Designing efficient variational quantum algorithms (VQAs) is crucial for transforming the theoretical advantages of quantum algorithms into practical applications. In this context, quantum architecture search (QAS) has been introduced to automate the search and design of VQAs. However, current mainstream QAS algorithms typically perform both global and local searches simultaneously, which can result in high search space complexity and optimization challenges. In this paper, we propose a hierarchical quantum architecture search framework based on a two-stage search structure. In the first stage, global exploration of the overall quantum circuit structure is performed, while in the second stage, local optimization of quantum gate selection is carried out. We provide a numerical analysis of the theoretical advantages of the proposed framework in reducing the search space. To evaluate practical performance, we conduct experiments on quantum chemistry tasks with different algorithm combinations integrated into the framework. The results demonstrate the effectiveness of the hierarchical search structure in automating quantum circuit design.Designing efficient variational quantum algorithms (VQAs) is crucial for transforming the theoretical advantages of quantum algorithms into practical applications. In this context, quantum architecture search (QAS) has been introduced to automate the search and design of VQAs. However, current mainstream QAS algorithms typically perform both global and local searches simultaneously, which can result in high search space complexity and optimization challenges. In this paper, we propose a hierarchical quantum architecture search framework based on a two-stage search structure. In the first stage, global exploration of the overall quantum circuit structure is performed, while in the second stage, local optimization of quantum gate selection is carried out. We provide a numerical analysis of the theoretical advantages of the proposed framework in reducing the search space. To evaluate practical performance, we conduct experiments on quantum chemistry tasks with different algorithm combinations integrated into the framework. The results demonstrate the effectiveness of the hierarchical search structure in automating quantum circuit design.

IEEE Transactions on Quantum EngineeringJan 1, 20249 citations

An alternate algorithm for directed quantum search

Tathagat Tulsi, Lov K. Grover, Apoorva D. Patel

May 2, 20050 citations

A Framework for Efficient Search of High-Distance Quantum Stabilizer Codes

Utsav Karia

Abstract Quantum stabilizer codes are essential for protecting quantum information, but systematic searches for high-distance codes become computationally prohibitive as code length increases. Existing code constructions exhibit structural regularities, yet no general framework quantifies how such constraints reduce the stabilizer-code search space or incorporates them into code searches. This project asks whether structural properties of known quantum codes can be formulated as mathematical constraints that quantitatively reduce search spaces while remaining useful for discovering high-distance codes. We develop a unified framework based on $q$ -Galois matrices and define the search-space retention factor as the asymptotic fraction of logarithmic search space retained after imposing a constraint. We derive retention factors for weight-spectrum, qudit-participation, overlap, support, Pauli-distribution, local non-commutation, graph-theoretic, and symmetry constraints, including combinations. We introduce finite-size correction factors $C$ and $C'$ and find empirically that they decay approximately as $\log n/n$ and $1/n$ , respectively. The framework is evaluated using 58,902 quantum-code parameter sets, including 34,775 codes with usable matrix data across $q=2,3,4,5,7,8$ ; 1,909 semi-perfect quantum codes are analyzed. We develop a general method to empirically estimate the weight-spectrum and average-weight for unresolved semi-perfect quantum codes, achieving runtime speedups ranging from $10^{8.3608}$ to $10^{193.9298}$ across 4 distinct unresolved codes. Runtime analysis validates that these reductions translate into substantial computational savings. Applying the framework to a $(14,3)$ qubit search produced a code detecting 91,765 of 91,770 errors of weight at most 4 and achieving 99.9999933% and 99.9733% of the theoretically optimal performance of $[[14,3,5]]_2$ code at $p=0.01$ . Thus, the framework converts structural properties into explicit candidate-space reductions that can be imposed during code enumeration, providing a quantitative basis for reducing the computational cost of high-distance stabilizer-code searches.Abstract Quantum stabilizer codes are essential for protecting quantum information, but systematic searches for high-distance codes become computationally prohibitive as code length increases. Existing code constructions exhibit structural regularities, yet no general framework quantifies how such constraints reduce the stabilizer-code search space or incorporates them into code searches. This project asks whether structural properties of known quantum codes can be formulated as mathematical constraints that quantitatively reduce search spaces while remaining useful for discovering high-distance codes. We develop a unified framework based on $q$-Galois matrices and define the search-space retention factor as the asymptotic fraction of logarithmic search space retained after imposing a constraint. We derive retention factors for weight-spectrum, qudit-participation, overlap, support, Pauli-distribution, local non-commutation, graph-theoretic, and symmetry constraints, including combinations. We introduce finite-size correction factors $C$ and $C'$ and find empirically that they decay approximately as $\log n/n$ and $1/n$, respectively. The framework is evaluated using 58,902 quantum-code parameter sets, including 34,775 codes with usable matrix data across $q=2,3,4,5,7,8$; 1,909 semi-perfect quantum codes are analyzed. We develop a general method to empirically estimate the weight-spectrum and average-weight for unresolved semi-perfect quantum codes, achieving runtime speedups ranging from $10^{8.3608}$ to $10^{193.9298}$ across 4 distinct unresolved codes. Runtime analysis validates that these reductions translate into substantial computational savings. Applying the framework to a $(14,3)$ qubit search produced a code detecting 91,765 of 91,770 errors of weight at most 4 and achieving 99.9999933% and 99.9733% of the theoretically optimal performance of $[[14,3,5]]_2$ code at $p=0.01$. Thus, the framework converts structural properties into explicit candidate-space reductions that can be imposed during code enumeration, providing a quantitative basis for reducing the computational cost of high-distance stabilizer-code searches.

