Alejandro Montanez-Barrera

The Quantum Approximate Optimization Algorithm (QAOA) is a promising algorithm for solving combinatorial optimization problems (COPs), with performance governed by variational parameters. While most prior work has focused on classically optimizing these parameters, we demonstrate that fixed linear ramp schedules, linear ramp QAOA (LR-QAOA), can efficiently approximate optimal solutions across diverse COPs. Simulations with up to 42 qubits and 400 layers suggest that the success probability scales with a coefficient that decreases as the number of layers increases. Comparisons with classical algorithms, including simulated annealing, Tabu Search, and branch-and-bound, show a scaling advantage for LR-QAOA. We show results of LR-QAOA on multiple QPUs (IonQ, Quantinuum, IBM) with up to 109 qubits and 100 layers, and circuits requiring 21,200 CNOT gates. Finally, we present a noise model based on two-qubit gate counts that accurately reproduces the experimental behavior of LR-QAOA.

Solving combinatorial optimization problems (COPs) is a promising application of quantum computation, with the Quantum Approximate Optimization Algorithm (QAOA) being one of the most studied quantum algorithms for solving them. However, multiple factors make the parameter search of the QAOA a hard optimization problem. In this work, we study transfer learning (TL), a methodology to reuse pre-trained QAOA parameters of one problem instance into different COP instances. This methodology can be used to alleviate the necessity of classical optimization to find good parameters for individual problems. To this end, we select small cases of the traveling salesman problem (TSP), the bin packing problem (BPP), the knapsack problem (KP), the weighted maximum cut (MaxCut) problem, the maximal independent set (MIS) problem, and portfolio optimization (PO), and find optimal parameters for p layers. We compare how well the parameters found for one problem adapt to the others. Among the different problems, BPP is the one that produces the best transferable parameters, maintaining the probability of finding the optimal solution above a quadratic speedup over random guessing for problem sizes up to 42 qubits and p = 10 layers. Using the BPP parameters, we perform experiments on IonQ Harmony and Aria, Rigetti Aspen-M-3, and IBM Brisbane of MIS instances for up to 18 qubits. The results indicate IonQ Aria yields the best overlap with the ideal probability distribution. Additionally, we show that cross-platform TL is possible using the D-Wave Advantage quantum annealer with the parameters found for BPP. We show an improvement in performance compared to the default protocols for MIS with up to 170 qubits. Our results suggest that there are QAOA parameters that generalize well for different COPs and annealing protocols.

In recent years, neutral atom-based quantum computation has been established as a competing alternative for the realization of fault-tolerant quantum computation. However, as with other quantum technologies, various sources of noise limit their performance. With processors continuing to scale up, new techniques are needed to characterize and compare them in order to track their progress. In this work, we present two systematic benchmarks that evaluate these quantum processors at scale. We use the quantum adiabatic algorithm (QAA) and the quantum approximate optimization algorithm (QAOA) to solve maximal independent set (MIS) instances of random unit-disk graphs. These benchmarks are scalable, relying not on prior knowledge of the system’s evolution but on the quality of the MIS solutions obtained. We benchmark quera_aquila and pasqal_fresnel on problem sizes up to 102 and 85 qubits, respectively. Overall, quera_aquila performs better on QAOA and QAA instances. Finally, we generate MIS instances of up to 1000 qubits, providing scalable benchmarks for evaluating future, larger processors as they become available.

Quantum computers have now surpassed classical simulation limits, yet noise continues to limit their practical utility. As the field shifts from proof-of-principle demonstrations to early deployments, there is no standard method for meaningfully and scalably comparing heterogeneous quantum hardware. Existing benchmarks typically focus on gate-level fidelity or constant-depth circuits, offering limited insight into algorithmic performance at depth. Here we introduce a benchmarking protocol based on the linear ramp quantum approximate optimization algorithm (LR-QAOA), a fixed-parameter, deterministic variant of QAOA. LR-QAOA quantifies a QPU’s ability to preserve a coherent signal as circuit depth increases, identifying when performance becomes statistically indistinguishable from random sampling. We apply this protocol to 24 quantum processors from six vendors, testing problems with up to 156 qubits and 10,000 layers across 1D-chains, native layouts, and fully connected topologies. This constitutes the most extensive cross-platform quantum benchmarking effort to date, with circuits reaching a million two-qubit gates. LR-QAOA offers a scalable, unified benchmark across platforms and architectures, making it a tool for tracking performance in quantum computing.

As quantum processing units (QPUs) scale toward hundreds of qubits, diagnosing noise-induced correlations (crosstalk) becomes critical for reliable quantum computation. In this work, we introduce Zero-Entropy Classical Shadows (ZECS), a diagnostic tool that uses information of a rank-one quantum state tomography (QST) reconstruction from classical shadow (CS) information to make a crosstalk diagnosis. We use ZECS on trapped ion and superconductive QPUs, including ionq_forte (36 qubits), ibm_brisbane (127 qubits), and ibm_fez (156 qubits), using from 1,000 to 6,000 samples. With these samples, we use ZECS to characterize crosstalk among disjoint qubit subsets across the full hardware. This information is then used to select low-crosstalk qubit subsets on ibm_fez for executing the Quantum Approximate Optimization Algorithm (QAOA) on a 20-qubit problem. Compared to the best qubit selection via Qiskit transpilation, our method improves solution quality by 10% and increases algorithmic coherence by 33%. ZECS offers a scalable and measurement-efficient approach to diagnosing crosstalk in large-scale QPUs.

Solving combinatorial optimization problems of the kind that can be codified by quadratic unconstrained binary optimization (QUBO) is a promising application of quantum computation. Some problems of this class suitable for practical applications such as the traveling salesman problem (TSP), the bin packing problem (BPP), or the knapsack problem (KP) have inequality constraints that require a particular cost function encoding. The common approach is the use of slack variables to represent the inequality constraints in the cost function. However, the use of slack variables considerably increases the number of qubits and operations required to solve these problems using quantum devices. In this work, we present an alternative method that does not require extra slack variables and consists of using an unbalanced penalization function to represent the inequality constraints in the QUBO. This function is characterized by larger penalization when the inequality constraint is not achieved than when it is. We evaluate our approach on the TSP, BPP, and KP, successfully encoding the optimal solution of the original optimization problem near the ground state cost Hamiltonian. Additionally, we employ D-Wave Advantage and D-Wave hybrid solvers to solve the BPP, surpassing the performance of the slack variables approach by achieving solutions for up to 29 items, whereas the slack variables approach only handles up to 11 items. This new approach can be used to solve combinatorial problems with inequality constraints with a reduced number of resources compared to the slack variables approach using quantum annealing or variational quantum algorithms.