Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Physics Letters

Experimental Realization of Arbitrary Accuracy Iterative Phase Estimation Algorithms on Ensemble Quantum Computers

Liu Xiu-Mei, Luo Jun, Xianping Sun

Published Dec 1, 2007• 17 citations
Publisher

Abstract

We report the first experimental demonstration of a nuclear magnetic resonance (NMR) realization of iterative phase estimation algorithms. Using feedback and iterations, we experimentally obtain the phase with 6 bits of precision on a two-qubit NMR quantum computer. Furthermore, we experimentally demonstrate the effect of gate noise on the iterative phase estimation algorithm. Our experimental results show that errors of measurements of the phase depend strongly on the precision of coupling gates. This experiment can be used as a benchmark for multi-qubit realizations of quantum information processing and precision measurements.

DOI
10.1088/0256-307x/24/12/007

Related papers

NMR experimental realization of seven-qubit D-J algorithm and controlled phase-shift gates with improved precision

Daxiu Wei, J. L. Luo, Xianping Sun +4 more

In this study, we report the experimental realization of seven-qubit Deutsch-Jozsa (D-J) algorithm and controlled phase-shift gates with improved precision using liquid state nuclear magnetic resonance (NMR). The experimental results have shown that transformationsU f in the seven-qubit D-J algorithm have been implemented with different pulse sequences, and whetherf is constant or balanced is determined by using only a single function call (U f ). Furthermore, we propose an experimental method to measure and correct the error in the controlled phase-shift gate that is simple and feasible in experiments, and can have precise phase shifts. These may offer the possibility of surmounting the difficulties of low signal-to-noise ratio (SNR) in multi-qubit NMR quantum computers, more complicated experimental techniques, and the increase of gate errors due to using a large number of imperfect selective pulses. These are also applied to more complicated quantum algorithms with more qubits, such as quantum Fourier transformation and Shor’s algorithm.

Chinese Science Bulletin•Jan 1, 2003•6 citations

Experimental Realization of Arbitrary Accuracy Iterative Phase Estimation Algorithms on Ensemble Quantum Computers

刘秀梅, 罗军, 孙献平

我们报导原子磁性的回声(NMR ) 的第一试验性的示范反复的阶段评价算法的实现。用反馈和重复,我们试验性地在一台 two-qubit NMR 量计算机上与 6 位精确获得阶段。而且,我们试验性地在反复的阶段评价算法上表明门噪音的效果。我们的试验性的结果证明阶段的大小的错误强烈取决于联合门的精确。这个实验能为量信息处理和精确大小的 multi-qubit 认识被用作一个基准。

Chinese Physics Letters•Jan 1, 2007•0 citations

Arbitrary accuracy iterative quantum phase estimation algorithm using a single ancillary qubit: A two-qubit benchmark

Miroslav Dobšíček, Göran Johansson, Vitaly S. Shumeiko +1 more

We discuss the implementation of an iterative quantum phase estimation algorithm with a single ancillary qubit. We suggest using this algorithm as a benchmark for multiqubit implementations. Furthermore, we describe in detail the smallest possible realization, using only two qubits, and exemplify with a superconducting circuit. We discuss the robustness of the algorithm in the presence of gate errors, and show that seven bits of precision is obtainable, even with very limited gate accuracies.

arXiv:quant-ph/0610214•Physical Review A•Sep 19, 2007•208 citations

Iterative quantum phase estimation on an IBM quantum processor

N.A. Zhuravlev, Ilya I. Beterov

Abstract An elementary algorithm of quantum phase estimation based on the modified Kitaev algorithm is implemented on two qubits of an IBM quantum processor. This algorithm includes adiabatic preparation of the initial state, controlled phase shift with allowance for the results of previous measurements of qubit states, and single measurement of the qubit quantum state in order to obtain each significant bit of the measured phase. Classical error correction is applied to determine the correct sequence of bits, which makes it possible to eliminate the influence of limited accuracy of two-qubit gates.