Aug 22, 20260 citations

Quantum Algorithms for Highly Structured Search Problems

Markus Hunziker, DAVID A. MEYER

Quantum Information ProcessingJun 1, 200212 citations

Search tree with probabilistic key comparison and quantum string sorting

Kamil Ravilevich Khadiev

In the framework of this work, a binary data structure is considered. search tree, specifically red-black tree as an implementation self-balancing search tree. We consider the case when procedure for comparing elements in a tree "noisy" or probabilistic. We present an algorithm that implements the main operations (adding, deleting, searching) with error probability O(1/n2) and running time t=O(log n) steps. And use the data structure to build a quantum algorithm sorting n strings of length k in O(n log n √k).In the framework of this work, a binary data structure is considered. search tree, specifically red-black tree as an implementation self-balancing search tree. We consider the case when procedure for comparing elements in a tree "noisy" or probabilistic. We present an algorithm that implements the main operations (adding, deleting, searching) with error probability O(1/n2) and running time t=O(log n) steps. And use the data structure to build a quantum algorithm sorting n strings of length k in O(n log n √k).

Academician O.B. Lupanov International Scientific Seminar "Discrete Mathematics and Its Applications"Jan 1, 20220 citations

Accelerated search for global extrema in structured quantum signals

Sachin S. Bharadwaj, Katepalli R. Sreenivasan

Extreme values of a physical system are rare by definition, yet they can govern some of its most consequential and anomalous behavior. Their sparsity makes them particularly costly to identify in large data sets. Quantum computation offers a potential way to reduce this cost. The challenge is that quantum amplitudes cannot simply be read, copied, compared, or marked using conventional search oracles. Here we introduce an algorithm for searching amplitude-encoded quantum signals that exploits their underlying structure. Through a nonlinear amplitude transformation, the algorithm identifies and certifies a global extremum while exponentially reducing the effective search space for structured signals. We establish a polylogarithmic query complexity in the data size $N$ , together with global completeness, efficient classical verification, and a measurable criterion for quantifying exploitable structure. We demonstrate the framework using computational turbulence data. Applied to line cuts of velocity gradients from a $1024^3$ simulation containing more than one billion grid points, the algorithm consistently isolates the extreme tail and reduces the median search space to $O(\log N)$ . The clustered structure characteristic of turbulence further accelerates the search. These results establish a direct connection between physical structure and quantum advantage in extreme-value search. For accessibility, the main text emphasizes the central ideas and results, while the theoretical derivations are provided in the Appendices.Extreme values of a physical system are rare by definition, yet they can govern some of its most consequential and anomalous behavior. Their sparsity makes them particularly costly to identify in large data sets. Quantum computation offers a potential way to reduce this cost. The challenge is that quantum amplitudes cannot simply be read, copied, compared, or marked using conventional search oracles. Here we introduce an algorithm for searching amplitude-encoded quantum signals that exploits their underlying structure. Through a nonlinear amplitude transformation, the algorithm identifies and certifies a global extremum while exponentially reducing the effective search space for structured signals. We establish a polylogarithmic query complexity in the data size $N$, together with global completeness, efficient classical verification, and a measurable criterion for quantifying exploitable structure. We demonstrate the framework using computational turbulence data. Applied to line cuts of velocity gradients from a $1024^3$ simulation containing more than one billion grid points, the algorithm consistently isolates the extreme tail and reduces the median search space to $O(\log N)$. The clustered structure characteristic of turbulence further accelerates the search. These results establish a direct connection between physical structure and quantum advantage in extreme-value search. For accessibility, the main text emphasizes the central ideas and results, while the theoretical derivations are provided in the Appendices.

quant-pharXiv:2610.04024Oct 6, 20260 citations

q

-Galois matrices and define the search-space retention factor as the asymptotic fraction of logarithmic search space retained after imposing a constraint. We derive retention factors for weight-spectrum, qudit-participation, overlap, support, Pauli-distribution, local non-commutation, graph-theoretic, and symmetry constraints, including combinations. We introduce finite-size correction factors

C

and

C'

and find empirically that they decay approximately as

\log n/n

and

1/n

, respectively. The framework is evaluated using 58,902 quantum-code parameter sets, including 34,775 codes with usable matrix data across

q=2,3,4,5,7,8

; 1,909 semi-perfect quantum codes are analyzed. We develop a general method to empirically estimate the weight-spectrum and average-weight for unresolved semi-perfect quantum codes, achieving runtime speedups ranging from

10^{8.3608}

10^{193.9298}

across 4 distinct unresolved codes. Runtime analysis validates that these reductions translate into substantial computational savings. Applying the framework to a

(14,3)

qubit search produced a code detecting 91,765 of 91,770 errors of weight at most 4 and achieving 99.9999933% and 99.9733% of the theoretically optimal performance of

[[14,3,5]]_2

code at

p=0.01

. Thus, the framework converts structural properties into explicit candidate-space reductions that can be imposed during code enumeration, providing a quantitative basis for reducing the computational cost of high-distance stabilizer-code searches.

N

, together with global completeness, efficient classical verification, and a measurable criterion for quantifying exploitable structure. We demonstrate the framework using computational turbulence data. Applied to line cuts of velocity gradients from a

1024^3

simulation containing more than one billion grid points, the algorithm consistently isolates the extreme tail and reduces the median search space to

O(\log N)

. The clustered structure characteristic of turbulence further accelerates the search. These results establish a direct connection between physical structure and quantum advantage in extreme-value search. For accessibility, the main text emphasizes the central ideas and results, while the theoretical derivations are provided in the Appendices.