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arXiv:1811.07683 · Physical Review Applied

Nonpairwise Interactions Induced by Virtual Transitions in Four Coupled Artificial Atoms

M. Schöndorf, Frank K. Wilhelm

Published Dec 10, 2019• 12 citations
arXivHTMLPDF

Abstract

While nonpairwise couplings are hard to implement in electronic systems, because the apparent interactions are two-body, such higher-order interactions could be beneficial in various applications. Studying a system of coupled artificial atoms (imagined as flux qubits), the authors show that $f\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}r\ensuremath{-}b\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}y$ local interactions appear via virtual coupler excitations, and that they can even be tuned into the strong-interaction regime. This theoretical exploration should serve as a starting point for circuit implementations of higher local interactions, especially in the context of adiabatic quantum computing.

DOI
10.1103/physrevapplied.12.064026

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While nonpairwise couplings are hard to implement in electronic systems, because the apparent interactions are two-body, such higher-order interactions could be beneficial in various applications. Studying a system of coupled artificial atoms (imagined as flux qubits), the authors show that f\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}r\ensuremath{-}b\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}y local interactions appear via virtual coupler excitations, and that they can even be tuned into the strong-interaction regime. This theoretical exploration should serve as a starting point for circuit implementations of higher local interactions, especially in the context of adiabatic quantum computing.
The field of quantum information has matured and various protocols implementing a quantum computer are being pursued. Most similar to a classical computer is the circuit model. In 2007 Aharonov et al. showed the equivalence between the circuit model and a quantum annealer, and with this proofed the universality of quantum annealing. Here the system starts in an easily preparable ground state and evolves adiabatically to a final ground state which yields the solution of the computational problem. However, equivalence with the circuit model requires multi-local interactions, i.e. interaction terms involving more than two subsystems. Natural interactions are only two-local, hence the construction or simulation of higher order couplers is indispensable for a universal quantum annealer. Also, four-local couplers allow compact implementation of error correction with the Bacon-Shor code. Four-local interactions can further serve as a tool for basic research. Here we show that in a specific flux qubit coupler design without ancilla qubits, four body interactions are induced by virtual coupler excitations. For specific parameter regimes they are even the leading effect and can be tuned up to the GHz range.
The field of quantum information has matured and various protocols implementing a quantum computer are being pursued. Most similar to a classical computer is the circuit model. In 2007 Aharonov et al. showed the equivalence between the circuit model and a quantum annealer, and with this proofed the universality of quantum annealing. Here the system starts in an easily preparable ground state and evolves adiabatically to a final ground state which yields the solution of the computational problem. However, equivalence with the circuit model requires multi-local interactions, i.e. interaction terms involving more than two subsystems. Natural interactions are only two-local, hence the construction or simulation of higher order couplers is indispensable for a universal quantum annealer. Also, four-local couplers allow compact implementation of error correction with the Bacon-Shor code. Four-local interactions can further serve as a tool for basic research. Here we show that in a specific flux qubit coupler design without ancilla qubits, four body interactions are induced by virtual coupler excitations. For specific parameter regimes they are even the leading effect and can be tuned up to the GHz range.
Nonpairwise multiqubit interactions present a useful resource for quantum information processors. Their implementation would facilitate more efficient quantum simulations of molecules and combinatorial optimization problems, and they could simplify error suppression and error correction schemes. Here, we present a superconducting circuit architecture in which a coupling module mediates two-local and three-local interactions between three flux qubits by design. The system Hamiltonian is estimated via multiqubit pulse sequences that implement Ramsey-type interferometry between all neighboring excitation manifolds in the system. The three-local interaction is coherently tunable over several MHz via the coupler flux biases and can be turned off, which is important for applications in quantum annealing, analog quantum simulation, and gate-model quantum computation.
The implementation of many-body interactions is relevant in various areas of quantum information. We present a superconducting device that implements a strong and tunable three-body interaction between superconducting quantum bits, with vanishing two-body interactions and robustness against noise and circuit parameter variations. These properties are confirmed by calculations based on the Born-Oppenheimer approximation, a two-level model for the coupling circuit, and numerical diagonalization. This circuit behaves as an ideal computational basis ZZZ coupler in a simulated three-qubit quantum annealing experiment. This work will be relevant for advanced quantum annealing protocols and future developments of high-order many-body interactions in quantum computers and simulators.
The field of quantum information has been a fast growing field of research in the last few decades. The reason for this development is the potentially immense power of quantum computers, capable of solving hard problems in a fraction of the time it would take a classical computer. Quantum annealers are a type of quantum computer that seek to solve computational problems by finding the ground state of a quantum system. This type of quantum computer has been implemented on a large scale using superconducting flux quantum bits, but the computational power is limited. One potential improvement to help in this context is the implementation of multi-body interactions between quantum bits. Many-body interactions would be useful in allowing quantum annealers to solve more complex problems that are relevant in various areas of quantum information and science and implementing quantum error correction. \n \nWe present a superconducting device that implements a strong and tunable in sign and magnitude three-body interaction between superconducting flux quantum bits. The circuit design proposed has vanishing two-body interactions and robustness against noise and parameter variations. This circuit behaves as an ideal computational basis ZZZ coupler in a simulated three-qubit quantum annealing experiment. These properties are confirmed by calculations based on the Born-Oppenheimer approximation, a two-level spin model for the coupling circuit, and full numerical diagonalization. \n \nThe proposed circuit is based on already available technology and therefore could be readily implemented in the next generation of quantum annealing hardware. This work will be relevant for advanced quantum annealing protocols and future developments of high-order many-body interactions in quantum computers and simulators.
The authors implement a classical counterpart of a scalable design for adiabatic quantum computation. The key element of this design is a coupler providing controllable coupling between two bistable elements (in our case superconducting rings with a single Josephson junction playing the role of a classical counterpart of superconducting flux qubits). The coupler is also a superconducting ring with a single Josephson junction that operates in the nonhysteretic mode with a screening parameter of about 0.9. The flux coupling between two bistable rings can be controlled by changing the magnetic flux through the coupler. Since the coupling amplitude is proportional to the derivative of the coupler’s current-flux relation, the coupling can be tuned from ferromagnetic to antiferromagnetic. In between the coupling can also be switched off.