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Register a new userHigh-fidelity and robust two-qubit gates for quantum-dot spin qubits in silicon
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A two-qubit controlled-NOT (CNOT) gate, realized by a controlled-phase (C-phase) gate combined with single-qubit gates, has been experimentally implemented recently for quantum-dot spin qubits in isotopically enriched silicon, a promising solid-state system for practical quantum computation. In the experiments, the single-qubit gates have been demonstrated with fault-tolerant control-fidelity, but the infidelity of the two-qubit C-phase gate is, primarily due to the electrical noise, still higher than the required error threshold for fault-tolerant quantum computation (FTQC). Here, by taking the realistic system parameters and the experimental constraints on the control pulses into account, we construct experimentally realizable high-fidelity CNOT gates robust against electrical noise with the experimentally measured $1/f^{1.01}$ noise spectrum and also against the uncertainty in the interdot tunnel coupling amplitude. Our optimal CNOT gate has about two orders of magnitude improvement in gate infidelity over the ideal C-phase gate constructed without considering any noise effect. Furthermore, within the same control framework, high-fidelity and robust single-qubit gates can also be constructed, paving the way for large-scale FTQC.
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The flip-flop qubit, encoded in the states with antiparallel donor-bound electron and donor nuclear spins in silicon, showcases long coherence times, good controllability, and, in contrast to other donor-spin-based schemes, long-distance coupling. Electron spin control near the interface, however, is likely to shorten the relaxation time by many orders of magnitude, reducing the overall qubit quality factor. Here, we theoretically study the multilevel system that is formed by the interacting electron and nuclear spins and derive analytical effective two-level Hamiltonians with and without periodic driving. We then propose an optimal control scheme that produces fast and robust single-qubit gates in the presence of low-frequency noise and relatively weak magnetic fields without relying on parametrically restrictive sweet spots. This scheme increases considerably both the relaxation time and the qubit quality factor.
Implementing high-fidelity two-qubit gates in single-electron spin qubits in silicon double quantum dots is still a major challenge. In this work, we employ analytical methods to design control pulses that generate high-fidelity entangling gates for quantum computers based on this platform. Using realistic parameters and initially assuming a noise-free environment, we present simple control pulses that generate CNOT, CPHASE, and CZ gates with average fidelities greater than 99.99% and gate times as short as 45 ns. Moreover, using the local invariants of the systems evolution operator, we show that a simple square pulse generates a CNOT gate in less than 27 ns and with a fidelity greater than 99.99%. Last, we use the same analytical methods to generate two-qubit gates locally equivalent to $sqrt{mathrm{CNOT}}$ and $sqrt{mathrm{CZ}}$ that are used to implement simple two-piece pulse sequences that produce high-fidelity CNOT and CZ gates in the presence of low-frequency noise.
Significant experimental advances in single-electron silicon spin qubits have opened the possibility of realizing long-range entangling gates mediated by microwave photons. Recently proposed iSWAP gates, however, require tuning qubit energies into resonance and have limited fidelity due to charge noise. We present a novel photon-mediated cross-resonance gate that is consistent with realistic experimental capabilities and requires no resonant tuning. Furthermore, we propose gate sequences capable of suppressing errors due to quasistatic noise for both the cross-resonance and iSWAP gates.
Universal quantum computation will require qubit technology based on a scalable platform, together with quantum error correction protocols that place strict limits on the maximum infidelities for one- and two-qubit gate operations. While a variety of qubit systems have shown high fidelities at the one-qubit level, superconductor technologies have been the only solid-state qubits manufactured via standard lithographic techniques which have demonstrated two-qubit fidelities near the fault-tolerant threshold. Silicon-based quantum dot qubits are also amenable to large-scale manufacture and can achieve high single-qubit gate fidelities (exceeding 99.9%) using isotopically enriched silicon. However, while two-qubit gates have been demonstrated in silicon, it has not yet been possible to rigorously assess their fidelities using randomized benchmarking, since this requires sequences of significant numbers of qubit operations ($gtrsim 20$) to be completed with non-vanishing fidelity. Here, for qubits encoded on the electron spin states of gate-defined quantum dots, we demonstrate Bell state tomography with fidelities ranging from 80% to 89%, and two-qubit randomized benchmarking with an average Clifford gate fidelity of 94.7% and average Controlled-ROT (CROT) fidelity of 98.0%. These fidelities are found to be limited by the relatively slow gate times employed here compared with the decoherence times $T_2^*$ of the qubits. Silicon qubit designs employing fast gate operations based on high Rabi frequencies, together with advanced pulsing techniques, should therefore enable significantly higher fidelities in the near future.
Quantum system characterization techniques represent the front line in the identification and mitigation of noise in quantum computing, but can be expensive in terms of quantum resources and time to repeatedly employ. Another challenging aspect is that parameters governing the performance of various operations tend to drift over time, and monitoring these is hence a difficult task. One of the most promising characterization techniques, gate set tomography (GST), provides a self-consistent estimate of the completely positive, trace-preserving (CPTP) maps for a complete set of gates, as well as preparation and measurement operators. We develop a method for performance optimization seeded by tomography (POST), which couples the power of GST with a classical optimization routine to achieve a consistent gate improvement in just a short number of steps within a given calibration cycle. By construction, the POST procedure finds the best available gate operation given the hardware, and is therefore robust to the effects of drift. Further, in comparison to other quantum error mitigation techniques, it builds upon a one-time application of GST. To demonstrate the performance of this method on a real quantum computer, we map out the operations of six qubit pairs on the superconducting emph{ibmq_poughkeepsie} quantum device. Under the restriction of logical-only control, we monitor the performance of the POST approach on a chosen CNOT gate over a period of six weeks. In this time, we achieve a consistent improvement in gate fidelity, averaging a fidelity increase of 21.1% as measured by randomized benchmarking. The POST approach should find wide applicability as it is hardware agnostic, and can be applied at the upper logical level or at a deeper pulse control level.
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