Quantum Improvements in Solving Cardinality-Constrained Binary Optimization

Cardinality-constrained binary optimization is a fundamental computational primitive with broad applications in machine learning, finance, and scientific computing. In this work, we introduce a Grover-based quantum algorithm that exploits the structure of the fixed-cardinality feasible subspace under a natural promise on solution existence. For quadratic objectives, our approach achieves ${O}\left(\sqrt{\frac{\binom{n}{k}}{{M}}}\right)$ Grover rotations for any fixed cardinality $k$ and degeneracy of the optima $M$, yielding an exponential reduction in the number of Grover iterations compared with unstructured search over $\{0,1\}^n$. Building on this result, we develop a hybrid classical--quantum framework based on the alternating direction method of multipliers (ADMM) algorithm. The proposed framework is guaranteed to output an $\epsilon$-approximate solution with a consistency tolerance $\epsilon + \delta$ using at most $ {O}\left(\sqrt{\binom{n}{k}}\frac{n^{6}k^{3/2} }{ \sqrt{M}\epsilon^2 \delta }\right)$ queries to a quadratic oracle, together with ${O}\left(\frac{n^{6}k^{3/2}}{\epsilon^2\delta}\right)$ classical overhead. Overall, our method suggests a practical use of quantum resources and demonstrates an exponential improvements over existing Grover-based approaches in certain parameter regimes, thereby paving the way toward quantum advantage in constrained binary optimization.

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arXiv2025

Classical Optimization Strategies for Variational Quantum Algorithms: A Systematic Study of Noise Effects and Parameter Efficiency

This study systematically benchmarks classical optimization strategies for the Quantum Approximate Optimization Algorithm when applied to Generalized Mean-Variance Problems under near-term Noisy Intermediate-Scale Quantum conditions. We evaluate Dual Annealing, Constrained Optimization by Linear Approximation, and the Powell Method across noiseless, sampling noise, and two thermal noise models. Our Cost Function Landscape Analysis revealed that the Quantum Approximate Optimization Algorithm angle parameters $γ$ were largely inactive in the noiseless regime. This insight motivated a parameter-filtered optimization approach, in which we focused the search space exclusively on the active $β$ parameters. This filtering substantially improved parameter efficiency for fast optimizers like Constrained Optimization by Linear Approximation (reducing evaluations from 21 to 12 in the noiseless case) and enhanced robustness, demonstrating that leveraging structural insights is an effective architecture-aware noise mitigation strategy for Variational Quantum Algorithms.

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arXiv2025

Experimental Demonstration of the PBR Test on a Superconducting Processor

We present an experimental implementation of the Pusey-Barrett-Rudolph (PBR) no-go theorem on IBM's 156-qubit Heron2 Marrakesh superconducting quantum processor. By preparing qubits in a set of non-orthogonal states and evolving them under carefully compiled unitary circuits, we test whether one can interpret the hidden variable model for quantum states as merely epistemic -- reflecting ignorance about some underlying physical reality. To account for realistic hardware imperfections, we derive noise-aware error tolerance based on decoherence models calibrated to the device's performance. Our results show that a significant majority of adjacent qubit pairs and adjacent five-qubit configurations yield outcome statistics that violate the epistemic bound, thus ruling out the epistemic interpretation of quantum mechanics. Furthermore, we observe a clear trend: the probability of passing the PBR test decreases as the spatial separation within the quantum processor between qubits increases, highlighting the sensitivity of this protocol to connectivity and coherence in Noisy Intermediate-Scale Quantum (NISQ) systems. These results demonstrate the PBR test as a promising device-level benchmark for quantumness in the presence of realistic noise.

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arXiv2025

Exponential Speed-ups for Structured Goemans-Williamson relaxations via Quantum Gibbs States and Pauli Sparsity

Quadratic Unconstrained Binary Optimization (QUBO) problems are prevalent in various applications and are known to be NP-hard. The seminal work of Goemans and Williamson introduced a semidefinite programming (SDP) relaxation for such problems, solvable in polynomial time that upper bounds the optimal value. Their approach also enables randomized rounding techniques to obtain feasible solutions with provable performance guarantees. In this work, we identify instances of QUBO problems where matrix multiplicative weight methods lead to quantum and quantum-inspired algorithms that approximate the Goemans-Williamson SDP exponentially faster than existing methods, achieving polylogarithmic time complexity relative to the problem dimension. This speedup is attainable under the assumption that the QUBO cost matrix is sparse when expressed as a linear combination of Pauli strings satisfying certain algebraic constraints, and leverages efficient quantum and classical simulation results for quantum Gibbs states. We demonstrate how to verify these conditions efficiently given the decomposition. Additionally, we explore heuristic methods for randomized rounding procedures and extract the energy of a feasible point of the QUBO in polylogarithmic time. While the practical relevance of instances where our methods excel remains to be fully established, we propose heuristic algorithms with broader applicability and identify Kronecker graphs as a promising class for applying our techniques. We conduct numerical experiments to benchmark our methods. Notably, by utilizing tensor network methods, we solve an SDP with $D = 2^{50}$ variables and extract a feasible point which is certifiably within $0.15\%$ of the optimum of the QUBO through our approach on a desktop, reaching dimensions millions of times larger than those handled by existing SDP or QUBO solvers, whether heuristic or rigorous.

