Quantum Simulations with Superconducting Networks
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REVIEW
Quantum Simulations with Superconducting Networks Rosario Fazio1,2 Received: 13 August 2020 / Accepted: 20 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The importance of a scientific discovery sometimes is also reflected in the impact it has in the most diverse situations. The discovery of the Josephson effect has been of fundamental importance in so many different areas, from fundamental to applied science and technology. More recently, it is also playing a pivotal role also in the emerging field of quantum technologies. In this brief note I would like to highlight the importance of the Josephson effect in the realisation of quantum simulators. Keywords Josephson effect · Superconducting networks · Quantum simulators Collective phenomena are ubiquitous in our world, governing the synchronous flashing of fireflies along the rivers of Malaysia or the evolution of financial markets. In physics they are present at all energy scales, in cosmology and high-energy physics as well as in condensed matter. Critical phenomena, probably the most prominent example of collective dynamics, occur in the most diverse situations, in simple liquids and in magnets as well as in the dynamics of the early universe. The beauty of collective phenomena is borne in their universal character, the microscopic details cease to be important and all the physical properties are governed by the behaviour of certain macroscopic observables. Collective behaviour emerges in complex (many-body) systems as a result of the interaction between its constituents. The exchange interaction between local magnetic moments is responsible for the onset of magnetism, interaction between fermionic or bosonic particles (electrons, atoms, excitons,...) leads to superconductivity and superfluidity. Strong interaction is believed to be at the root of still not completely understood phenomena as high temperature superconductivity or in the fractional quantum Hall effect. The importance in understanding the behaviour of complex many-body systems is accompanied by the enormous difficulty in computing their properties. Even though, over the years, powerful numerical and analytical Rosario Fazio
[email protected] 1
The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
2
Dipartimento di Fisica, Universit`a di Napoli Federico II, Monte S. Angelo, 80126 Naples, Italy
techniques have been developed, many important problems are still waiting for a solution. The reason of the difficulties in reaching a coherent and exhaustive description of strongly correlated quantum phenomena is rooted in the fact that the dimension of the Hilbert space of a many-body quantum system is exponentially large in the number of particles. Therefore, the simulation of a quantum system on a classical computer requires exponentially large resources. By contrast, Feynman in 1982 [1] proposed that a quantum system could be efficiently simulated by using a number of qubits that scales polynomially w
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