Semiconductor spin qubits may be coupled through a superconducting cavity to generate an entangling two-qubit gate. However, the fidelity of such an operation will be reduced by a variety of error mechanisms such as charge and magnetic noise, phonons, cavity loss, transitions to nonqubit states, and, for electrons in silicon, excitation into other valley eigenstates. Here, we model the effects of these error sources and the valley degree of freedom on the performance of a cavity-mediated two-qubit $\mathrm{i}$ swap gate. For valley splittings inadequately large relative to the interdot tunnel coupling within each qubit, we find that valley excitation may be a limiter to the fidelity of this two-qubit gate. In addition, we show trade-offs between gating times and exposure to various error sources, identifying optimal operating regimes and device improvements that would have the greatest impact on the fidelity of the cavity-mediated spin $\mathrm{i}$ swap gate. Importantly, we find that, while the impact of charge noise and phonon relaxation favor operation in the regime where the qubits are most spinlike to reduce sensitivity to these sources of noise, the combination of hyperfine noise and valley physics shifts the optimal regime to chargelike qubits with stronger effective spin-photon coupling so that gate times can be made as short as possible. In this regime, the primary limitation is the need to avoid Landau-Zener transitions as the gate is implemented.Semiconductor spin qubits may be coupled through a superconducting cavity to generate an entangling two-qubit gate. However, the fidelity of such an operation will be reduced by a variety of error mechanisms such as charge and magnetic noise, phonons, cavity loss, transitions to nonqubit states, and, for electrons in silicon, excitation into other valley eigenstates. Here, we model the effects of these error sources and the valley degree of freedom on the performance of a cavity-mediated two-qubit $\mathrm{i}$swap gate. For valley splittings inadequately large relative to the interdot tunnel coupling within each qubit, we find that valley excitation may be a limiter to the fidelity of this two-qubit gate. In addition, we show trade-offs between gating times and exposure to various error sources, identifying optimal operating regimes and device improvements that would have the greatest impact on the fidelity of the cavity-mediated spin $\mathrm{i}$swap gate. Importantly, we find that, while the impact of charge noise and phonon relaxation favor operation in the regime where the qubits are most spinlike to reduce sensitivity to these sources of noise, the combination of hyperfine noise and valley physics shifts the optimal regime to chargelike qubits with stronger effective spin-photon coupling so that gate times can be made as short as possible. In this regime, the primary limitation is the need to avoid Landau-Zener transitions as the gate is implemented.

arXiv:2208.11151Physical Review AppliedDec 27, 202210 citations

Implementing Qubits with Superconducting Integrated Circuits

Michel Devoret, John M. Martinis

Quantum Information ProcessingOct 1, 2004230 citations

Phase gate of one qubit simultaneously controlling n qubits in a cavity or coupled to a resonator

Chui‐Ping Yang, Yu-xi Liu, Franco Nori

We propose how to realize a three-step controlled-phase gate of one qubit simultaneously controlling $n$ qubits in a cavity or coupled to a resonator. The $n$ two-qubit controlled-phase gates, forming this multiqubit phase gate, can be performed simultaneously. The operation time of this phase gate is independent of the number $n$ of qubits. This phase gate controlling at once $n$ qubits is insensitive to the initial state of the cavity mode and can be used to produce an analogous CNOT gate simultaneously acting on $n$ qubits. We present two alternative approaches to implement this gate. One approach is based on tuning the qubit frequency while the other method tunes the resonator frequency. Using superconducting qubits coupled to a resonator as an example, we show how to implement the proposed gate with one superconducting qubit simultaneously controlling $n$ qubits selected from $N$ qubits coupled to a resonator ( $1<n<N$ ). We also give a discussion on realizing the proposed gate with atoms, by using one cavity initially in an arbitrary state.We propose how to realize a three-step controlled-phase gate of one qubit simultaneously controlling $n$ qubits in a cavity or coupled to a resonator. The $n$ two-qubit controlled-phase gates, forming this multiqubit phase gate, can be performed simultaneously. The operation time of this phase gate is independent of the number $n$ of qubits. This phase gate controlling at once $n$ qubits is insensitive to the initial state of the cavity mode and can be used to produce an analogous CNOT gate simultaneously acting on $n$ qubits. We present two alternative approaches to implement this gate. One approach is based on tuning the qubit frequency while the other method tunes the resonator frequency. Using superconducting qubits coupled to a resonator as an example, we show how to implement the proposed gate with one superconducting qubit simultaneously controlling $n$ qubits selected from $N$ qubits coupled to a resonator ($1<n<N$). We also give a discussion on realizing the proposed gate with atoms, by using one cavity initially in an arbitrary state.

