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Eunok Bae

Publications and source records attributed to Eunok Bae.

10 recordsLinked to original sources
arXiv2026

Reducing Circuit Resources in Grover's Algorithm via Constraint-Aware Initialization

Grover's search algorithm provides a quadratic speedup over classical brute-force search in terms of query complexity and is widely used as a versatile subroutine in numerous quantum algorithms, including those for combinatorial problems with large search spaces. For such problems, it is natural to reduce the effective search space by incorporating problem constraints at the initialization step, which in Grover's algorithm can be achieved by preparing structured initial states that encode constraint information. In this work, we present a systematic framework with a simple preprocessing procedure for constraint-aware initialization in Grover's algorithm, focusing on problems with linear constraints. While such structured initial states can reduce the number of oracle queries required to obtain a solution, their preparation incurs additional circuit-level costs. We therefore offer a conservative circuit-level resource analysis, showing that the resulting constraint-aware initialization can improve resource efficiency in terms of gate counts and circuit depth. The validity of the framework is further demonstrated numerically using the exact-cover problem. Overall, our results indicate that this approach serves as a practical baseline for achieving more resource-efficient implementations of Grover's algorithm compared to the standard uniform initialization.

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arXiv2025

Two Variations of Quantum Phase Estimation for Reducing Circuit Error Rates: Application to the Harrow--Hassidim--Lloyd Algorithm

We introduce two variations of the quantum phase estimation algorithm: quantum shifted phase estimation and quantum punctured phase estimation. The shifted method employs a bit-string left shift to discard the most significant bit and focus on lower-order phase components, and the punctured method removes qubits corresponding to known phase bits, thereby streamlining the circuit. To demonstrate the effectiveness of the two variations, we integrate them into a hybrid quantum-classical implementation of the Harrow--Hassidim--Lloyd algorithm for solving linear systems. The hybrid method leverages both quantum and classical processors to identify and remove unnecessary qubits and gates. As a result, our method reduces qubit and gate counts compared to previous implementations, leading to lower overall circuit error rates on current hardware. Experimental demonstrations on IBM superconducting hardware confirm the error-mitigation effectiveness of the proposed hybrid method.

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arXiv2025

Near-Optimal Parameter Tuning of Level-1 QAOA for Ising Models

The Quantum Approximate Optimisation Algorithm (QAOA) tackles combinatorial optimisation problems by encoding their solutions into the ground state of an Ising Hamiltonian prepared by a $p$-level parameterised circuit, with the angles tuned classically. Parameter optimisation is widely regarded as a central bottleneck, even for the shallowest circuits. Focusing on QAOA at $p=1$ (QAOA$_1$), we show that tuning the two angles $(\gamma, \beta)$ for weighted Ising models is not a black-box search but a structured signal-processing problem. We prove that the QAOA$_1$ expectation value is a partial Fourier series in $\gamma$ whose frequencies are determined explicitly by the problem's couplings and fields, giving instance-wise bandwidth bounds and, via the Nyquist--Shannon theorem, the sampling resolution needed to avoid the aliasing that causes coarse-grid searches to return spurious optima. We then eliminate the mixer angle analytically, computing $\beta^*(\gamma)$ in closed form to reduce the search to one dimension, and apply a subdivision algorithm that locates the globally optimal $\gamma$ in polynomial time with a certificate of optimality when the weights are commensurable and bounded. For regular weighted graphs, we further prove the conventional wisdom that the globally optimal $\gamma^* \in \mathbb{R}^+$ concentrates near zero and coincides with the first local optimum, giving a rigorous account of the empirical success of small-angle initialisation and allowing gradient descent to replace exhaustive line searches. Validated within Recursive QAOA (RQAOA) on weighted instances of 128 and 256 qubits, our method consistently outperforms both coarsely optimised RQAOA and semidefinite programming.

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arXiv2024

Modified Recursive QAOA for Exact Max-Cut Solutions on Bipartite Graphs: Closing the Gap Beyond QAOA Limit

Quantum Approximate Optimization Algorithm (QAOA) is a quantum-classical hybrid algorithm proposed with the goal of approximately solving combinatorial optimization problems such as the MAX-CUT problem. It has been considered a potential candidate for achieving quantum advantage in the Noisy Intermediate-Scale Quantum era and has been extensively studied. However, the performance limitations of low-level QAOA have also been demonstrated across various instances. In this work, we first analytically prove the performance limitations of level-1 QAOA in solving the MAX-CUT problem on bipartite graphs. To this end, we derive an upper bound for the approximation ratio based on the average degree of bipartite graphs. Second, we demonstrate that Recursive QAOA (RQAOA), which recursively reduces graph size using QAOA as a subroutine, outperforms the level-1 QAOA. However, the performance of RQAOA exhibits limitations as the graph size increases. Finally, we show that RQAOA with a restricted parameter regime can fully address these limitations. Surprisingly, this modified RQAOA always finds the exact maximum cut for any bipartite graphs and even for a more general graph with parity-signed weights.

