arXiv subjects

Anthony Wilkie

Publications and source records attributed to Anthony Wilkie.

5 recordsLinked to original sources

arXiv2026

Partitioned-Constraint QAOA (PC-QAOA): Structural State Preparation and Penalty Enforcement for Quantum Optimization

Constrained combinatorial optimization remains challenging for quantum algorithms because feasibility must be explicitly enforced, typically through penalty terms or problem-specific mixers. We introduce Partitioned-Constraint QAOA (PC-QAOA), which partitions constraints into those enforced structurally and those enforced energetically. Structural constraints are handled via feasible-state preparation and a Grover mixer that preserves feasibility, while the remaining constraints are enforced through penalties. We show that constraints with disjoint support can be prepared in parallel with little error accumulation. We identify broad classes of constraints (including cardinality, assignment, and flow conservation) that admit efficient structural enforcement, and introduce a variational gadget construction that extends this approach to arbitrary low-support constraints. Across 413 completed instances spanning multiple constraint families, PC-QAOA substantially improves feasibility and solution quality at shallow depth relative to penalty-based QAOA, demonstrating the value of partial structural enforcement.

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arXiv2025

Efficient circuits for leaf-separable state preparation

Efficient state preparation is a challenging and important problem in quantum computing. In this work, we present a recursive state preparation algorithm that combines logarithmic-depth Dicke state circuits with Hamming weight encoders for efficiently preparing ``leaf-separable" quantum states. The algorithm is built on binary partition trees, generalized weight distribution blocks (gWDBs), and leaf-level encoders. We evaluate the performance of the algorithm by numerically simulating it on randomly generated target states with between 4 and 15 qubits. Compared to general state preparation approaches which require $O(2^n)$ CX gates, our algorithm achieves a circuit depth of $O(k\log\frac{n}{k} + 2^k)$ and uses $O(n(k+2^k))$ two-qubit gates, where $k < n$ denotes the subtree size. We also compare implementations of the algorithm with and without the use of ancilla qubits, providing a detailed analysis of the trade-offs in circuit depth and two-qubit gate counts. These results contribute to scalable state preparation for quantum algorithms that require structured inputs such as Dicke or near-Dicke states.

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arXiv2025

An Exclusive-Sum-of-Products Pipeline for QAOA

The quantum approximate optimization algorithm is commonly used to solve combinatorial optimization problems. While unconstrained problems map naturally into the algorithm, incorporating constraints typically requires penalizing constraint violations in the objective function. In this work, we propose an alternative approach that encodes constraints as Boolean expressions in exclusive-sum-of-products (ESOP) form before penalization. We test this method on the maximum independent set problem using graphs with 3 to 20 vertices and find that ESOP constraint formulations achieve higher approximation ratios than standard constraint penalization methods, with percent increases of up to 30.3%. Furthermore, ESOP constraint formulations result in higher approximation ratios than standard QAOA penalization approaches after one layer of the algorithm on approximately 64% of the tested graphs.

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arXiv2024

Quantum approximate optimization algorithm with random and subgraph phase operators

The quantum approximate optimization algorithm (QAOA) is a promising quantum algorithm that can be used to approximately solve combinatorial optimization problems. The usual QAOA ansatz consists of an alternating application of the cost and mixer Hamiltonians. In this work, we study how using Hamiltonians other than the usual cost Hamiltonian, dubbed custom phase operators, can affect the performance of QAOA. We derive an expected value formula for QAOA with custom phase operators at $p = 1$ and show numerically that some of these custom phase operators can achieve higher approximation ratio than the original algorithm implementation. Out of all the graphs tested at $p=1$, 0.036\% of the random custom phase operators, 75.9\% of the subgraph custom phase operators, 95.1\% of the triangle-removed custom phase operators, and 93.9\% of the maximal degree edge-removed custom phase operators have a higher approximation ratio than the original QAOA implementation. Furthermore, we numerically simulate these phase operators for $p=2$ and $p=3$ levels of QAOA and find that there exist a large number of subgraph, triangle-removed, and maximal degree edge-removed custom phase operators that have a higher approximation ratio than QAOA at the same depth. These findings open up the question of whether better phase operators can be designed to further improve the performance of QAOA.

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arXiv2024

An angle rounding parameter initialization technique for ma-QAOA

The multi-angle quantum approximate optimization algorithm (ma-QAOA) is a recently introduced algorithm that gives at least the same approximation ratio as the quantum approximate optimization algorithm (QAOA) and, in most cases, gives a significantly higher approximation ratio than QAOA. One drawback to ma-QAOA is that it uses significantly more classical parameters than QAOA, so the classical optimization component more complex. In this paper, we motivate a new parameter initialization strategy in which angles are initially randomly set to multiples of $π/8$ between $-π$ and $π$ and this vector is used to seed one round of BFGS. We find that this parameter initialization strategy gives average approximation ratios of $0.900$, $0.982$, and $0.997$ for $p = 1, 2, 3$ layers of ma-QAOA. This is comparable to the average approximation ratios of ma-QAOA where the optimal parameters are found using BFGS with 1 random starting seed, which are $0.900$, $0.982$, and $0.996$. We also test another parameter initialization strategy in which angles corresponding to maximal degree vertices in the graph are set to 0 while all other are randomly initialized to random multiples of $π/8$. Using this strategy, the average approximation ratios are $0.897$, $0.984$, and $0.997$.

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