Our Research

Advancing Quantum Computing from First Principles

QUBO-Centric Optimization under Nonlinear Hamiltonian Dynamics ▪ Approximate Optimization with Rigorous Quantum–Classical Baselines ▪ End-to-End Runtime Benchmarking for Quantum Advantage Claims ▪ Time-to-ε Analysis for Practical Optimization Performance ▪ Physics-Inspired Solvers for Large-Scale Combinatorial Optimization ▪ Quantum–Classical Scaling Analyses Beyond Asymptotic Narratives ▪ Benchmark-Driven Evaluation of Hybrid Optimization Pipelines ▪ Runtime-Accurate Assessment of NISQ Optimization Workflows ▪ Topology-Agnostic QUBO Solving for Hybrid Quantum Integration ▪ Local Certification Methods for Quantum Operations and Channels ▪ Hypothesis-Testing Frameworks for Quantum Validation ▪ Operational Optimization via Time-Space Network Formulations ▪ Integrated Disruption Management with Solver-Based Decision Support ▪ From Approximate Optimization Theory to Production-Grade Hybrid Deployment ▪ Scientifically Grounded Quantum-Readiness for Enterprise Optimization QUBO-Centric Optimization under Nonlinear Hamiltonian Dynamics ▪ Approximate Optimization with Rigorous Quantum–Classical Baselines ▪ End-to-End Runtime Benchmarking for Quantum Advantage Claims ▪ Time-to-ε Analysis for Practical Optimization Performance ▪ Physics-Inspired Solvers for Large-Scale Combinatorial Optimization ▪ Quantum–Classical Scaling Analyses Beyond Asymptotic Narratives ▪ Benchmark-Driven Evaluation of Hybrid Optimization Pipelines ▪ Runtime-Accurate Assessment of NISQ Optimization Workflows ▪ Topology-Agnostic QUBO Solving for Hybrid Quantum Integration ▪ Local Certification Methods for Quantum Operations and Channels ▪ Hypothesis-Testing Frameworks for Quantum Validation ▪ Operational Optimization via Time-Space Network Formulations ▪ Integrated Disruption Management with Solver-Based Decision Support ▪ From Approximate Optimization Theory to Production-Grade Hybrid Deployment ▪ Scientifically Grounded Quantum-Readiness for Enterprise Optimization QUBO-Centric Optimization under Nonlinear Hamiltonian Dynamics ▪ Approximate Optimization with Rigorous Quantum–Classical Baselines ▪ End-to-End Runtime Benchmarking for Quantum Advantage Claims ▪ Time-to-ε Analysis for Practical Optimization Performance ▪ Physics-Inspired Solvers for Large-Scale Combinatorial Optimization ▪ Quantum–Classical Scaling Analyses Beyond Asymptotic Narratives ▪ Benchmark-Driven Evaluation of Hybrid Optimization Pipelines ▪ Runtime-Accurate Assessment of NISQ Optimization Workflows ▪ Topology-Agnostic QUBO Solving for Hybrid Quantum Integration ▪ Local Certification Methods for Quantum Operations and Channels ▪ Hypothesis-Testing Frameworks for Quantum Validation ▪ Operational Optimization via Time-Space Network Formulations ▪ Integrated Disruption Management with Solver-Based Decision Support ▪ From Approximate Optimization Theory to Production-Grade Hybrid Deployment ▪ Scientifically Grounded Quantum-Readiness for Enterprise Optimization QUBO-Centric Optimization under Nonlinear Hamiltonian Dynamics ▪ Approximate Optimization with Rigorous Quantum–Classical Baselines ▪ End-to-End Runtime Benchmarking for Quantum Advantage Claims ▪ Time-to-ε Analysis for Practical Optimization Performance ▪ Physics-Inspired Solvers for