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arXiv:1712.07326

Experimental Demonstration of Quantum Tunneling in IBM Quantum Computer

Narendra N. Hegade, Kortikar, Nachiket L., Das, Bikramaditya, Behera, Bikash K., Panigrahi, Prasanta K.

Published Dec 20, 2017• 23 citations
arXivHTMLPDF

Abstract

Quantum computers are the promising candidates for simulation of large quantum systems, which is a daunting task to perform in a classical computer. Here, we report the experimental realization of quantum tunneling of a single particle through different types of potential barriers by performing digital quantum simulations using IBM quantum computers. We consider two and three-qubit systems to visualize the tunneling process and illustrate its unique quantum nature. We observe the tunneling and oscillations of the particles in a step-well, double-well, and multi-well potentials through our experimental results. One may extend the proposed quantum circuits and simulation techniques used here for observing the tunneling phenomena for multi-particle systems in different potentials.

DOI
10.48550/arxiv.1712.07326

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Quantum computers are the promising candidates for simulation of large quantum systems, which is a daunting task to perform in a classical computer. Here, we report the experimental realization of quantum tunneling of a single particle through different types of potential barriers by performing digital quantum simulations using IBM quantum computers. We consider two and three-qubit systems to visualize the tunneling process and illustrate its unique quantum nature. We observe the tunneling and oscillations of the particles in a step-well, double-well, and multi-well potentials through our experimental results. One may extend the proposed quantum circuits and simulation techniques used here for observing the tunneling phenomena for multi-particle systems in different potentials.
It is well known that quantum computers are superior to classical computers in efficiently simulating quantum systems. Here we report the first experimental simulation of quantum tunneling through potential barriers, a widespread phenomenon of a unique quantum nature, via NMR techniques. Our experiment is based on a digital particle simulation algorithm and requires very few spin-1/2 nuclei without the need of ancillary qubits. The occurrence of quantum tunneling through a barrier, together with the oscillation of the state in potential wells, are clearly observed through the experimental results. This experiment has clearly demonstrated the possibility to observe and study profound physical phenomena within even the reach of small quantum computers.
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A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because of the number of gates and qubits necessary, however, digital quantum particle simulations remain untested. A contributing factor to the system size required is the number of ancillary qubits needed to implement matrix exponentials of the potential operator. Here, we show that a set of tunneling problems may be investigated with no ancillary qubits and a cost of one single-qubit operator per time step for the potential evolution, eliminating at least half of the quantum gates required for the algorithm and more than that in the general case. Such simulations are within reach of current quantum computer architectures.
In the usual quantum tunneling, a low-energy quantum particle penetrates across a physical barrier of higher potential energy, by traversing a classically forbidden region, and finally escapes into another region. In an analogous scenario, a classical particle inside a closed regular region in the phase space is dynamically bound from escaping to other regions of the phase space. Here, the physical potential barrier is replaced by dynamical barriers which separate different regions of the phase space. However, in the quantum regime, the system can overcome such dynamical barriers and escape through them, giving rise to dynamical tunneling. In chaotic Hamiltonian systems, dynamical tunneling refers to quantum tunneling between states whose classical limits correspond to symmetry-related regular regions separated by a chaotic zone between which any classical transport is prohibited. Here, an experimental realization of dynamical tunneling in spin systems is reported using nuclear magnetic resonance (NMR) architecture. In particular, dynamical tunneling in quantum kicked tops of spin-1 and spin-3/2 systems using two- and three-qubit NMR registers is investigated. By extracting time-dependent expectation values of the angular momentum operator components, size-dependent tunneling behavior for various initial states is systematically investigated. Further, by monitoring the adverse effects of dephasing noise on the tunneling oscillations, we assert the importance of quantum coherence in enabling dynamical tunneling.
A quantum computer (QC) is a device that performs operations according to the rules of quantum theory. There are various types of QCs of which nowadays the two most important ones considered for practical realization are the gate-based QC and the quantum annealer (QA). Practical realizations of gate-based QCs consist of less than 100 qubits while QAs with more than 2000 qubits are commercially available.In the gate model QC, a universal QC, a computation (or quantum algorithm) consists of a sequence of quantum gate operations (unitary transformations) that changes the internal state of the QC. Quantum annealing is a technique for finding the global minimum of a quadratic function of binary variables by exploiting quantum fluctuations. Its main potential targets are combinatorial optimization problems featuring a discrete search space with many local minima.We present results of simulating on the IBM Quantum Experience devices and on the D-Wave 2X QA with more than 1000 qubits. Simulations of both types of QCs are performed by first modeling them as zero-temperature quantum systems of interacting spin-1/2 particles and then emulating their dynamics by solving the time-dependent Schrödinger equation. Our software allows for the simulation of a 48-qubit gate-based QC on the Sunway TaihuLight supercomputer.We also briefly report about EQUIPE, a user group, established by Forschungszentrum Jülich, to Enable QUantum Information Processing in Europe and about JUNIQ, a Jülich User Infrastructure for Research and Development in Quantum Computing, offering European users from science and industry user support and access to various QC simulators and eventually technologies on various stages of maturity (D-Wave QA, multi-qubit devices for QC without error correction from e.g. IBM, Google, Rigetti Computing, …, and experimental devices).