arXiv:0912.4242Dec 21, 20093 citations

Phase gate of one qubit simultaneously controlling n qubits in a cavity

Chui‐Ping Yang, Yu-xi Liu, Franco Nori

We propose how to realize a three-step controlled-phase gate of one qubit simultaneously controlling $n$ qubits in a cavity or coupled to a resonator. The $n$ two-qubit controlled-phase gates, forming this multiqubit phase gate, can be performed simultaneously. The operation time of this phase gate is independent of the number $n$ of qubits. This phase gate controlling at once $n$ qubits is insensitive to the initial state of the cavity mode and can be used to produce an analogous cnot gate simultaneously acting on $n$ qubits. We present two alternative approaches to implement this gate. One approach is based on tuning the qubit frequency while in the other method the resonator frequency is tuned. Using superconducting qubits coupled to a resonator as an example, we show how to implement the proposed gate with one superconducting qubit simultaneously controlling $n$ qubits selected from $N$ qubits coupled to a resonator ( $1<n<N$ ). We also give a discussion on realizing the proposed gate with atoms, by using one cavity initially in an arbitrary state.We propose how to realize a three-step controlled-phase gate of one qubit simultaneously controlling $n$ qubits in a cavity or coupled to a resonator. The $n$ two-qubit controlled-phase gates, forming this multiqubit phase gate, can be performed simultaneously. The operation time of this phase gate is independent of the number $n$ of qubits. This phase gate controlling at once $n$ qubits is insensitive to the initial state of the cavity mode and can be used to produce an analogous cnot gate simultaneously acting on $n$ qubits. We present two alternative approaches to implement this gate. One approach is based on tuning the qubit frequency while in the other method the resonator frequency is tuned. Using superconducting qubits coupled to a resonator as an example, we show how to implement the proposed gate with one superconducting qubit simultaneously controlling $n$ qubits selected from $N$ qubits coupled to a resonator ($1<n<N$). We also give a discussion on realizing the proposed gate with atoms, by using one cavity initially in an arbitrary state.

arXiv:0907.4201Physical Review AJun 17, 201074 citations

Implementing Qubits with Superconducting Integrated Circuits

Michel Devoret, John M. Martinis

Springer eBooksApr 2, 200754 citations

\mathrm{i}

swap gate. For valley splittings inadequately large relative to the interdot tunnel coupling within each qubit, we find that valley excitation may be a limiter to the fidelity of this two-qubit gate. In addition, we show trade-offs between gating times and exposure to various error sources, identifying optimal operating regimes and device improvements that would have the greatest impact on the fidelity of the cavity-mediated spin

\mathrm{i}

swap gate. Importantly, we find that, while the impact of charge noise and phonon relaxation favor operation in the regime where the qubits are most spinlike to reduce sensitivity to these sources of noise, the combination of hyperfine noise and valley physics shifts the optimal regime to chargelike qubits with stronger effective spin-photon coupling so that gate times can be made as short as possible. In this regime, the primary limitation is the need to avoid Landau-Zener transitions as the gate is implemented.

We propose how to realize a three-step controlled-phase gate of one qubit simultaneously controlling

n

qubits in a cavity or coupled to a resonator. The

n

two-qubit controlled-phase gates, forming this multiqubit phase gate, can be performed simultaneously. The operation time of this phase gate is independent of the number

n

of qubits. This phase gate controlling at once

n

qubits is insensitive to the initial state of the cavity mode and can be used to produce an analogous CNOT gate simultaneously acting on

n

qubits. We present two alternative approaches to implement this gate. One approach is based on tuning the qubit frequency while the other method tunes the resonator frequency. Using superconducting qubits coupled to a resonator as an example, we show how to implement the proposed gate with one superconducting qubit simultaneously controlling

n

qubits selected from

N

qubits coupled to a resonator (

1<n<N

). We also give a discussion on realizing the proposed gate with atoms, by using one cavity initially in an arbitrary state.