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

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

Published Oct 21, 2021• 0 citations
OpenAlex

Abstract

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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In recent advancements of quantum computing utilizing spin qubits, it has been demonstrated that this platform possesses the potential for implementing two-qubit gates with fidelities exceeding 99.5%. However, as with other qubit platforms, it is not feasible to completely turn qubit couplings off. This study aims to investigate the impact of coherent error matrices in gate set tomography by employing a double quantum dot. We evaluate the infidelity caused by residual exchange between spins and compare various mitigation approaches, including the use of adjusted timing through simple drives, considering different parameter settings in the presence of charge noise. Furthermore, we extend our analysis to larger arrays of exchange-coupled spin qubits to provide an estimation of the expected fidelity. In particular, we demonstrate the influence of residual exchange on a single-qubit Y gate and the native two-qubit SWAP gate in a linear chain. Our findings emphasize the significance of accounting for residual exchange when scaling up spin-qubit devices and highlight the tradeoff between the effects of charge noise and residual exchange in mitigation techniques. Published by the American Physical Society 2024

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Fidelity of a sequence of SWAP operations on a spin chain

Robert E. Throckmorton, S. Das Sarma

We consider the ``transport'' of the state of a spin across a Heisenberg-coupled spin chain via the use of repeated SWAP gates, starting with one of two states---one in which the leftmost spin is down and the others up, and one in which the leftmost two spins are in a singlet state (i.e., they are entangled), and the others are again all up. More specifically, we transport the state of the leftmost spin in the first case and the next-to-leftmost spin in the second to the other end of the chain, and then back again. We accomplish our SWAP operations here by increasing the exchange coupling between the two spins that we operate on from a base value $J$ to a larger value ${J}_{\text{SWAP}}$ for a time $t=\ensuremath{\pi}\ensuremath{\hbar}/4{J}_{\text{SWAP}}$. We determine the fidelity of this sequence of operations in a number of situations---one in which only nearest-neighbor coupling exists between spins and there is no magnetic dipole-dipole coupling or noise (the most ideal case), one in which we introduce next-nearest-neighbor coupling, but none of the other effects, and one in which all of these effects are present. In the last case, the noise is assumed to be quasistatic, i.e., the exchange couplings are each drawn from a Gaussian distribution, truncated to only nonnegative values. We plot the fidelity as a function of ${J}_{\text{SWAP}}$ to illustrate various effects, namely crosstalk due to coupling to other spins, as well as noise, that are detrimental to our ability to perform a SWAP operation. Our theory should be useful to the ongoing experimental efforts in building semiconductor-based spin quantum computer architectures.