Large-Scale Combinatorial Optimization ▪ Quantum–Classical Scaling Analyses Beyond Asymptotic Narratives ▪ Benchmark-Driven Evaluation of Hybrid Optimization Pipelines ▪ Runtime-Accurate Assessment of NISQ Optimization Workflows ▪ Topology-Agnostic QUBO Solving for Hybrid Quantum Integration ▪ Local Certification Methods for Quantum Operations and Channels ▪ Hypothesis-Testing Frameworks for Quantum Validation ▪ Operational Optimization via Time-Space Network Formulations ▪ Integrated Disruption Management with Solver-Based Decision Support ▪ From Approximate Optimization Theory to Production-Grade Hybrid Deployment ▪ Scientifically Grounded Quantum-Readiness for Enterprise Optimization QUBO-Centric Optimization under Nonlinear Hamiltonian Dynamics ▪ Approximate Optimization with Rigorous Quantum–Classical Baselines ▪ End-to-End Runtime Benchmarking for Quantum Advantage Claims ▪ Time-to-ε Analysis for Practical Optimization Performance ▪ Physics-Inspired Solvers for Large-Scale Combinatorial Optimization ▪ Quantum–Classical Scaling Analyses Beyond Asymptotic Narratives ▪ Benchmark-Driven Evaluation of Hybrid Optimization Pipelines ▪ Runtime-Accurate Assessment of NISQ Optimization Workflows ▪ Topology-Agnostic QUBO Solving for Hybrid Quantum Integration ▪ Local Certification Methods for Quantum Operations and Channels ▪ Hypothesis-Testing Frameworks for Quantum Validation ▪ Operational Optimization via Time-Space Network Formulations ▪ Integrated Disruption Management with Solver-Based Decision Support ▪ From Approximate Optimization Theory to Production-Grade Hybrid Deployment ▪ Scientifically Grounded Quantum-Readiness for Enterprise Optimization QUBO-Centric Optimization under Nonlinear Hamiltonian Dynamics ▪ Approximate Optimization with Rigorous Quantum–Classical Baselines ▪ End-to-End Runtime Benchmarking for Quantum Advantage Claims ▪ Time-to-ε Analysis for Practical Optimization Performance ▪ Physics-Inspired Solvers for Large-Scale Combinatorial Optimization ▪ Quantum–Classical Scaling Analyses Beyond Asymptotic Narratives ▪ Benchmark-Driven Evaluation of Hybrid Optimization Pipelines ▪ Runtime-Accurate Assessment of NISQ Optimization Workflows ▪ Topology-Agnostic QUBO Solving for Hybrid Quantum Integration ▪ Local Certification Methods for Quantum Operations and Channels ▪ Hypothesis-Testing Frameworks for Quantum Validation ▪ Operational Optimization via Time-Space Network Formulations ▪ Integrated Disruption Management with Solver-Based Decision Support ▪ From Approximate Optimization Theory to Production-Grade Hybrid Deployment ▪ Scientifically Grounded Quantum-Readiness for Enterprise Optimization QUBO-Centric Optimization under Nonlinear Hamiltonian Dynamics ▪ Approximate Optimization with Rigorous Quantum–Classical Baselines ▪ End-to-End Runtime Benchmarking for Quantum Advantage Claims ▪ Time-to-ε Analysis for Practical Optimization Performance ▪ Physics-Inspired Solvers for Large-Scale Combinatorial Optimization ▪ Quantum–Classical Scaling Analyses Beyond Asymptotic Narratives ▪ Benchmark-Driven Evaluation of Hybrid Optimization Pipelines ▪ Runtime-Accurate Assessment of NISQ Optimization Workflows ▪ Topology-Agnostic QUBO Solving for Hybrid Quantum Integration ▪ Local Certification Methods for Quantum Operations