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Trapped Ion Chain as a Neural Network: Fault-Tolerant Quantum Computation

M. Ll. Pons, V. Ahufinger, Christof Wunderlich, Anna Sanpera, Sibylle Braungardt, Aditi Sen De, Ujjwal Sen, Maciej Lewenstein

Published Jul 3, 2006• 2 citations
OpenAlex

Abstract

We demonstrate the possibility of realizing a neural network in a chain of trapped ions with induced long range interactions. Such models permit to store information distributed over the whole system. The storage capacity of such network, which depends on the phonon spectrum of the system, can be controlled by changing the external trapping potential. We analyze the implementation of fault-tolerant universal quantum information processing in such systems.

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The use of trapped atomic ions in the field of quantum information processing is briefly reviewed. We summarize the basic mechanisms required for logic gates and the use of the gates in demonstrating simple algorithms. We discuss the potential of trapped ions to reach fault-tolerant error levels in a large-scale system, and highlight some of the problems that will be faced in achieving this goal. Possible near-term applications in applied and basic science, such as in metrology and quantum simulation, are briefly discussed.

Laser Physics Letters•Jan 25, 2011•98 citations
We demonstrate the possibility of realizing a neural network in a chain of trapped ions with induced long range interactions. Such models permit to store information distributed over the whole system. The storage capacity of such network, which depends on the phonon spectrum of the system, can be controlled by changing the external trapping potential. We analyze the implementation of fault-tolerant universal quantum information processing in such systems.
We consider experimentally feasible chains of trapped ions with pseudospin 1∕21∕21∕2 and find models that can potentially be used to implement error-resistant quantum computation. Similar in spirit to classical neural networks, the error resistance of the system is achieved by encoding the qubits distributed over the whole system. We therefore call our system a quantum neural network and present a quantum neural network model of quantum computation. Qubits are encoded in a few quasi degenerated low-energy levels of the whole system, separated by a large gap from the excited states and large energy barriers between themselves. We investigate protocols for implementing a universal set of quantum logic gates in the system by adiabatic passage of a few low-lying energy levels of the whole system. Naturally appearing and potentially dangerous distributed noise in the system leaves the fidelity of the computation virtually unchanged, if it is not too strong. The computation is also naturally resilient to local perturbations of the spins.
Quantum computers promise to solve models of important physical processes, optimize complex cost functions, and challenge cryptography in ways that are intractable using current computers. In order to achieve these promises, quantum computers must both increase in size and decrease error rates. To increase the system size, we report on the design, construction, and operation of an integrated trapped ion quantum computer consisting of a chain of 15 171Yb+ ions with all-to-all connectivity and high-fidelity gate operations. In the process, we identify a physical mechanism that adversely affects gate fidelity in long ion chains. Residual heating of the ions from noisy electric fields creates decoherence due to the weak confinement of the ions transverse to a focused addressing laser. We demonstrate this effect in chains of up to 25 ions and present a model that accurately describes the observed decoherence. To mitigate this noise source, we first propose a new sympathetic cooling scheme to periodically re-cool the ions throughout a quantum circuit, and then demonstrate its capability in a proof-of-concept experiment. One path to suppress error rates in quantum computers is through quantum error correction schemes that combine multiple physical qubits into logical qubits that robustly store information within an entangled state. These extra degrees of freedom enable the detection and correction of errors. Fault-tolerant circuits contain the spread of errors while operating the logical qubit and are essential for realizing error suppression in practice. We demonstrate fault-tolerant preparation, measurement, rotation, and stabilizer measurement of a distance-3 Bacon-Shor logical qubit in our quantum computer. The result is an encoded logical qubit with error rates lower than the error of the entangling operations required to operate it.
A major challenge for quantum computation in ion trap systems is scalable integration of error correction and fault tolerance. We analyze a distributed architecture with rapid high-fidelity local control within nodes and entangled links between nodes alleviating long-distance transport. We demonstrate fault-tolerant operator measurements which are used for error correction and nonlocal gates. This scheme is readily applied to linear ion traps which cannot be scaled up beyond a few ions per individual trap but which have access to a probabilistic entanglement mechanism. A proof-of-concept system is presented which is within the reach of current experiment.
We study quantum information processing in complex disordered many body systems that can be implemented by using lattices of ultracold atomic gases and trapped ions. We demonstrate, first in the short range case, the generation of entanglement and the local realization of quantum gates in a disordered magnetic model describing a quantum spin glass. We show that in this case it is possible to achieve fidelities of quantum gates higher than in the classical case. Complex systems with long range interactions, such as ions chains or dipolar atomic gases, can be used to model neural network Hamiltonians. For such systems, where both long range interactions and disorder appear, it is possible to generate long range bipartite entanglement. We provide an efficient analytical method to calculate the time evolution of a given initial state, which in turn allows us to calculate its quantum correlations.
The use of trapped atomic ions in the field of quantum information processing is briefly reviewed. We summarize the basic mechanisms required for logic gates and the use of the gates in demonstrating simple algorithms. We discuss the potential of trapped ions to reach fault-tolerant error levels in a large-scale system, and highlight some of the problems that will be faced in achieving this goal. Possible near-term applications in applied and basic science, such as in metrology and quantum simulation, are briefly discussed.