arXiv:2004.04746•Physical review. B./Physical review. B•Jul 27, 2020•6 citations
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 γ\gammaγ 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 JSWAPJ_\text{SWAP}JSWAP​, 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 JSWAPJ_\text{SWAP}JSWAP​, beyond which infidelity begins to increase.
We examine how dissipation and gate timing errors affect the fidelity of a sequence of swap gates on a chain of interacting qubits in comparison to noise in the interqubit interaction. Although interqubit interaction noise and gate timing errors are always present in any qubit platform, dissipation is a special case that can arise in multivalley semiconductor spin qubit systems, such as Si-based qubits, where dissipation may be used as a general model for valley leakage. 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 distance between the qubits. Dissipation is modeled through the term $\ensuremath{-}i\ensuremath{\gamma}\mathbf{1}$ in the Hamiltonian, and $\ensuremath{\gamma}$ is chosen so as to be consistent with the experimentally observed intervalley tunneling in Si. We show that randomness in the dissipation parameter should have little to no effect on the swap gate fidelity in the currently fabricated Si circuits. We introduce quasistatic noise in the interqubit interaction and random gate timing error and average the fidelities over 10 000 realizations for each set of parameters. The fidelities are then plotted against JSWAP{J}_{\mathrm{SWAP}}JSWAP​, the strength of the exchange coupling corresponding to the swap gate. We find that dissipation decreases the fidelity of the swap operation---though the effect is small compared to that of the known noise in the interqubit interaction---and that gate timing error creates an effective optimal value of JSWAP{J}_{\mathrm{SWAP}}JSWAP​, beyond which infidelity begins to increase.
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.
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 i\mathrm{i}iswap 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 i\mathrm{i}iswap 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.
The spin of an electron confined in semiconductor quantum dots is currently a promising candidate for quantum bit (qubit) implementations. Taking advantage of the existing CMOS integration technologies, such devices can offer a platform for large scale quantum computation. However, a quantum mechanical framework bridging a device's physical design and operational parameters to the qubit's energy space is lacking. Furthermore, the spin to charge coupling introduced by intrinsic or induced spin-orbit interaction (SOI) exposes the qubits to charge noise compromising their coherence properties and inducing quantum gate errors. We present here a comodeling framework for double quantum dot (DQD) devices and their charge noise environments. We use a combination of an electrostatic potential solver, full configuration interaction quantum mechanical methods, and two-level-fluctuator models to study the quantum gate performance in realistic device designs and operation conditions. We utilize the developed models together alongside the single electron solutions of the quantum dots to simulate one- and two-qubit gates in the presence of charge noise. We find an inverse correlation between quantum gate errors and quantum dot confinement frequencies. We calculate X-gate fidelities >97>97%>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 9191%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.
In recent advancements of quantum computing utilizing spin qubits, it has been demonstrated that this platform possesses the potential for implementing two-qubit gates with fidelities exceeding 99.5%. However, as with other qubit platforms, it is not feasible to completely turn qubit couplings off. This study aims to investigate the impact of coherent error matrices in gate set tomography by employing a double quantum dot. We evaluate the infidelity caused by residual exchange between spins and compare various mitigation approaches, including the use of adjusted timing through simple drives, considering different parameter settings in the presence of charge noise. Furthermore, we extend our analysis to larger arrays of exchange-coupled spin qubits to provide an estimation of the expected fidelity. In particular, we demonstrate the influence of residual exchange on a single-qubit Y gate and the native two-qubit SWAP gate in a linear chain. Our findings emphasize the significance of accounting for residual exchange when scaling up spin-qubit devices and highlight the tradeoff between the effects of charge noise and residual exchange in mitigation techniques. Published by the American Physical Society 2024
We consider the ``transport'' of the state of a spin across a Heisenberg-coupled spin chain via the use of repeated SWAP gates, starting with one of two states---one in which the leftmost spin is down and the others up, and one in which the leftmost two spins are in a singlet state (i.e., they are entangled), and the others are again all up. More specifically, we transport the state of the leftmost spin in the first case and the next-to-leftmost spin in the second to the other end of the chain, and then back again. We accomplish our SWAP operations here by increasing the exchange coupling between the two spins that we operate on from a base value JJJ to a larger value JSWAP{J}_{\text{SWAP}}JSWAP​ for a time $t=\ensuremath{\pi}\ensuremath{\hbar}/4{J}_{\text{SWAP}}$. We determine the fidelity of this sequence of operations in a number of situations---one in which only nearest-neighbor coupling exists between spins and there is no magnetic dipole-dipole coupling or noise (the most ideal case), one in which we introduce next-nearest-neighbor coupling, but none of the other effects, and one in which all of these effects are present. In the last case, the noise is assumed to be quasistatic, i.e., the exchange couplings are each drawn from a Gaussian distribution, truncated to only nonnegative values. We plot the fidelity as a function of JSWAP{J}_{\text{SWAP}}JSWAP​ to illustrate various effects, namely crosstalk due to coupling to other spins, as well as noise, that are detrimental to our ability to perform a SWAP operation. Our theory should be useful to the ongoing experimental efforts in building semiconductor-based spin quantum computer architectures.