and Channels ▪ Hypothesis-Testing Frameworks for Quantum Validation ▪ Operational Optimization via Time-Space Network Formulations ▪ Integrated Disruption Management with Solver-Based Decision Support ▪ From Approximate Optimization Theory to Production-Grade Hybrid Deployment ▪ Scientifically Grounded Quantum-Readiness for Enterprise Optimization QUBO-Centric Optimization under Nonlinear Hamiltonian Dynamics ▪ Approximate Optimization with Rigorous Quantum–Classical Baselines ▪ End-to-End Runtime Benchmarking for Quantum Advantage Claims ▪ Time-to-ε Analysis for Practical Optimization Performance ▪ Physics-Inspired Solvers for Large-Scale Combinatorial Optimization ▪ Quantum–Classical Scaling Analyses Beyond Asymptotic Narratives ▪ Benchmark-Driven Evaluation of Hybrid Optimization Pipelines ▪ Runtime-Accurate Assessment of NISQ Optimization Workflows ▪ Topology-Agnostic QUBO Solving for Hybrid Quantum Integration ▪ Local Certification Methods for Quantum Operations and Channels ▪ Hypothesis-Testing Frameworks for Quantum Validation ▪ Operational Optimization via Time-Space Network Formulations ▪ Integrated Disruption Management with Solver-Based Decision Support ▪ From Approximate Optimization Theory to Production-Grade Hybrid Deployment ▪ Scientifically Grounded Quantum-Readiness for Enterprise Optimization QUBO-Centric Optimization under Nonlinear Hamiltonian Dynamics ▪ Approximate Optimization with Rigorous Quantum–Classical Baselines ▪ End-to-End Runtime Benchmarking for Quantum Advantage Claims ▪ Time-to-ε Analysis for Practical Optimization Performance ▪ Physics-Inspired Solvers for Large-Scale Combinatorial Optimization ▪ Quantum–Classical Scaling Analyses Beyond Asymptotic Narratives ▪ Benchmark-Driven Evaluation of Hybrid Optimization Pipelines ▪ Runtime-Accurate Assessment of NISQ Optimization Workflows ▪ Topology-Agnostic QUBO Solving for Hybrid Quantum Integration ▪ Local Certification Methods for Quantum Operations and Channels ▪ Hypothesis-Testing Frameworks for Quantum Validation ▪ Operational Optimization via Time-Space Network Formulations ▪ Integrated Disruption Management with Solver-Based Decision Support ▪ From Approximate Optimization Theory to Production-Grade Hybrid Deployment ▪ Scientifically Grounded Quantum-Readiness for Enterprise Optimization QUBO-Centric Optimization under Nonlinear Hamiltonian Dynamics ▪ Approximate Optimization with Rigorous Quantum–Classical Baselines ▪ End-to-End Runtime Benchmarking for Quantum Advantage Claims ▪ Time-to-ε Analysis for Practical Optimization Performance ▪ Physics-Inspired Solvers for Large-Scale Combinatorial Optimization ▪ Quantum–Classical Scaling Analyses Beyond Asymptotic Narratives ▪ Benchmark-Driven Evaluation of Hybrid Optimization Pipelines ▪ Runtime-Accurate Assessment of NISQ Optimization Workflows ▪ Topology-Agnostic QUBO Solving for Hybrid Quantum Integration ▪ Local Certification Methods for Quantum Operations and Channels ▪ Hypothesis-Testing Frameworks for Quantum Validation ▪ Operational Optimization via Time-Space Network Formulations ▪ Integrated Disruption Management with Solver-Based Decision Support ▪ From Approximate Optimization Theory to Production-Grade Hybrid Deployment ▪ Scientifically Grounded Quantum-Readiness for Enterprise Optimization

