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Physica A Statistical Mechanics and its Applications

Enhancing qubit information with quantum thermal noise

Nicolas Gillard, Étienne Belin, François Chapeau‐Blondeau

Published May 17, 2018• 14 citations
Publisher
DOI
10.1016/j.physa.2018.05.099

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From a qubit in a noisy state affected by an uncontrolled decohering environment represented by a thermal bath at temperature T , estimation of the norm of its Bloch vector is considered, equivalent to estimation of its purity or of its linear entropy. The performance in estimation is assessed by the quantum Fisher information. When the qubit can be prepared with an optimal orientation precisely matched to the thermal noise, the estimation performance always degrades with an increasing temperature of the bath. On the contrary, for a non‐optimal orientation of the qubit, the possibility of an enhancement of the estimation performance with an increasing temperature of the bath is demonstrated. Such behaviour shows that increased decoherence is not necessarily associated with poorer informational performance, and can be compared with stochastic resonance or useful noise effects previously reported in classical (non‐quantum) estimation.
The task fundamental to quantum communication and coding is considered which consists of detecting between two possible states of a noisy qubit, with a performance assessed by the overall probability of detection error. The detection process operates in the presence of decoherence represented by a quantum thermal noise at an arbitrary temperature. With uneven prior probabilities of the two states, as the noise temperature is increased, non‐monotonic evolutions are reported for the performance, which does not uniformly degrade. Regimes are found where higher noise temperatures are more favourable to detection, with relation to stochastic resonance effects where noise reveals beneficial to information processing.
Quantum noise or decoherence is a major factor impacting the performance of quantum technologies. On the qubit, an important quantum noise, often relevant in practice, is the thermal noise or generalized amplitude damping noise, describing the interaction with a thermal bath at an arbitrary temperature. A qubit thermal noise however cannot be modeled nor directly simulated with a few elementary Pauli operators, but instead requires specific operators. Our main goal here is to construct a circuit model for simulating the thermal noise from standard elementary qubit operators. Starting from a common quantum-operation model based on Kraus operators and an associated qubit-environment model, we derive a proper Stinespring dilated representation for the thermal noise. This dilated unitary model is then decomposed in terms of simple elementary qubit operators, and converted into a circuit based on elementary quantum gates. We arrive at our targeted simulator circuit for the thermal noise, coming with built-in easy control on the noise parameters. The noise simulator is then physically implemented and tested on an IBM-Q quantum processor. The simulator represents a useful addition to existing libraries of quantum circuits for quantum processors, and it offers a new tool for investigating quantum signal and information processing having to cope with thermal noise.