Quantum Electronics•May 19, 2021•1 citation

Randomized benchmarking of single- and multi-qubit control in liquid-state NMR quantum information processing

Colm A. Ryan, M Laforest, R Laflamme

Being able to quantify the level of coherent control in a proposed device implementing a quantum information processor (QIP) is an important task for both comparing different devices and assessing a device's prospects with regards to achieving fault-tolerant quantum control. We implement in a liquid-state nuclear magnetic resonance QIP the randomized benchmarking protocol presented by Knill et al (2008 Phys. Rev. A 77 012307). We report an error per randomized π/2 pulse of 1.3±0.1 × 10 −4 with a single-qubit QIP and show an experimentally relevant error model where the randomized benchmarking gives a signature fidelity decay which is not possible to interpret as a single error per gate. We explore and experimentally investigate multi-qubit extensions of this protocol and report an average error rate for one- and two-qubit gates of 4.7±0.3 × 10 −3 for a three-qubit QIP. We estimate that these error rates are still not decoherence limited and thus can be improved with modifications to the control hardware and software.

arXiv:0808.3973•New Journal of Physics•Jan 23, 2009•120 citations

Demonstration of Sufficient Control for Two Rounds of Quantum Error Correction in a Solid State Ensemble Quantum Information Processor

Osama Moussa, Jonathan Baugh, Colm A. Ryan +1 more

We report the implementation of a 3-qubit quantum error-correction code on a quantum information processor realized by the magnetic resonance of carbon nuclei in a single crystal of malonic acid. The code corrects for phase errors induced on the qubits due to imperfect decoupling of the magnetic environment represented by nearby spins, as well as unwanted evolution under the internal Hamiltonian. We also experimentally demonstrate sufficiently high-fidelity control to implement two rounds of quantum error correction. This is a demonstration of state-of-the-art control in solid state nuclear magnetic resonance, a leading test bed for the implementation of quantum algorithms.

arXiv:1108.4842•Physical Review Letters•Oct 10, 2011•50 citations
We report the first experimental demonstration of a nuclear magnetic resonance (NMR) realization of iterative phase estimation algorithms. Using feedback and iterations, we experimentally obtain the phase with 6 bits of precision on a two-qubit NMR quantum computer. Furthermore, we experimentally demonstrate the effect of gate noise on the iterative phase estimation algorithm. Our experimental results show that errors of measurements of the phase depend strongly on the precision of coupling gates. This experiment can be used as a benchmark for multi-qubit realizations of quantum information processing and precision measurements.
In this study, we report the experimental realization of seven-qubit Deutsch-Jozsa (D-J) algorithm and controlled phase-shift gates with improved precision using liquid state nuclear magnetic resonance (NMR). The experimental results have shown that transformationsU f in the seven-qubit D-J algorithm have been implemented with different pulse sequences, and whetherf is constant or balanced is determined by using only a single function call (U f ). Furthermore, we propose an experimental method to measure and correct the error in the controlled phase-shift gate that is simple and feasible in experiments, and can have precise phase shifts. These may offer the possibility of surmounting the difficulties of low signal-to-noise ratio (SNR) in multi-qubit NMR quantum computers, more complicated experimental techniques, and the increase of gate errors due to using a large number of imperfect selective pulses. These are also applied to more complicated quantum algorithms with more qubits, such as quantum Fourier transformation and Shor’s algorithm.
Abstract An elementary algorithm of quantum phase estimation based on the modified Kitaev algorithm is implemented on two qubits of an IBM quantum processor. This algorithm includes adiabatic preparation of the initial state, controlled phase shift with allowance for the results of previous measurements of qubit states, and single measurement of the qubit quantum state in order to obtain each significant bit of the measured phase. Classical error correction is applied to determine the correct sequence of bits, which makes it possible to eliminate the influence of limited accuracy of two-qubit gates.
Being able to quantify the level of coherent control in a proposed device implementing a quantum information processor (QIP) is an important task for both comparing different devices and assessing a device's prospects with regards to achieving fault-tolerant quantum control. We implement in a liquid-state nuclear magnetic resonance QIP the randomized benchmarking protocol presented by Knill et al (2008 Phys. Rev. A 77 012307). We report an error per randomized π/2 pulse of 1.3±0.1 × 10 −4 with a single-qubit QIP and show an experimentally relevant error model where the randomized benchmarking gives a signature fidelity decay which is not possible to interpret as a single error per gate. We explore and experimentally investigate multi-qubit extensions of this protocol and report an average error rate for one- and two-qubit gates of 4.7±0.3 × 10 −3 for a three-qubit QIP. We estimate that these error rates are still not decoherence limited and thus can be improved with modifications to the control hardware and software.
We report the implementation of a 3-qubit quantum error-correction code on a quantum information processor realized by the magnetic resonance of carbon nuclei in a single crystal of malonic acid. The code corrects for phase errors induced on the qubits due to imperfect decoupling of the magnetic environment represented by nearby spins, as well as unwanted evolution under the internal Hamiltonian. We also experimentally demonstrate sufficiently high-fidelity control to implement two rounds of quantum error correction. This is a demonstration of state-of-the-art control in solid state nuclear magnetic resonance, a leading test bed for the implementation of quantum algorithms.