What we do?

Quantumz.io (QMZ) research spans practical optimization, quantum computing evaluation, and quantum information theory. A major focus is the development of physics-inspired classical algorithms that deliver strong real-world performance on optimization problems often associated with quantum computing. This includes scalable solvers such as VeloxQ and related simulated bifurcation approaches, with a consistent emphasis on conventional hardware deployment and competitive or superior results.

Another core direction is rigorous evaluation of quantum advantage claims. The work emphasizes end-to-end runtime accounting, strong classical baselines, and operationally relevant metrics. Instead of treating quantum advantage as a marketing label, QMZ approaches it as a measurable systems-level question shaped by runtime definitions, overheads, and benchmark design.

QMZ also contributes to foundational quantum information research combining theoretical rigor with resource-efficiency considerations that matter for deployment and benchmarking. Overall, the portfolio is best described as physics-inspired computation and quantum-tech evaluation with a strong emphasis on scalable, implementable methods.

Papers worth reading

  • VeloxQ: A Fast and Efficient QUBO Solver
    (arXiv:2501.19221)

    A high-performance physics-inspired QUBO/HUBO solver with strong scalability on conventional hardware.

  • Recent quantum runtime (dis)advantages
    (arXiv:2510.06337)

    A rigorous runtime framework showing why current quantum speedup claims often fail under full overhead accounting.

  • Closing the Quantum-Classical Scaling Gap in Approximate Optimization
    (arXiv:2505.22514)

    A strong classical SBM benchmark that closes a reported quantum annealing scaling advantage in QUBO optimization.

  • Local certification of unitary operations
    (arXiv:2312.17037)

    A resource-efficient method for locally certifying unitary quantum operations without auxiliary entanglement in many cases.

  • Disruption Management in Airline Operations: A Solver-based Approach using Time-Space Network Optimization (AIRS)
    (arXiv:2510.26831)

    An optimization-based airline disruption recovery system for fast, integrated aircraft, crew, and passenger replanning.

VeloxQ: A Fast and Efficient QUBO Solver
(arXiv:2501.19221)

A high-performance physics-inspired QUBO/HUBO solver with strong scalability on conventional hardware.

VeloxQ is our high-performance solver for Quadratic Unconstrained Binary Optimization (QUBO) problems, a core class of optimization tasks appearing in logistics, finance, energy, and scheduling. It is built to deliver strong results on conventional computing infrastructure, without depending on specialized quantum hardware. In benchmarking, VeloxQ matches or outperforms leading classical and quantum solvers in both runtime and solution quality, making it a practical option for organizations that need scalable optimization now.

VeloxQ solves not only QUBO, but also HUBO problems. It’s based on classical dynamics rather than thermal annealing. It is benchmarked against quantum annealers, digital-quantum methods, simulated bifurcation, parallel annealing, tropical tensor networks, branch-and-bound methods, and GPU brute-force solvers. Our results show strong performance in both runtime and solution quality, along with excellent scalability on large sparse instances. VeloxQ consistently reaches near-optimal solutions and is well suited for future hybrid quantum-classical workflows.

Notes:

  • Physics-inspired, non-thermal dynamics-based optimization for QUBO/HUBO instances.
  • Designed for deployment on standard CPU/GPU infrastructure.
  • Benchmarked against both advanced classical solvers and quantum approaches.
  • Strong scalability on very large sparse optimization problems.
  • Near-optimal practical performance, including agreement with exact solvers on smaller benchmarks.


Recent quantum runtime (dis)advantages
(arXiv:2510.06337)

A rigorous runtime framework showing why current quantum speedup claims often fail under full overhead accounting.

We focus on a key issue in quantum computing commercialization: how runtime should be measured in fair quantum-vs-classical comparisons. Many quantum advantage claims rely on incomplete timing metrics that exclude important overheads.

The framework introduced here uses end-to-end runtime definitions and shows that, under realistic accounting and stronger classical baselines, current NISQ hardware does not yet deliver runtime advantage. The result is a more reliable basis for evaluating performance claims and investment decisions.

We define experimentally grounded runtime metrics for both gate-based and annealing quantum computers, explicitly including overheads such as embedding/programming, readout, transpilation, and thermalization where relevant.

It revisits several published quantum advantage claims, including approximate QUBO optimization, a restricted implementation of Simon’s problem, and a reported hybrid quantum-classical runtime advantage.

A central conclusion is that favorable results often disappear once full runtime accounting and stronger classical baselines are applied. The analysis also emphasizes the need for appropriate comparison metrics, such as time-to-epsilon, and rigorous baseline selection.

Notes:

  • End-to-end runtime definitions that are operationally meaningful for quantum experiments.
  • A methodology for selecting strong classical reference implementations.
  • Reassessment of annealing-based speedup claims under realistic overhead accounting.
  • Wall-clock analysis showing that query complexity advantage does not guarantee runtime advantage.
  • Stricter benchmarking criteria for credible runtime-based quantum advantage claims in the NISQ era.


Closing the Quantum-Classical Scaling Gap in Approximate Optimization
(arXiv:2505.22514)

A strong classical SBM benchmark that closes a reported quantum annealing scaling advantage in QUBO optimization.

