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Chinese Physics B

Preservation of quantum states via a super-Zeno effect on ensemble quantum computers

Ren Ting-Ting, Luo Jun, Xianping Sun, Mingsheng Zhan

Published Nov 1, 2009• 5 citations
Publisher

Abstract

Following a recent proposal by Dhar et al (2006 Phys. Rev. Lett. 96 100405), we demonstrate experimentally the preservation of quantum states in a two-qubit system based on a super-Zeno effect using liquid-state nuclear magnetic resonance techniques. Using inverting radiofrequency pulses and delicately selecting time intervals between two pulses, we suppress the effect of decoherence of quantum states. We observe that preservation of the quantum state |11⟩ with the super-Zeno effect is three times more efficient than the ordinary one with the standard Zeno effect.

DOI
10.1088/1674-1056/18/11/017

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Following a recent proposal by Dhar et al (2006 Phys. Rev. Lett. 96 100405), we demonstrate experimentally the preservation of quantum states in a two-qubit system based on a super-Zeno effect using liquid-state nuclear magnetic resonance techniques. Using inverting radiofrequency pulses and delicately selecting time intervals between two pulses, we suppress the effect of decoherence of quantum states. We observe that preservation of the quantum state |11⟩ with the super-Zeno effect is three times more efficient than the ordinary one with the standard Zeno effect.
We construct an algorithm for suppressing the transitions of a quantum mechanical system, initially prepared in a subspace P of the full Hilbert space of the system, to outside this subspace by subjecting it to a sequence of unequally spaced short-duration pulses. Each pulse multiplies the amplitude of the vectors in the subspace by -1. The number of pulses required by the algorithm to limit the leakage probability to epsilon in time increases as T exp[square root log(T(2)/epsilon)], compared to T(2)epsilon(-1) in the standard quantum Zeno effect.
We experimentally demonstrate the freezing of evolution of quantum states in one- and two-dimensional subspaces of two qubits, on an NMR quantum information processor. State evolution was frozen and leakage of the state from its subspace to an orthogonal subspace was successfully prevented using super-Zeno sequences [Phys. Rev. Lett. 96, 100405 (2006)], comprising a set of radio frequency (rf) pulses punctuated by pre-selected time intervals. We demonstrate the efficacy of the scheme by preserving different types of states, including separable and maximally entangled states in one- and two-dimensional subspaces of two qubits. The change in the experimental density matrices was tracked by carrying out full state tomography at several time points. We use the fidelity measure for the one-dimensional case and the leakage (fraction) into the orthogonal subspace for the two-dimensional case, as qualitative indicators to estimate the resemblance of the density matrix at a later time to the initially prepared density matrix. For the case of entangled states, we additionally compute an entanglement parameter to indicate the presence of entanglement in the state at different times. We experimentally demonstrate that the super-Zeno scheme is able to successfully confine state evolution to the one- or two-dimensional subspace being protected.
We construct an algorithm for suppressing the transitions of a quantum mechanical system, initially prepared in a subspace P of the full Hilbert space of the system, to outside this subspace by subjecting it to a sequence of unequally spaced short-duration pulses. Each pulse multiplies the amplitude of the vectors in the subspace by -1. The number of pulses required by the algorithm to limit the leakage probability to εεε in time TTT increases as Texp⁡[log⁡(T2/ε)]T \exp[ \sqrt{\log(T^2/ε)}]Texp[log(T2/ε)​], compared to T2ε−1T^2 ε^{-1}T2ε−1 in the standard quantum Zeno effect.
Projective measurements are an essential element of quantum mechanics. In most cases, they cause an irreversible change of the quantum system on which they act. However, measurements can also be used to stabilize quantum states from decay processes, which is known as the quantum Zeno effect (QZE). Here, we demonstrate this effect for the case of a superposition state of a nuclear spin qubit, using an ancilla to perform the measurement. As a result, the quantum state of the qubit is protected against dephasing without relying on an ensemble nature of NMR experiments. We also propose a scheme to protect an arbitrary state by using QZE.
We experimentally demonstrate a dynamic fashion of quantum Zeno effect in nuclear magnetic resonance systems. The frequent measurements are implemented through quantum entanglement between the target qubit(s) and the measuring qubit, which dynamically results from the unitary evolution of duration ${\ensuremath{\tau}}_{m}$ due to dispersive coupling. Experimental results testify to the presence of ``the critical measurement time effect,'' that is, the quantum Zeno effect does not occur when ${\ensuremath{\tau}}_{m}$ takes some critical values, even if the measurements are frequent enough. Moreover, we provide an experimental demonstration of an entanglement preservation mechanism based on such a dynamic quantum Zeno effect.