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arXiv:1910.08741 · Physical Review Research

Native three-body interaction in superconducting circuits

Simon Panyella Pedersen, K. S. Christensen, N. T. Zinner

Published Nov 22, 2019• 23 citations
arXivHTMLPDF

Abstract

This paper shows how a superconducting circuit can implement three qubits interacting via a direct three-body coupling. As the coupling is direct, the timescale of the interaction is extremely fast, on the order of a nanosecond. This coupling can be used to implement a controlled operation relevant for quantum computing, where the control is a quantum degree of freedom, and the operation time is so short that noise becomes much less relevant. The approach is general and could be used to implement other direct multi-qubit interactions in superconducting circuits.

DOI
10.1103/physrevresearch.1.033123

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This paper shows how a superconducting circuit can implement three qubits interacting via a direct three-body coupling. As the coupling is direct, the timescale of the interaction is extremely fast, on the order of a nanosecond. This coupling can be used to implement a controlled operation relevant for quantum computing, where the control is a quantum degree of freedom, and the operation time is so short that noise becomes much less relevant. The approach is general and could be used to implement other direct multi-qubit interactions in superconducting circuits.
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 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.
Nonpairwise multibody interactions have recently attracted much attention due to their promising applications in the realm of quantum information science and technology. In this work, we propose a method to synthesize a nonpairwise three-body interaction of superconducting qubits using a coupler qubit dispersively coupled to two spatially separated qubits and a microwave pulse. This interaction describes physical processes of an excitation from the coupler qubit to two spatially separated qubits and the reverse process. We show that the interaction can be utilized to deterministically generate three-body Greenberger-Horne-Zeilinger (GHZ) entangled states, transfer the state of the coupler qubit into a two-qubit entangled state, and construct three-qubit controlled-controlled-phase and Toffoli gates. Our proposal only requires a coupler qubit and a single-step operation; thus, the system architecture and method are quite simple. As examples, we numerically simulate the dynamics of the system, and the numerical results demonstrate that high-fidelity preparation of the proposed three-body GHZ entangled state and quantum gates is feasible with current superconducting circuit technology. This approach is general and applicable to a wide range of quantum systems.
Superconducting qubits provide a competitive platform for quantum simulation of complex dynamics that lies at the heart of quantum many-body systems, because of the flexibility and scalability afforded by the nature of microfabrication. However, in a multiqubit device, the physical form of couplings between qubits is either an electric (capacitor) or magnetic field (inductor), and the associated quadratic field energy determines that only two-body interaction in the Hamiltonian can be directly realized. Here, we propose and experimentally synthesize a three-body spin-chirality interaction in a superconducting circuit based on Floquet engineering. By periodically modulating the resonant frequencies of the qubits connected with each other via capacitors, we can dynamically turn on and off qubit–qubit couplings and further create chiral flows of the excitations in the three-qubit circular loop. Our result is a step toward engineering dynamical and many-body interactions in multiqubit superconducting devices, which potentially expands the degree of freedom in quantum simulation tasks.
A quantum computer is an information processing machine, much like an ordinary classical computer, but its function is based on quantum mechanical principles. To be able to construct such a machine would be a fantastic accomplishment---to have total control over a quantum system is a dream for both physicists and science-fiction enthusiasts. The basic information unit in a quantum computer is the quantum bit, or qubit for short. A quantum computer consists of many coupled qubits. To get a single qubit to work properly, would be a major step towards building this machine. Here we study two different qubit ideas. The central element in both setups is the superconducting tunnel junction---the Josephson junction. By connecting the Josephson junctions to standard electronics in a clever way, a qubit can be realised. With these constructions it is in principle very easy to manipulate and read out the quantum probabilities, by varying voltages and currents in time. However, this ease of manipulation has a cost: strong interactions with uncontrolled degrees of freedom of the environment transfer information from the qubit. For superconducting qubits this decoherence is typically very fast. There are ways to deal with the decoherence. One way is to tune the circuit parameters so that the decoherence becomes minimal. Another way is to engineer the qubits so fast so that the effect of decoherence becomes small. In this thesis, we will apply both these strategies. Specifically, the measurement speed of the second qubit we study, turns out to be very sensitive to the topology of the phase space of the detector variables.
Superconducting circuits form one of the most promising hardware platforms for building a quantum computer. As the quantum computing system gets more complex as we increase the size, employing simple circuit designs and control strategies can make the task of building a large scale quantum computer easier. This thesis describes a novel control strategy that utilises spin-echo techniques and native interaction in superconducting circuits, which reduces the cost of calibrating pulsed two-qubit gates. Spin-echo pulses are used to rescale the always-on Hamiltonian, and the timings of spin-echo pulses encode the effective coupling strengths. In collaboration with the NMR group in Oxford, two methods for scaling this technique to large numbers of qubits were explored. In the first approach, pulse sequences for an all-to-all coupled system are obtained numerically using linear programming, and it finds the time-optimal solution for up to twenty qubits and the near time-optimal solution for up to hundreds of qubits. Another approach based on graph colouring finds the near time-optimal pulse sequence analytically, allowing pulse sequences for any number of qubits. An idea based on the Hamiltonian rescaling technique was applied to implementing the variational quantum eigensolver algorithm and error mitigation on two superconducting qubits. In contrast to previous studies, the residual dispersive coupling between qubits was used for computation instead of regarding it as a source of error. Lastly, the detailed dynamics of the residual dispersive coupling in superconducting circuits were investigated to predict the practicality of spin-echo-based quantum computing on superconducting circuits. The Hamiltonian rescaling protocol assumes the always-on coupling to be diagonal, such as Ising Hamiltonian, but deviation from the pure Ising interaction was observed in the strongly coupled superconducting qubits. The origin of the deviation was identified analytically, and the circuit design criteria to suppress the deviation are presented.