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Title
Abstract
Figures
Decoherence and Limitations
Conclusions
References

Quantum Simulators

Profile image of Franco NoriFranco Nori

Abstract

Quantum simulators are controllable quantum systems that can be used to simulate other quantum systems. Being able to tackle problems that are intractable on classical computers, quantum simulators would provide a means of exploring new physical phenomena. We present an overview of how quantum simulators may become a reality in the near future as the required technologies are now within reach. Quantum simulators, relying on the coherent control of neutral atoms, ions, photons, or electrons, would allow studying problems in various fields including condensed-matter physics, high-energy physics, cosmology, atomic physics, and quantum chemistry.

Figures (3)
ways of simulating this quantum phase transition with arrays of cavities (22 or arrays of Josephson junctions (27). (B) Magnetic quantum phase transitior simulated in (6) using trapped calcium ions. The interactions of individua spins were realized by coupling the internal levels (representing the spin-1/z states) with a resonant RF field, whereas the spin-spin interactions wer simulated by using a state-dependent optical dipole force implemented by « walking wave. Fig. 1. Examples of analog quantum simulation of quantum phase transitions using ultracold neutral atoms (A) and trapped ions (B). (A) The schematics of the quantum phase transition from a superfluid to a Mott insulator phase realized in (12) by using rubidium atoms trapped in an optical lattice. The ratio between the tunneling energy and the on-site interaction energy was controlled by adjusting the lattice potential depth such that the quantum phase transition could take place. There are alternative
ways of simulating this quantum phase transition with arrays of cavities (22 or arrays of Josephson junctions (27). (B) Magnetic quantum phase transitior simulated in (6) using trapped calcium ions. The interactions of individua spins were realized by coupling the internal levels (representing the spin-1/z states) with a resonant RF field, whereas the spin-spin interactions wer simulated by using a state-dependent optical dipole force implemented by « walking wave. Fig. 1. Examples of analog quantum simulation of quantum phase transitions using ultracold neutral atoms (A) and trapped ions (B). (A) The schematics of the quantum phase transition from a superfluid to a Mott insulator phase realized in (12) by using rubidium atoms trapped in an optical lattice. The ratio between the tunneling energy and the on-site interaction energy was controlled by adjusting the lattice potential depth such that the quantum phase transition could take place. There are alternative
about 10 to 50 um and about the same for 2D Coulomb crystals. In arrays of quantum dots, the spacing between dots is about 0.1 um. In superconducting circuits, the distance between junctions can be less than a micrometer. In the case of electrons on helium the distance between neighboring sites would be about 1 um. These interqubit distances (from 0.1 to 10 um) should be compared with the far smaller average interatomic distances in solids, which are <1 nm. The systems shown above realize a 1- or 2D array of qubits, which can be manipulated in different manners. The larger distances between qubits make quantum simulators more controllable and easier to measure. Therefore, they can be thought of as toy models of the magnified lattice structure of a “solid,” with a magnification factor of three orders of magnitude. Fig. 2. One-dimensional or 2D arrays of qubits plus controls could be used to simulate various models in condensed-matter physics. Examples of physical systems that could implement such analog quantum simulators include the following: atoms in optical lattices (20) (A) or in 1D (B) or 2D (C) arrays of cavities (21, 22); ions in linear ion chains (D), 2D arrays of planar traps (24) (E), or 2D Coulomb crystals (23) (F); or electrons in quantum dot arrays created by a 2D mesh (13, 26) (G), or arrays of superconducting circuits (28) (H), or trapped on the surface of liquid helium (30) (I). The average distance between the atoms is, in the case of optical lattices, less than 1 um; in 2D arrays of cavities, it would scale as the ratio between the wavelength and the refractive index. As for the interion distances in ion trap arrays, they should be
about 10 to 50 um and about the same for 2D Coulomb crystals. In arrays of quantum dots, the spacing between dots is about 0.1 um. In superconducting circuits, the distance between junctions can be less than a micrometer. In the case of electrons on helium the distance between neighboring sites would be about 1 um. These interqubit distances (from 0.1 to 10 um) should be compared with the far smaller average interatomic distances in solids, which are <1 nm. The systems shown above realize a 1- or 2D array of qubits, which can be manipulated in different manners. The larger distances between qubits make quantum simulators more controllable and easier to measure. Therefore, they can be thought of as toy models of the magnified lattice structure of a “solid,” with a magnification factor of three orders of magnitude. Fig. 2. One-dimensional or 2D arrays of qubits plus controls could be used to simulate various models in condensed-matter physics. Examples of physical systems that could implement such analog quantum simulators include the following: atoms in optical lattices (20) (A) or in 1D (B) or 2D (C) arrays of cavities (21, 22); ions in linear ion chains (D), 2D arrays of planar traps (24) (E), or 2D Coulomb crystals (23) (F); or electrons in quantum dot arrays created by a 2D mesh (13, 26) (G), or arrays of superconducting circuits (28) (H), or trapped on the surface of liquid helium (30) (I). The average distance between the atoms is, in the case of optical lattices, less than 1 um; in 2D arrays of cavities, it would scale as the ratio between the wavelength and the refractive index. As for the interion distances in ion trap arrays, they should be
Table 1: Potential applications of quantum simulators and the physical systems in which they could be imple- mented. This is not an exhaustive list. By DQS we mean any physical system that can implement a Digita Quantum Simulator. Asterisks denote actual experimental realizations.
Table 1: Potential applications of quantum simulators and the physical systems in which they could be imple- mented. This is not an exhaustive list. By DQS we mean any physical system that can implement a Digita Quantum Simulator. Asterisks denote actual experimental realizations.

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F. Cucchietti

2011

This work was funding by the Spanish MEC projects TOQATA (FIS2008-00784), QOIT (Consolider Ingenio 2010), ACUTE, ERC Advanced Grant QUAGATUA, EU STREP NAMEQUAM, partly (E. Sz.) by the Hungarian Research Fund (OTKA) under Grant No. 68340, the Barcelona Supercomputing Center - Centro Nacional de Supercomputacion (FI2008-3-0029, FI2009-1-0019) (A.N.), and Alexander von Humboldt Foundation (M.L.).

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Quo vadis quantum simulators?
Cristiane Morais Smith

2019

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Simulating quantum mechanics on a quantum computer
Bruce Boghosian

Physica D: Nonlinear Phenomena, 1998

Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrödinger equation for interacting many-body systems are presented in some detail. These algorithms would make it possible to simulate nonrelativistic quantum systems on a quantum computer with an exponential speedup compared to simulations on classical computers. Issues involved in simulating relativistic systems of Dirac and gauge particles are discussed. * Expanded version of a talk given by WT at the PhysComp '96 conference,

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