We re-examine a prominent claim that quantum annealing achieves superior scaling in approximate QUBO optimization. The results show that a strong classical alternative, the Simulated Bifurcation Machine (SBM), can match or exceed the reported quantum scaling, effectively closing the claimed quantum-classical gap.
The study also highlights how strongly such conclusions depend on the selected classical baseline and the runtime definition. For organizations evaluating optimization technologies, it reinforces the need to benchmark against the best available classical methods before drawing strategic conclusions.

The analysis uses a Simulated Bifurcation Machine based on nonlinear Hamiltonian dynamics and chaotic behavior rather than thermal annealing. The method is implemented with a symplectic Euler scheme and supports massive GPU parallelism through many replicas. Benchmarking is extended to significantly larger instances than those used in the original quantum-advantage claim, showing that SBM closes the reported scaling gap.

The paper also demonstrates that small problem sizes and loose approximation targets can produce misleading scaling conclusions, and argues for larger, structurally diverse benchmarks with tighter optimality gaps.

Notes:

  • Optimization modeled via nonlinear Hamiltonian dynamics and chaotic behavior.
  • GPU-friendly parallelism through many independent replicas.
  • Enhanced discretization strategy to improve solver behavior.
  • Classical SBM matching or outperforming previously reported quantum scaling trends.
  • Strong critique of runtime-definition sensitivity and finite-size benchmarking effects.


Local certification of unitary operations
(arXiv:2312.17037)

A resource-efficient method for locally certifying unitary quantum operations without auxiliary entanglement in many cases.

Reliable verification of quantum operations is essential for practical quantum computing, benchmarking, and deployment. We address local certification of unitary operations in distributed settings and shows that, in many cases, efficient certification is possible using local operations and limited classical communication. This reduces reliance on costly entanglement resources while still supporting robust validation of quantum devices and protocols.

We extend quantum hypothesis testing to the certification of unitary channels, where the objective is to minimize type-II error subject to a fixed type-I error threshold. A key contribution is the link between local certification performance and the product numerical range of unitary matrices.

The analysis shows that the optimal local strategy typically does not require auxiliary entanglement and can be implemented with a single round of one-way classical communication. It also compares local and global strategies, showing that local optimality is common but not universal, and discusses applications to certification of von Neumann measurements.

Notes:

  • Local unitary certification formulated as a constrained hypothesis-testing problem.
  • Certification performance linked to the product numerical range of unitary matrices.
  • Optimal local strategies typically avoid auxiliary entanglement.
  • Single-round one-way classical communication is sufficient in the optimal local setting.
  • Clear characterization of regimes where local certification is optimal versus where global methods can do better.


Disruption Management in Airline Operations: A Solver-based Approach using Time-Space Network Optimization (AIRS)
(arXiv:2510.26831)

An optimization-based airline disruption recovery system for fast, integrated aircraft, crew, and passenger replanning.

AIRS is our optimization-based disruption recovery system for airline day-of-operations management. It addresses irregular operations such as delays, cancellations, maintenance events, and crew disruptions by generating integrated recovery plans across aircraft, crew, and passengers.
The system is designed to operate within real operational decision windows and to reduce recovery costs compared with manual or sequential approaches. This makes AIRS a scalable decision-support capability for airline operations control centers.

AIRS combines a Time-Space Network (TSN) formulation with mixed-integer linear programming (MILP) to jointly model aircraft and crew recovery under practical constraints, including legality, maintenance windows, slot capacities, and routing continuity. The AIRS.ACR module performs integrated aircraft-crew recovery, while AIRS.PaxR handles passenger re-accommodation using greedy assignment and lightweight evolutionary search while preserving aircraft-crew feasibility.

The architecture balances integrated optimization with tractability by separating passenger recovery from the most tightly coupled operational constraints. The system is also designed for deployment with configurable data inputs and operationally actionable outputs.

Key properties (technical notes):

  • TSN-based integrated model for aircraft and crew recovery under operational constraints.
  • MILP optimization core with search-space control for tractable recovery planning.
  • Two-stage architecture: ACR (aircraft/crew) and PaxR (passenger recovery).
  • Designed for practical decision windows in airline operations control centers.
  • Deployment-oriented structured inputs and outputs for integration with airline workflows.