arXiv:2307.15177 · Physical review. B./Physical review. B

Assessing quantum dot SWAP gate fidelity using tensor network methods

Jacob R. Taylor, Nathan L. Foulk, S. Das Sarma

Published Apr 1, 2024• 2 citations

Abstract

Advanced tensor network numerical methods are used to explore the fidelity of repeated SWAP operations on a system comprising 20--100 quantum dot spin qubits in the presence of valley leakage and electrostatic crosstalk. The fidelity of SWAP gates is largely unaffected by Zeeman splitting and valley splitting, except when these parameters come into resonance. The fidelity remains independent of the overall valley phase for valley eigenstates, while for generic valley states, some minor corrections arise. We analyze the fidelity scaling for long qubit chains without valley effects, where crosstalk represents the only error source.

DOI: 10.1103/physrevb.109.165403

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arXiv:2307.15177 · Physical review. B./Physical review. B

Assessing quantum dot SWAP gate fidelity using tensor network methods

Jacob R. Taylor, Nathan L. Foulk, S. Das Sarma

Published Apr 1, 2024• 2 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.109.165403

Related papers

Valley leakage and gate timing errors in SWAP operations of Si-based spin qubits.

Nathan L. Foulk, Robert E. Throckmorton, S. Das Sarma

We investigate the fidelity of a sequence of SWAP gates on a Si-based quantum dot (QD) spin qubit chain. We particularly examine how valley leakage and gate timing error affect the gate fidelity compared to charge noise, which is always present. In our Hamiltonian, each qubit is coupled via Heisenberg exchange to every other qubit in the chain, with the strength of the exchange interaction decreasing exponentially with qubit distance. Valley leakage is modeled through a dissipation term $\gamma$ as appropriate for the experimentally observed intervalley tunneling effect. We show that randomness in the valley leakage parameter has little to no effect on the SWAP gate fidelity in the currently fabricated Si circuits. We introduce disorder in the forms of charge noise and gate timing error and average the fidelities of 10,000 calculations for each set of parameters. The fidelities are then plotted against $J_\text{SWAP}$ , the strength of the exchange coupling corresponding to the SWAP gate. We find that valley leakage decreases the fidelity of the SWAP operation -- though the effect is small compared to that of the known charge noise -- and that gate timing error creates an effective optimal value of $J_\text{SWAP}$ , beyond which infidelity begins to increase.We investigate the fidelity of a sequence of SWAP gates on a Si-based quantum dot (QD) spin qubit chain. We particularly examine how valley leakage and gate timing error affect the gate fidelity compared to charge noise, which is always present. In our Hamiltonian, each qubit is coupled via Heisenberg exchange to every other qubit in the chain, with the strength of the exchange interaction decreasing exponentially with qubit distance. Valley leakage is modeled through a dissipation term $\gamma$ as appropriate for the experimentally observed intervalley tunneling effect. We show that randomness in the valley leakage parameter has little to no effect on the SWAP gate fidelity in the currently fabricated Si circuits. We introduce disorder in the forms of charge noise and gate timing error and average the fidelities of 10,000 calculations for each set of parameters. The fidelities are then plotted against $J_\text{SWAP}$, the strength of the exchange coupling corresponding to the SWAP gate. We find that valley leakage decreases the fidelity of the SWAP operation -- though the effect is small compared to that of the known charge noise -- and that gate timing error creates an effective optimal value of $J_\text{SWAP}$, beyond which infidelity begins to increase.

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The effect of valley splitting on the readout of qubit states is theoretically investigated in a three-quantum-dot (QD) system. A single unit of the three-QD system consists of qubit-QDs and a channel-QD that is connected to a conventional transistor. The nonlinear source–drain current characteristics under resonant-tunneling effects are used to distinguish different qubit states. Using nonequilibrium Green functions, the current formula for the three-QD system is derived when each QD has two valley energy levels. Two valley states in each QD are considered to be affected by variations in the fabrication process. We found that when valley splitting is smaller than Zeeman splitting, the current nonlinearity can improve the readout, provided that the nonuniformity of the valley energy levels is small. Conversely, when the valley splitting is larger than the Zeeman splitting, the nonuniformity degraded the readout. In both cases, we showed that there are regions where the measurement time tmeas is much less than the decoherence time tdec such that tdec/tmeas>100. This suggests that less than 1% measurement error is anticipated, which opens up the possibility of implementing surface codes even in the presence of valley splitting.The effect of valley splitting on the readout of qubit states is theoretically investigated in a three-quantum-dot (QD) system. A single unit of the three-QD system consists of qubit-QDs and a channel-QD that is connected to a conventional transistor. The nonlinear source–drain current characteristics under resonant-tunneling effects are used to distinguish different qubit states. Using nonequilibrium Green functions, the current formula for the three-QD system is derived when each QD has two valley energy levels. Two valley states in each QD are considered to be affected by variations in the fabrication process. We found that when valley splitting is smaller than Zeeman splitting, the current nonlinearity can improve the readout, provided that the nonuniformity of the valley energy levels is small. Conversely, when the valley splitting is larger than the Zeeman splitting, the nonuniformity degraded the readout. In both cases, we showed that there are regions where the measurement time tmeas is much less than the decoherence time tdec such that tdec/tmeas>100. This suggests that less than 1% measurement error is anticipated, which opens up the possibility of implementing surface codes even in the presence of valley splitting.

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arXiv:2308.11308Physical Review ResearchFeb 9, 202411 citations

\gamma

as appropriate for the experimentally observed intervalley tunneling effect. We show that randomness in the valley leakage parameter has little to no effect on the SWAP gate fidelity in the currently fabricated Si circuits. We introduce disorder in the forms of charge noise and gate timing error and average the fidelities of 10,000 calculations for each set of parameters. The fidelities are then plotted against

J_\text{SWAP}

, the strength of the exchange coupling corresponding to the SWAP gate. We find that valley leakage decreases the fidelity of the SWAP operation -- though the effect is small compared to that of the known charge noise -- and that gate timing error creates an effective optimal value of

J_\text{SWAP}

, beyond which infidelity begins to increase.

>97%

in the simulated Si-MOS devices at a typical TLF density of ${10}^{11}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. We also find that exchange driven two-qubit SWAP gates show higher sensitivity to charge noise with fidelities down to

91%

in the presence of the same density of TLFs. We further investigate the one- and two-qubit gate fidelities at different TLF densities. We find that given the small size of the quantum dots, sensitivity of a quantum gate to the distance between the noise sources and the quantum dot creates a strong variability in the quantum gate fidelities, which can compromise the device yields in scaled qubit technologies.

\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.