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A tunable coupling scheme for implementing high-fidelity two-qubit gates
Fei Yan, Philip Krantz, Youngkyu Sung, Morten Kjaergaard, Dan Campbell, Joel I. J. Wang, Terry P. Orlando, Simon Gustavsson, William D. Oliver
TL;DR
The paper develops a tunable-coupler framework for controlling effective qubit–qubit interactions. It derives the interaction using a Schrieffer–Wolff transformation and shows that a zero-coupling point is guaranteed under stated assumptions.
Problem
The paper addresses how to derive and control effective qubit–qubit coupling in a three-mode superconducting circuit while accounting for direct and virtual interactions.
Method
The approach models coupled transmon modes and applies a second-order Schrieffer–Wolff transformation in the dispersive regime to decouple the coupler.
Results
A zero of the effective coupling is guaranteed for arbitrarily small C12 because the first bracket term vanishes as ωc approaches infinity.
Takeaways & Limitations
The derived effective Hamiltonian provides a coupling-control point within the analyzed superconducting-circuit model.
Takeaways & Limitations
The derivation assumes weak anharmonicity, αλ ≪∆j, uses uniform detuning estimates, and assumes the coupler is in its ground state.
Abstract
from arXiv · showhide
The prospect of computational hardware with quantum advantage relies critically on the quality of quantum gate operations. Imperfect two-qubit gates is a major bottleneck for achieving scalable quantum information processors. Here, we propose a generalizable and extensible scheme for a two-qubit coupler switch that controls the qubit-qubit coupling by modulating the coupler frequency. Two-qubit gate operations can be implemented by operating the coupler in the dispersive regime, which is non-invasive to the qubit states. We investigate the performance of the scheme by simulating a universal two-qubit gate on a superconducting quantum circuit, and find that errors from known parasitic effects are strongly suppressed. The scheme is compatible with existing high-coherence hardware, thereby promising a higher gate fidelity with current technologies.
Supplementary material:
The supplementary material is associated with the paper titled “A tunable coupling scheme for implementing high-fidelity two-qubit gates” and lists its authors.
- The supplementary material accompanies a paper on tunable coupling schemes for high-fidelity two-qubit gates.
- The listed paper title emphasizes tunable coupling as the route to high-fidelity two-qubit gates.
- The author list includes Fei Yan, Philip Krantz, Youngkyu Sung, Morten Kjaergaard, and additional collaborators.
CIRCUIT HAMILTONIAN AND QUANTIZATION
The circuit is modeled as three coupled tunable transmon modes, with capacitive couplings and Josephson nonlinearities forming the basis for its Hamiltonian.
- CIRCUIT HAMILTONIAN AND QUANTIZATION: The circuit contains two qubit modes and one center coupler mode, each modeled as a tunable transmon qubit.The modes are labeled 1, 2, and c.
- CIRCUIT HAMILTONIAN AND QUANTIZATION: The capacitive network includes qubit–coupler couplings C1c and C2c, direct qubit coupling C12, and dominant mode capacitances.
- CIRCUIT HAMILTONIAN AND QUANTIZATION: Each mode contributes charging and Josephson potential energies, with Φ0 = h/2e defining the superconducting flux quantum.
- CIRCUIT HAMILTONIAN AND QUANTIZATION: In the transmon regime, EJλ/ECλ ≫1, the system is represented by coupled Duffing oscillators.
- CIRCUIT HAMILTONIAN AND QUANTIZATION: The Hamiltonian separates into three mode Hamiltonians and the qubit–coupler and direct qubit–qubit interaction terms.
- CIRCUIT HAMILTONIAN AND QUANTIZATION: The model retains counter-rotating interaction terms because they can contribute significantly when the coupler frequency greatly exceeds the qubit frequency.
SCHRIEFFER-WOLFF TRANSFORMATION
The Schrieffer–Wolff transformation removes the coupler perturbatively and yields an effective qubit–qubit Hamiltonian under dispersive and weak-anharmonicity assumptions.
- SCHRIEFFER-WOLFF TRANSFORMATION: The Schrieffer–Wolff transformation diagonalizes the Hamiltonian to decouple the coupler from the effective qubit system.
- SCHRIEFFER-WOLFF TRANSFORMATION: The transformation assumes weak anharmonicity, αλ ≪∆j, and uses a uniform detuning value for estimating frequency shifts.
- SCHRIEFFER-WOLFF TRANSFORMATION: The derivation keeps terms through second order in the qubit–coupler couplings and treats g12 as second-order small.
- SCHRIEFFER-WOLFF TRANSFORMATION: Counter-rotating processes contribute significantly in the strong dispersive regime, where ωc ≫ωj and |∆j| ≈|Σj|.
- SCHRIEFFER-WOLFF TRANSFORMATION: The coupler is assumed to remain in its ground state while qubit interactions proceed through virtual non-computational states.The relevant intermediate states include |010⟩ and |111⟩.
- SCHRIEFFER-WOLFF TRANSFORMATION: The effective coupling has a guaranteed zero for arbitrarily small C12 because its first bracket term vanishes as ωc approaches infinity.