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arXiv:quant-ph/0608212 · Physical Review A

Decoherence in a scalable adiabatic quantum computer

Sahel Ashhab, J. R. Johansson, Franco Nori

Published Nov 21, 2006• 87 citations
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Abstract

We consider the effects of decoherence on Landau-Zener crossings encountered in a large-scale adiabatic-quantum-computing setup. We analyze the dependence of the success probability---i.e., the probability for the system to end up in its new ground state---on the noise amplitude and correlation time. We determine the optimal sweep rate that is required to maximize the success probability. We then discuss the scaling of decoherence effects with increasing system size. We find that those effects can be important for large systems, even if they are small for each of the small building blocks.

DOI
10.1103/physreva.74.052330

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quant-pharXiv:2605.25008•May 26, 2026
We consider the effects of decoherence on Landau-Zener crossings encountered in a large-scale adiabatic-quantum-computing setup. We analyze the dependence of the success probability---i.e., the probability for the system to end up in its new ground state---on the noise amplitude and correlation time. We determine the optimal sweep rate that is required to maximize the success probability. We then discuss the scaling of decoherence effects with increasing system size. We find that those effects can be important for large systems, even if they are small for each of the small building blocks.
We have studied the decoherence properties of adiabatic quantum computation (AQC) in the presence of in general non-Markovian, e.g., low-frequency, noise. The developed description of the incoherent Landau-Zener transitions shows that the global AQC maintains its properties even for decoherence larger than the minimum gap at the anticrossing of the two lowest-energy levels. The more efficient local AQC, however, does not improve scaling of the computation time with the number of qubits nnn as in the decoherence-free case. The scaling improvement requires phase coherence throughout the computation, limiting the computation time and the problem size nnn.
We study the effect of an environment consisting of noninteracting two level systems on Landau-Zener transitions with an interest on the performance of an adiabatic quantum computer. We show that if the environment is initially at zero temperature, it does not affect the transition probability. An excited environment, however, will always increase the probability of making a transition out of the ground state. For the case of equal intermediate gaps, we find an analytical upper bound for the transition probability in the limit of large number of environmental spins. We show that such an environment will only suppress the probability of success for adiabatic quantum computation by at most a factor close to 1/2.
We study the effect of an environment consisting of noninteracting two level systems on Landau-Zener transitions with an interest on the performance of an adiabatic quantum computer. We show that if the environment is initially at zero temperature, it does not affect the transition probability. An excited environment, however, will always increase the probability of making a transition out of the ground state. For the case of equal intermediate gaps, we find an analytical upper bound for the transition probability in the limit of large number of environmental spins. We show that such an environment will only suppress the probability of success for adiabatic quantum computation by at most a factor close to 1/2.
We analyze the performance of adiabatic quantum computation (AQC) subject to decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization of the adiabatic approximation. In contrast to closed systems, we show that a system may initially be in an adiabatic regime, but then undergo a transition to a regime where adiabaticity breaks down. As a consequence, the success of AQC depends sensitively on the competition between various pertinent rates, giving rise to optimality criteria.
Decoherence causes the decay of the quantum information that is stored in highly correlated states during quantum computation. It is thus a limiting factor for all implementations of a quantum computer. Because a scalable quantum computer with hundreds or thousands of qubits is not available yet, experimental data about decoherence rates was restricted to small quantum registers. With solid state nuclear magnetic resonance we create highly correlated multiqubit states that serve as a model quantum register and measure their decay. By measuring the decay as a function of the system size, we determined the scaling of the decoherence rate with the number of qubits. Using the same system, we also used decoupling techniques to reduce the coupling between system and environment and thereby the decoherence rate by more than an order of magnitude, independent of the system size. For the free decay as well as for the decoupled case, we found a relatively weak scaling with system size, which could be fitted to a power law $\ensuremath{\propto}{\overline{K}}^{p}$ with an exponent $p\ensuremath{\approx}1∕2$. This raises the prospect for large-scale quantum computation.
In this work, we investigate the effects of heat-bath-induced colored noise on nonreciprocal Landau-Zener tunneling. We perform numerical calculations of the instantaneous energy levels and find that noise induces stochastic fluctuations in these levels. Beyond such fluctuations, sufficiently large nonreciprocity parameters enable noise to further trigger the emergence of multiple exceptional points. The corresponding tunneling probability is significantly modified by colored noise. On the one hand, colored noise generally enhances the tunneling probability under nonadiabatic sweeping. On the other hand, it can break the reciprocity of Landau-Zener tunneling in the adiabatic limit. In particular, for large nonreciprocity parameters, the adiabatic tunneling probability is insensitive to noise and determined by exceptional points. We plot the phase diagram of tunneling probability as a function of the sweep rate and nonreciprocity parameter, for different amplitudes and correlation times of colored noise. Analytically, we derive the exact expression for the tunneling probability in the absence of noise and an approximate solution in the white-noise limit, employing Weber functions and the Wiener-Hermite expansion method. Some implications of our theory are discussed.