Preparation of pseudo-pure states by line-selective pulses in nuclear magnetic resonance

Peng, Xinhua; Zhu, Xiwen; Fang, Xiaowen; Feng, Mang; Gao, Keli; Yang, Xiaodong; Liu, Maili

doi:10.1016/s0009-2614(01)00421-3

Cited by 63 publications

(21 citation statements)

References 19 publications

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“…We control the fluctuation of the temperature to be within 0.1K such that the effect of the chemical shift variations is suppressed. This system is first prepared into a pseudo-pure state (PPS) ρ 0 = 1−ε 16 I + ε |0000 0000| with I representing the 16 × 16 unity operator and ε ≈ 10 −5 the polarization, using the line-selective-transition method [23,24]. It needs two gradient ascent pulse engineering (GRAPE) pulses [30] and two gradient field pulses.…”

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confidence: 99%

Experimental realization of quantum algorithm for solving linear systems of equations

et al. 2014

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Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an N × N matrix A and a vector b, find the vector x that satisfies A x = b. It has been shown that using the algorithm one could obtain the solution encoded in a quantum state |x using O(log N ) quantum operations, while classical algorithms require at least O(N ) steps. If one is not interested in the solution x itself but certain statistical feature of the solution x|M |x (M is some quantum mechanical operator), the quantum algorithm will be able to achieve exponential speedup over the best classical algorithm as N grows. Here we report a proof-of-concept experimental demonstration of the quantum algorithm using a 4-qubit nuclear magnetic resonance (NMR) quantum information processor. For all the three sets of experiments with different choices of b, we obtain the solutions with over 96% fidelity. This experiment is a first implementation of the algorithm. Because solving linear systems is a common problem in nearly all fields of science and engineering, we will also discuss the implication of our results on the potential of using quantum computers for solving practical linear systems.

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confidence: 99%

Experimental realization of quantum algorithm for solving linear systems of equations

et al. 2014

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“…where J ij is the scalar coupling strength between the ith and jth nucleus. equilibrium state, using the line-selective method [47]. Here, ε ≈ 10 −5 denotes the polarization, and I denotes the 8×8 identity matrix.…”

Section: Experimental Realizationsmentioning

confidence: 99%

Single-Loop and Composite-Loop Realization of Nonadiabatic Holonomic Quantum Gates in a Decoherence-Free Subspace

et al. 2019

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High-fidelity quantum gates are essential for large scale quantum computation, which can naturally be realized in a noise resilient way. It is well-known that geometric manipulation and decoherence-free subspace encoding are promising ways towards robust quantum computation. Here, by combining the advantages of both strategies, we propose and experimentally realize universal holonomic quantum gates in both a single-loop and composite scheme, based on nonadiabatic and non-Abelian geometric phases, in a decoherence-free subspace with nuclear magnetic resonance. Our experiment only employs two-body resonant spin-spin interactions and thus is experimental friendly. In particularly, we also experimentally verify that the composite scheme is more robust against the pulse errors over the single-loop scheme. Therefore, our experiment provides a promising way towards faithful and robust geometric quantum manipulation.

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“…Starting from the equilibrium state, we first initialized the system into the pseudopure state (PPS) with the line-selective method [43,44]:…”

Section: (I) Initial State Preparationmentioning

confidence: 99%

Floquet-engineered quantum state transfer in spin chains

et al. 2019

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Preparation of pseudo-pure states by line-selective pulses in nuclear magnetic resonance

Cited by 63 publications

References 19 publications

Experimental realization of quantum algorithm for solving linear systems of equations

Experimental realization of quantum algorithm for solving linear systems of equations

Single-Loop and Composite-Loop Realization of Nonadiabatic Holonomic Quantum Gates in a Decoherence-Free Subspace

Floquet-engineered quantum state transfer in spin chains

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