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Physical Review A

Decoherence in large quantum registers under variable interaction with the environment

Marko Lovrić, Hans Georg Krojanski, Dieter Suter

Published Apr 3, 2007• 65 citations
Publisher

Abstract

Effective quantum-information processing requires coherent control of large numbers of qubits on a time scale that is short compared to the decoherence time of the system. It is therefore important to extrapolate and measure decoherence times for large quantum registers and to determine the effect of different couplings between system and environment on the decoherence rate. For this purpose, we have experimentally realized a system that allows one to generate model quantum registers with more than 100 qubits and measure the decay of the information in these states while adjusting the strength of the interaction between the quantum register and the environment. Our results indicate a power-law dependence of the decoherence rate on the number of qubits in the system, with an exponent of the order of 0.5. This behavior remains qualitatively unchanged when the coupling strength to the environment is reduced by about an order of magnitude.

DOI
10.1103/physreva.75.042305

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Effective quantum-information processing requires coherent control of large numbers of qubits on a time scale that is short compared to the decoherence time of the system. It is therefore important to extrapolate and measure decoherence times for large quantum registers and to determine the effect of different couplings between system and environment on the decoherence rate. For this purpose, we have experimentally realized a system that allows one to generate model quantum registers with more than 100 qubits and measure the decay of the information in these states while adjusting the strength of the interaction between the quantum register and the environment. Our results indicate a power-law dependence of the decoherence rate on the number of qubits in the system, with an exponent of the order of 0.5. This behavior remains qualitatively unchanged when the coupling strength to the environment is reduced by about an order of magnitude.
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.
Among the biggest obstacles for building larger (and thus more powerful) quantum-information processors is decoherence, the decay of quantum-information by the coupling between the quantum register and its environment. Procedures for reducing decoherence processes will be essential for successful operation of larger quantum processors. We study model quantum registers consisting of up to 4900 qubits and measure their decay as a function of the register size. We demonstrate that appropriate sequences of qubit rotations reduce the coupling between system and environment for all sizes of the quantum register, thus preserving the quantum-information 50 times longer than without decoupling.
The dynamical evolution of a quantum register of arbitrary length coupled to an environment of arbitrary coherence length is predicted within a relevant model of decoherence. The results are reported for quantum bits (qubits) coupling individually to different environments (``independent decoherence'') and qubits interacting collectively with the same reservoir (``collective decoherence''). In both cases, explicit decoherence functions are derived for any number of qubits. The decay of the coherences of the register is shown to strongly depend on the input states: We show that this sensitivity is a characteristic of both types of coupling (collective and independent) and not only of the collective coupling, as has been reported previously. A nontrivial behavior (``recoherence'') is found in the decay of the off-diagonal elements of the reduced density matrix in the specific situation of independent decoherence. Our results lead to the identification of decoherence-free states in the collective decoherence limit. These states belong to subspaces of the system's Hilbert space that do not get entangled with the environment, making them ideal elements for the engineering of ``noiseless'' quantum codes. We also discuss the relations between decoherence of the quantum register and computational complexity based on the dynamical results obtained for the register density matrix.
Among the most important parameters for the usefulness of quantum computers are the size of the quantum register and the decoherence time for the quantum information. The decoherence time is expected to get shorter with the number of correlated qubits, but experimental data are only available for small numbers of qubits. Solid-state nuclear magnetic resonance allows one to correlate large numbers of qubits (several hundred) and measure their decoherence rates. We use a modified magnetic dipole-dipole interaction to correlate the proton spins in a solid sample and observe the decay of the resulting highly correlated states. By systematically varying the number of correlated spins, we measure the increase of the decoherence rate with the size of the quantum register.
Minimizing the effect of decoherence on a quantum register must be a central part of any strategy to realize scalable quantum-information processing. Apart from the strength of the coupling to the environment, the decoherence rate is determined by the system level structure and by the spectral composition of the noise trace that the environment generates. Here, we discuss a relatively simple model that allows us to study these different effects quantitatively in detail. We evaluate the effect that the perturbation has on a nuclear magnetic resonance system while it performs a Grover search algorithm.
Reliable processing of quantum information for developing quantum technologies requires precise control of out-of-equilibrium many-body systems. This is a highly challenging task because the fragility of quantum states to external perturbations increases with the system size. Here, we report on a series of experimental quantum simulations that quantify the sensitivity of a controlled Hamiltonian evolution to perturbations that drive the system away from the targeted evolution. Based on out-of-time ordered correlations, we demonstrate that the decay rate of the process fidelity increases with the effective number KKK of correlated qubits as ${K}^{\ensuremath{\alpha}}$. As a function of the perturbation strength, we observe a decoherence scaling transition of the exponent $\ensuremath{\alpha}$ between two distinct dynamical regimes. In the limiting case below the critical perturbation strength, the exponent $\ensuremath{\alpha}$ drops sharply below 1, and there is no inherent limit to the number of qubits that can be controlled. This resilient quantum feature of the controlled dynamics of quantum information is promising for reliable control of large quantum systems.