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Deriving Effective Coupling Strength With Born-Oppenheimer Approx.

Conrad Wichmann

Published Aug 5, 2024• 0 citations
Publisher

Abstract

Tunable couplers have been important in the development of superconducting quantum computers. The ability to maintain zero coupling between qubits during operation, a feature of high-fidelity quantum gates, has been shown to be possible with the use of tunable couplers. As an example, Sete et al., 2021 showed this was possible with a tunable coupler between transmons: the qubit-coupler and qubit-qubit couplings create a net effective coupling strength between the qubits that can be tuned to zero. However, the derivation of the effective coupling strength between the qubits is quite complex. We propose a simpler method of obtaining this effective coupling with the Born-Oppenheimer approximation.

DOI
10.2172/2426443

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Tunable couplers have been important in the development of superconducting quantum computers. The ability to maintain zero coupling between qubits during operation, a feature of high-fidelity quantum gates, has been shown to be possible with the use of tunable couplers. As an example, Sete et al., 2021 showed this was possible with a tunable coupler between transmons: the qubit-coupler and qubit-qubit couplings create a net effective coupling strength between the qubits that can be tuned to zero. However, the derivation of the effective coupling strength between the qubits is quite complex. We propose a simpler method of obtaining this effective coupling with the Born-Oppenheimer approximation.
The development of high-fidelity quantum gates is paramount to the scalability of quantum pro- cessors. Tunable couplers have played a key role in the realization of these low error rate quantum gates in superconducting circuits. However, the derivation of the effective coupling strength between the qubits is usually enabled by a Schrieffer-Wolff transformation, which is complex and requires prior-knowledge of the proper generator for the transformation. We propose a simpler method of obtaining this effective coupling using an approach similar to the Born-Oppenheimer approximation.
The development of high-fidelity quantum gates is paramount to the scalability of quantum processors. Tunable couplers have played a key role in the realization of these low error rate quantum gates in superconducting circuits. However, the derivation of the effective coupling strength between the qubits is usually enabled by a Schrieffer-Wolff transformation, which is complex and requires prior-knowledge of the proper generator for the transformation. We propose a simpler method of obtaining this effective coupling using an approach similar to the Born-Oppenheimer approximation.
For a variety of superconducting qubits, tunable interactions are achieved through mutual inductive coupling to a coupler circuit containing a nonlinear Josephson element. In this paper, we derive the general interaction mediated by such a circuit under the Born-Oppenheimer approximation. This interaction naturally decomposes into a classical part, with origin in the classical circuit equations, and a quantum part, associated with the coupler's zero-point energy. Our result is nonperturbative in the qubit-coupler coupling strengths and in the coupler nonlinearity. This can lead to significant departures from previous, linear theories for the interqubit coupling, including nonstoquastic and many-body interactions. Our analysis provides explicit and efficiently computable series for any term in the interaction Hamiltonian and can be applied to any superconducting qubit type. We conclude with a numerical investigation of our theory using a case study of two coupled flux qubits, and in particular study the regime of validity of the Born-Oppenheimer approximation.
Tunable couplers, which turn on and off the interaction between qubits, have emerged as a key means to achieve low error rates in superconducting quantum computers. Conventional devices using one transmon qubit exhibit unwanted residual coupling, though, especially at the high detuning that is desirable for suppressing crosstalk errors. To solve this critical problem, the author proposes a tunable coupler based on two transmons that satisfies the ideal conditions of no residual coupling and fast two-qubit gate operations at high detuning. This double-transmon coupler is expected to become standard for superconducting architectures by eliminating unwanted coupling during idle time.
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.
Tunable couplers in superconducting quantum computers have enabled fast and accurate two-qubit gates, with reported high fidelities over 99% in various architectures and gate-implementation schemes. However, there are few tunable couplers whose performance in multiqubit systems is clarified, except for the most widely used one: single-transmon coupler (STC). Achieving similar accuracy to isolated two-qubit systems remains challenging due to various undesirable couplings but is necessary for scalability. In this work, we numerically analyze a system of three fixed-frequency qubits coupled via two double-transmon couplers (DTCs) where nearest-neighbor qubits are highly detuned and also next-nearest-neighbor ones are nearly resonant. The DTC is a recently proposed tunable coupler, which consists of two fixed-frequency transmons coupled through a common loop with an additional Josephson junction. We find that the DTC cannot only reduce undesired residual couplings sufficiently, as well as in isolated two-qubit systems, but also enables implementations of 30-ns CZ gates and individual and simultaneous 10-ns π / 2 pulses with fidelities over 99.99%. For comparison, we also investigate the system where the DTCs are replaced by the STCs. The results show that the DTC outperforms the STC in terms of both residual coupling suppression and gate accuracy in the above systems. From these results, we expect that the DTC architecture is promising for realizing high-performance, scalable superconducting quantum computers. Published by the American Physical Society 2024