Polynomial T-depth quantum solvability of noisy binary linear problem: from quantum-sample preparation to main computation

Song, Wooyeong; Lim, Youngrong; Jeong, Kabgyun; Lee, Jinhyoung; Park, Jung Jun; Kim, M. S.; Bang, Jeongho

doi:10.1088/1367-2630/ac94ef

Cited by 3 publications

(2 citation statements)

References 36 publications

(66 reference statements)

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“…the initial-state reflection in our case, other than the data-access. We have used a similar approach in the previous work [33]. Nevertheless, if we consider a local-purpose system for data search only, one may think of an algorithm that uses only the one-hot encoding, for example, by developing a useful method to prepare or process the W-type entangled state.…”

Section: Discussionmentioning

confidence: 99%

T-depth-optimized quantum search with quantum data-access machine

Jun Park,

Baek,

Kim

et al. 2023

Quantum Sci. Technol.

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Quantum search algorithms offer a remarkable advantage of quadratic reduction in query complexity using quantum superposition principle. However, how an actual architecture may access and handle the database in a quantum superposed state has been largely unexplored so far; the quantum state of data was simply assumed to be prepared and accessed by a black-box operation---so-called quantum oracle, even though this process, if not appropriately designed, may adversely diminish the quantum query advantage. Here, we introduce an efficient quantum data-access process, dubbed as quantum data-access machine (QDAM), and present a general architecture for quantum search algorithm. We analyze the runtime of our algorithm in view of the fault-tolerant quantum computation (FTQC) consisting of logical qubits within an effective quantum error correction code. Specifically, we introduce a measure involving two computational complexities, i.e. quantum query and T-depth complexities, which can be critical to assess performance since the logical non-Clifford gates, such as the T (i.e., π/8 rotation) gate, are known to be costliest to implement in FTQC. Our analysis shows that for N searching data, a QDAM model exhibiting a logarithmic, i.e., O(logN), growth of the T-depth complexity can be constructed. Further analysis reveals that our QDAM-embedded quantum search requires O(√N × logN) runtime cost. Our study thus demonstrates that the quantum data search algorithm can truly speed up over classical approaches with the logarithmic T-depth QDAM as a key component.

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Section: Discussionmentioning

confidence: 99%

T-depth-optimized quantum search with quantum data-access machine

Jun Park,

Baek,

Kim

et al. 2023

Quantum Sci. Technol.

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“…Consequently, this work improves the NLP-solving algorithm in the linearithmic order than the GKZ algorithm [4] including Ref. [5,43,44].…”

Section: < L a T E X I T S H A 1 _ B A S E 6 4 = " U M Y M J L H Z 9 ...mentioning

confidence: 99%

Sample-size-reduction of quantum states for the noisy linear problem

Jeong

2023

Preprint

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Quantum supremacy poses that a realistic quantum computer can perform a calculation that classical computers cannot in any reasonable amount of time. It has become a topic of significant research interest since the birth of the field, and it is intrinsically based on the efficient construction of quantum algorithms. It has been shown that there exists an expeditious way to solve the noisy linear (or learning with errors) problems in quantum machine learning theory via a well-posed quantum sampling over pure quantum states. In this paper, we propose an advanced method to reduce the sample size in the noisy linear structure, through a technique of randomizing quantum states, namely, ε-random technique. Particularly, we show that it is possible to reduce a quantum sample size in a quantum random access memory (QRAM) to the linearithmic order, in terms of the dimensions of the input-data. Thus, we achieve a shorter run-time for the noisy linear problem.

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Sample-size-reduction of quantum states for the noisy linear problem

Jeong

2023

Annals of Physics

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Polynomial T-depth quantum solvability of noisy binary linear problem: from quantum-sample preparation to main computation

Cited by 3 publications

References 36 publications

T-depth-optimized quantum search with quantum data-access machine

T-depth-optimized quantum search with quantum data-access machine

Sample-size-reduction of quantum states for the noisy linear problem

Sample-size-reduction of quantum states for the noisy linear problem

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