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arXiv2024

Investigating controlled teleportation capability of quantum states with respect to $k$-separability

Quantum teleportation is an essential application of quantum entanglement. The examination of teleportation fidelity in two-party standard teleportation schemes reveals a critical threshold distinguishing separable and entangled states. For separable states, their teleportation fidelities cannot exceed the threshold, emphasizing the significance of entanglement. We extend this analysis to multi-party scenarios known as controlled teleportation. Our study provides thresholds that $N$-qudit $k$-separable states cannot exceed in a controlled teleportation scheme, where $N \ge 3$ and $2 \le k \le N$. This not only establishes a standard for utilizing a given quantum state as a resource in controlled teleportation but also enhances our understanding of the influence of the entanglement structure on controlled teleportation performance. In addition, we show that genuine multipartite entanglement is not a prerequisite for achieving a high controlled teleportation capability.

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arXiv2023

Genuine multipartite entanglement measures based on multi-party teleportation capability

Quantifying entanglement is vital to understand entanglement as a resource in quantum information processing, and many entanglement measures have been suggested for this purpose. When mathematically defining an entanglement measure, we should consider the distinguishability between entangled and separable states, the invariance under local transformation, the monotonicity under local operations and classical communication, and the convexity. These are reasonable requirements but may be insufficient, in particular when taking into account the usefulness of quantum states in multi-party quantum information processing. Therefore, if we want to investigate multipartite entanglement as a resource, then it can be necessary to consider the usefulness of quantum states in multi-party quantum information processing when we define a multipartite entanglement measure. In this paper, we define new multipartite entanglement measures for three-qubit systems based on the three-party teleportation capability, and show that these entanglement measures satisfy the requirements for being genuine multipartite entanglement measures. We also generalize our entanglement measures for $N$-qubit systems, where $N \ge 4$, and discuss that these quantities may be good candidates to measure genuine multipartite entanglement.

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arXiv2023

Recursive QAOA outperforms the original QAOA for the MAX-CUT problem on complete graphs

Quantum approximate optimization algorithms are hybrid quantum-classical variational algorithms designed to approximately solve combinatorial optimization problems such as the MAX-CUT problem. In spite of its potential for near-term quantum applications, it has been known that quantum approximate optimization algorithms have limitations for certain instances to solve the MAX-CUT problem, at any constant level $p$. Recently, the recursive quantum approximate optimization algorithm, which is a non-local version of quantum approximate optimization algorithm, has been proposed to overcome these limitations. However, it has been shown by mostly numerical evidences that the recursive quantum approximate optimization algorithm outperforms the original quantum approximate optimization algorithm for specific instances. In this paper, we analytically prove that the recursive quantum approximate optimization algorithm is more competitive than the original one to solve the MAX-CUT problem for complete graphs with respect to the approximation ratio.

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arXiv2021

Quantum algorithm based on the $\varepsilon$-random linear disequations for the continuous hidden shift problem

There have been several research works on the hidden shift problem, quantum algorithms for the problem, and their applications. However, all the results have focused on discrete groups with discrete oracle functions. In this paper, we define the continuous hidden shift problem on $\mathbb{R}^n$ with a continuous oracle function as an extension of the hidden shift problem, and also define the $\varepsilon$-random linear disequations which is a generalization of the random linear disequations. By employing the newly defined concepts, we show that there exists a quantum computational algorithm which solves this problem in time polynomial in $n$.

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arXiv2015

Stability theorem of depolarizing channels for the minimal output quantum Rényi entropies

We show that the stability theorem of the depolarizing channel holds for the output quantum $p$-Rényi entropy for $p \ge 2$ or $p=1$, which is an extension of the well known case $p=2$. As an application, we present a protocol in which Bob determines whether Alice prepares a pure quantum state close to a product state. In the protocol, Alice transmits to Bob multiple copies of a pure state through a depolarizing channel, and Bob estimates its output quantum $p$-Rényi entropy. By using our stability theorem, we show that Bob can determine whether her preparation is appropriate.

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