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Physical Review B

Fully microwave-tunable universal gates in superconducting qubits with linear couplings and fixed transition frequencies

Chad T. Rigetti, Michel Devoret

Published Apr 5, 2010• 355 citations
Publisher

Abstract

A register of quantum bits with fixed transition frequencies and weakly coupled to one another through simple linear circuit elements is an experimentally minimal architecture for a small-scale superconducting quantum information processor. Presently, the known schemes for implementing two-qubit gates in this system require microwave signals having amplitudes and frequencies precisely tuned to meet a resonance condition, leaving only the signal phases as free experimentally adjustable parameters. Here, we report a minimal and robust microwave scheme to generate fast, tunable universal two-qubit gates: simply irradiate one qubit (the ``control'') at the transition frequency of another (the ``target''). The effective coupling between them is then switched on by tuning only the frequency of this single drive tone; the drive amplitude adjusts the effective coupling strength; and the drive phase selects the particular two-qubit gate implemented. This cross-resonance effect turns on linearly with the ratio of the drive amplitude $\ensuremath{\Omega}$ to the qubit-qubit detuning $\ensuremath{\Delta}$, as compared with earlier proposals that turn on as ${(\ensuremath{\Omega}/\ensuremath{\Delta})}^{4}$.

DOI
10.1103/physrevb.81.134507

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A register of quantum bits with fixed transition frequencies and weakly coupled to one another through simple linear circuit elements is an experimentally minimal architecture for a small-scale superconducting quantum information processor. Presently, the known schemes for implementing two-qubit gates in this system require microwave signals having amplitudes and frequencies precisely tuned to meet a resonance condition, leaving only the signal phases as free experimentally adjustable parameters. Here, we report a minimal and robust microwave scheme to generate fast, tunable universal two-qubit gates: simply irradiate one qubit (the control'') at the transition frequency of another (the target''). The effective coupling between them is then switched on by tuning only the frequency of this single drive tone; the drive amplitude adjusts the effective coupling strength; and the drive phase selects the particular two-qubit gate implemented. This cross-resonance effect turns on linearly with the ratio of the drive amplitude \ensuremathΩ\ensuremath{\Omega}\ensuremathΩ to the qubit-qubit detuning \ensuremathΔ\ensuremath{\Delta}\ensuremathΔ, as compared with earlier proposals that turn on as (\ensuremathΩ/\ensuremathΔ)4{(\ensuremath{\Omega}/\ensuremath{\Delta})}^{4}(\ensuremathΩ/\ensuremathΔ)4.
Generating high-fidelity, tunable entanglement between qubits is crucial for realizing gate-based quantum computation. In superconducting circuits, tunable interactions are often implemented using flux-tunable qubits or coupling elements, adding control complexity and noise sources. Here, we realize a tunable ZZZZZZ interaction between two transmon qubits with fixed frequencies and fixed coupling, induced by driving both transmons off-resonantly. We show tunable coupling over one order of magnitude larger than the static coupling, and change the sign of the interaction, enabling cancellation of the idle coupling. Further, this interaction is amenable to large quantum processors: the drive frequency can be flexibly chosen to avoid spurious transitions, and because both transmons are driven, it is resilient to microwave crosstalk. We apply this interaction to implement a controlled phase (CZ) gate with a gate fidelity of 99.43(1)%99.43(1)\%99.43(1)% as measured by cycle benchmarking, and we find the fidelity is limited by incoherent errors.
Generating high-fidelity, tunable entanglement between qubits is crucial for realizing gate-based quantum computation. In superconducting circuits, tunable interactions are often implemented using flux-tunable qubits or coupling elements, adding control complexity and noise sources. Here, we realize a tunable ZZ interaction between two transmon qubits with fixed frequencies and fixed coupling, induced by driving both transmons off resonantly. We show tunable coupling over 1 order of magnitude larger than the static coupling, and change the sign of the interaction, enabling cancellation of the idle coupling. Further, this interaction is amenable to large quantum processors: the drive frequency can be flexibly chosen to avoid spurious transitions, and because both transmons are driven, it is resilient to microwave cross talk. We apply this interaction to implement a controlled phase (CZ) gate with a gate fidelity of 99.43(1)% as measured by cycle benchmarking, and we find the fidelity is limited by incoherent errors.
Fixed-frequency superconducting qubits demonstrate remarkable success as platforms for stable and scalable quantum computing. Cross-resonance gates have been the workhorse of fixed-coupling, fixed-frequency superconducting processors, leveraging the entanglement generated by driving one qubit resonantly with a neighbor’s frequency to achieve high-fidelity, universal controlled- () gates. Here, we use on-resonant and off-resonant microwave drives to go beyond cross-resonance, realizing natively interesting two-qubit gates that are not equivalent to gates. In particular, we implement and benchmark native i , , i SWAP , and b gates; in fact, any SU ( 4 ) unitary can be achieved using these techniques. Furthermore, we apply these techniques for an efficient construction of the B gate: a perfect entangler from which any two-qubit gate can be reached in only two applications. We show that these native two-qubit gates are better than their counterparts compiled from cross-resonance gates. We elucidate the resonance conditions required to drive each two-qubit gate and provide a novel frame tracking technique to implement them in Qiskit. Published by the American Physical Society 2024
In the circuit quantum electrodynamics architecture, both the resonance frequency and the coupling of superconducting qubits to microwave field modes can be controlled via external electric and magnetic fields to explore qubit-photon dynamics in a wide parameter range. Here, we experimentally demonstrate and analyze a scheme for tuning the coupling between a transmon qubit and a microwave resonator using a single coherent drive tone. We treat the transmon as a three-level system, with the qubit subspace defined by the ground and the second excited states. If the drive frequency matches the difference between the resonator and the qubit frequencies, a Jaynes-Cummings-type interaction is induced, which is tunable in both amplitude and phase. We show that coupling strengths of about 10 MHz can be achieved in our setup, limited only by the anharmonicity of the transmon qubit. This scheme has been successfully used to generate microwave photons with a controlled temporal shape [M. Pechal et al., Phys. Rev. X 4, 041010 (2014)] and can be directly implemented with superconducting quantum devices featuring larger anharmonicity for higher coupling strengths.
Tunable couplers have recently become one of the most powerful tools for implementing two-qubit gates between superconducting qubits.A tunable coupler typically includes a nonlinear element, such as a superconducting quantum interference device, which is used to tune the resonance frequency of an LC circuit connecting two qubits.Here we propose a complimentary approach where instead of tuning the resonance frequency of the tunable coupler by applying a quasistatic control signal, we excite by microwave the degree of freedom associated with the coupler itself.Because of strong effective longitudinal coupling between the coupler and the qubits, the frequency of this transition strongly depends on the computational state, leading to different phase accumulations in different states.Using this method, we experimentally demonstrate a controlled-Z gate of 44-ns duration on a fluxonium-based quantum processor, obtaining a fidelity of 97.6% ± 0.4% characterized by cross-entropy benchmarking.