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arXiv2025

Iterative quantum optimisation with a warm-started quantum state

We provide a method to prepare a warm-started quantum state from measurements with an iterative framework to enhance the quantum approximate optimisation algorithm (QAOA). The numerical simulations show the method can effectively address the "stuck issue" of the standard QAOA using a single-string warm-started initial state described in [Cain et al., 2023]. When applied to the $3$-regular MaxCut problem, our approach achieves an improved approximation ratio, with a lower bound that iteratively converges toward the best classical algorithms for $p=1$ standard QAOA. Additionally, in the context of the discrete global minimal variance portfolio (DGMVP) model, simulations reveal a more favourable scaling of identifying the global minimal compared to the QAOA standalone, the single-string warm-started QAOA and a classical constrained sampling approach.

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arXiv2024

Quantifying the advantages of applying quantum approximate algorithms to portfolio optimisation

We present a quantum algorithm for portfolio optimisation. Specifically, We present an end-to-end quantum approximate optimisation algorithm (QAOA) to solve the discrete global minimum variance portfolio (DGMVP) model. This model finds a portfolio of risky assets with the lowest possible risk contingent on the number of traded assets being discrete. We provide a complete pipeline for this model and analyses its viability for noisy intermediate-scale quantum computers. We design initial states, a cost operator, and ansätze with hard mixing operators within a binary encoding. Further, we perform numerical simulations to analyse several optimisation routines, including layerwise optimisation, utilising COYBLA and dual annealing. Finally, we consider the impacts of thermal relaxation and stochastic measurement noise. We find dual annealing with a layerwise optimisation routine provides the most robust performance. We observe that realistic thermal relaxation noise levels preclude quantum advantage. However, stochastic measurement noise will dominate when hardware sufficiently improves. Within this regime, we numerically demonstrate a favourable scaling in the number of shots required to obtain the global minimum -- an indication of quantum advantage in portfolio optimisation.

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arXiv2024

Quasi-binary encoding based quantum alternating operator ansatz

This paper proposes a quasi-binary encoding based algorithm for solving a specific quadratic optimization models with discrete variables, in the quantum approximate optimization algorithm (QAOA) framework. The quadratic optimization model has three constraints: 1. Discrete constraint, the variables are required to be integers. 2. Bound constraint, each variable is required to be greater than or equal to an integer and less than or equal to another integer. 3. Sum constraint, the sum of all variables should be a given integer. To solve this optimization model, we use quasi-binary encoding to encode the variables. For an integer variable with upper bound $U_i$ and lower bound $L_i$, this encoding method can use at most $2\log_2 (U_i-L_i+1)$ qubits to encode the variable. Moreover, we design a mixing operator specifically for this encoding to satisfy the hard constraint model. In the hard constraint model, the quantum state always satisfies the constraints during the evolution, and no penalty term is needed in the objective function. In other parts of the QAOA framework, we also incorporate ideas such as CVaR-QAOA and parameter scheduling methods into our QAOA algorithm. In the financial field, by introducing precision, portfolio optimization problems can be reduced to the above model. We will use portfolio optimization cases for numerical simulation. We design an iterative method to solve the problem of coarse precision caused by insufficient qubits of the simulators or quantum computers. This iterative method can refine the precision by multiple few-qubit experiments.

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arXiv2022

A Logarithm Depth Quantum Converter: From One-hot Encoding to Binary Encoding

Within the quantum computing, there are two ways to encode a normalized vector $\{ α_i \}$. They are one-hot encoding and binary coding. The one-hot encoding state is denoted as $\left | ψ_O^{(N)} \right \rangle=\sum_{i=0}^{N-1} α_i \left |0 \right \rangle^{\otimes N-i-1} \left |1 \right \rangle \left |0 \right \rangle ^{\otimes i}$ and the binary encoding state is denoted as $\left | ψ_B^{(N)} \right \rangle=\sum_{i=0}^{N-1} α_i \left |b_i \right \rangle$, where $b_i$ is interpreted in binary of $i$ as the tensor product sequence of qubit states. In this paper, we present a method converting between the one-hot encoding state and the binary encoding state by taking the Edick state as the transition state, where the Edick state is defined as $\left | ψ_E^{(N)} \right \rangle=\sum_{i=0}^{N-1} α_i \left |0 \right \rangle^{\otimes N-i-1} \left |1 \right \rangle ^{\otimes i}$. Compared with the early work, our circuit achieves the exponential speedup with $O(\log^2 N)$ depth and $O(N)$ size.

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