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Simulation and analysis of quantum phase estimation algorithm in the presence of incoherent quantum noise channels

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Muhammad Faizan, Muhammad Faryad

Quantum Physics · Submitted 28 Jul 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The simulation results indicate that the standard deviation of the eigenvalue of the unitary operator has strong exponential dependence upon the error probability of individual qubits.

how it is stated · hedged possibility 0.80 read the record →

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arXiv ID2307.15675 (version 3)
Pith ID5BPVLIBR, Pith's permanent record of this paper and its review
CitationMuhammad Faizan, Muhammad Faryad. "Simulation and analysis of quantum phase estimation algorithm in the presence of incoherent quantum noise channels." arXiv:2307.15675 (2023). https://pith.science/paper/5BPVLIBR
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,508 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.23 · human participants 0.01 · controlled comparison 0.09 · randomized assignment 0.01 · states quantitative result 0.83 · compares with prior results 0.08 · mentions code or data availability 0.02.

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arXiv listing abstract v3. Results and the main claim are underlined; .

The quantum phase estimation (QPE) is one of the fundamental algorithms based on the quantum Fourier transform. It has applications in order-finding, factoring, and finding the eigenvalues of unitary operators. The major challenge in running QPE and other quantum algorithms is the noise in quantum computers. In the present work, we study the impact of incoherent noise on QPE, modeled as trace-preserving and completely positive quantum channels. Different noise models such as depolarizing, phase flip, bit flip, and bit-phase flip are taken to understand the performance of the QPE in the presence of noise. The simulation results indicate that the standard deviation of the eigenvalue of the unitary operator has strong exponential dependence upon the error probability of individual qubits. However, the standard deviation increases only linearly with the number of qubits for fixed error probability when that error probability is small.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The quantum phase estimation (QPE) is one of the fundamental algorithms based on the quantum Fourier transform. background 1.00 0.03 0.02 asserted 1.00
s1 It has applications in order-finding, factoring, and finding the eigenvalues of unitary operators. background 1.00 0.04 0.02 asserted 1.00
s2 The major challenge in running QPE and other quantum algorithms is the noise in quantum computers. background 0.98 0.04 0.02 asserted 1.00
s3 In the present work, we study the impact of incoherent noise on QPE, modeled as trace-preserving and completely positive quantum channels. contribution 0.82 0.88 0.04 asserted 0.95
s4 Different noise models such as depolarizing, phase flip, bit flip, and bit-phase flip are taken to understand the performance of the QPE in the presence of noise. method 0.97 0.80 0.03 asserted 0.90
s5 The simulation results indicate that the standard deviation of the eigenvalue of the unitary operator has strong exponential dependence upon the error probability of individual qubits. result 1.00 0.93 0.67 hedged possibility 0.80
s6 However, the standard deviation increases only linearly with the number of qubits for fixed error probability when that error probability is small. result 0.99 0.91 0.27 asserted 0.99

What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The quantum phase estimation (QPE) is one of the fundamental algorithms based on the quantum Fourier transform. It has applications in order-finding, factoring, and finding the eigenvalues of unitary operators. The major challenge in running QPE and other quantum algorithms is the noise in quantum computers. In the present work, we study the impact of incoherent noise on QPE, modeled as trace-preserving and completely positive quantum channels. Different noise models such as depolarizing, phase flip, bit flip, and bit-phase flip are taken to understand the performance of the QPE in the presence of noise. The simulation results indicate that the standard deviation of the eigenvalue of the unitary operator has strong exponential dependence upon the error probability of individual qubits. However, the standard deviation increases only linearly with the number of qubits for fixed error probability when that error probability is small.

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1 arXiv paper cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Uses its data or values 1 paper
  • This quantity is evaluated by rerunning the same experiment as in Fig. [ref] but with additional random noise: the ground state energies of the $H'_k$'s are now sampled according to normal distributions extracted from Table 1 and Fig. 2 of [ref] .

    Algorithmic error mitigation for quantum eigenvalues estimation · $p$-th order mitigation of Trotter errors · 0.99

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