High-Fidelity State Preparation, Quantum Control, and Readout of an Isotopically Enriched Silicon Spin Qubit
Adam Mills, Charles R. Guinn, Mayer M. Feldman, Anthony J. Sigillito, Michael J. Gullans, Matthew T. Rakher, Joseph Kerckhoff, Clayton A. C. Jackson, J. R. Petta
Quantum systems must be prepared, controlled, and measured with high fidelity in order to perform complex quantum algorithms. Control fidelities have greatly improved in silicon spin qubits but state-preparation and readout fidelities have generally been poor. By operating with low electron temperatures and employing high-bandwidth cryogenic amplifiers, we demonstrate single-qubit readout visibilities $>99\mathrm{%}$, exceeding the threshold for quantum error correction. In the same device, we achieve average single-qubit control fidelities $>99.95\mathrm{%}$. Our results show that silicon spin qubits can be operated with high overall operation fidelity.
Quantum systems must be prepared, controlled, and measured with high fidelity in order to perform complex quantum algorithms. Control fidelities have greatly improved in silicon spin qubits but state-preparation and readout fidelities have generally been poor. By operating with low electron temperatures and employing high-bandwidth cryogenic amplifiers, we demonstrate single-qubit readout visibilities >99\mathrm{%}, exceeding the threshold for quantum error correction. In the same device, we achieve average single-qubit control fidelities >99.95\mathrm{%}. Our results show that silicon spin qubits can be operated with high overall operation fidelity.
Silicon spin qubits satisfy the necessary criteria for quantum information processing. However, a demonstration of high-fidelity state preparation and readout combined with high-fidelity single- and two-qubit gates, all of which must be present for quantum error correction, has been lacking. We use a two-qubit Si/SiGe quantum processor to demonstrate state preparation and readout with fidelity greater than 97%, combined with both single- and two-qubit control fidelities exceeding 99%. The operation of the quantum processor is quantitatively characterized using gate set tomography and randomized benchmarking. Our results highlight the potential of silicon spin qubits to become a dominant technology in the development of intermediate-scale quantum processors.
Abstract Among the many types of qubit presently being investigated for a future quantum computer, silicon spin qubits with millions of qubits on a single chip are uniquely positioned to enable quantum computing. However, it has not been clear whether the outstanding high-fidelity operations and long coherence times shown by silicon spin qubits fabricated in academic settings 1–8 can be reliably reproduced when the qubits are manufactured in a semiconductor foundry 9–11 . Here we show precise qubit operation of silicon two-qubit devices made with standard semiconductor tooling in a 300-mm foundry environment. Of the key metrics, single- and two-qubit control fidelities exceed 99% for all four devices, and the state preparation and measurement fidelities reach up to 99.9%, as evidenced by gate set tomography. We report spin lifetime and coherence up to T 1 = 9.5 s, T2∗=40.6μs T 2 * = 40.6 μ s and T2Hahn=1.9ms T 2 Hahn = 1.9 ms . We determine that residual nuclear spin-carrying isotopes contribute substantially to operational errors, identifying further isotopic purification as a clear pathway to even higher performance.
Abstract Universal quantum computation will require qubit technology based on a scalable platform1, together with quantum error correction protocols that place strict limits on the maximum infidelities for one- and two-qubit gate operations2, 3. Although various qubit systems have shown high fidelities at the one-qubit level4–10, the only solid-state qubits manufactured using standard lithographic techniques that have demonstrated two-qubit fidelities near the fault-tolerance threshold6 have been in superconductor systems. Silicon-based quantum dot qubits are also amenable to large-scale fabrication and can achieve high single-qubit gate fidelities (exceeding 99.9 per cent) using isotopically enriched silicon11, 12. Two-qubit gates have now been demonstrated in a number of systems13–15, but as yet an accurate assessment of their fidelities using Clifford-based randomized benchmarking, which uses sequences of randomly chosen gates to measure the error, has not been achieved. 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 per cent, and two-qubit randomized benchmarking with an average Clifford gate fidelity of 94.7 per cent and an average controlled-rotation fidelity of 98 per cent. These fidelities are found to be limited by the relatively long gate times used here compared with the decoherence times of the qubits. Silicon qubit designs employing fast gate operations with high Rabi frequencies16, 17, together with advanced pulsing techniques18, should therefore enable much higher fidelities in the near future.
Semiconducting qubits are a promising platform for quantum computers. In particular, silicon spin qubits have made a number of advancements recently including long coherence times, high-fidelity single-qubit gates, two-qubit gates, and high-fidelity readout. However, all operations likely require improvement in fidelity and speed, if possible, to realize a quantum computer. Readout fidelity and speed, in general, are limited by circuit challenges centered on extracting low signal from a device in a dilution refrigerator connected to room temperature amplifiers by long coaxial cables with relatively high capacitance. Readout fidelity specifically is limited by the time it takes to reliably distinguish qubit states relative to the characteristic decay time of the excited state, T1. This dissertation explores the use of heterojunction bipolar transistor (HBT) circuits to amplify the readout signal of silicon spin qubits at cryogenic temperatures. The cryogenic amplification approach has numerous advantages including low implementation overhead, low power relative to the available cooling power, and high signal gain at the mixing chamber stage leading to around a factor of ten speedup in readout time for a similar signal-to-noise ratio. The faster readout time generally increases fidelity, since it is much faster than the T1 time. Two HBT amplification circuits have been designed and characterized. One design is a low-power, base-current biased configuration with non-linear gain (CB-HBT), and the second is a linear-gain, AC-coupled configuration (AC-HBT). They can operate at powers of 1 and 10 μW, respectfully, and not significantly heat electrons. The noise spectral density referred to the input for both circuits is around 15 to 30 fA/√Hz, which is low compared to previous cases such as the dual-stage, AC-coupled HEMT circuit at ~ 70 fA/√Hz. Both circuits achieve charge sensitivity between 300 and 400 μe/√Hz, which approaches the best alternatives (e.g., RF-SET at ~ 140 μe/√Hz) but with much less implementation overhead. For the single-shot latched charge readout performed, both circuits achieve high-fidelity readout in times < 10 μs with bit error rates < 10-3, which is a great improvement over previous work at > 70 μs. The readout speed-up in principle also reduces the production of errors due to excited state relaxation by a factor of ~ 10. All of these results are possible with relatively simple, low-power transistor circuits which can be mounted close to the qubit device at the mixing chamber stage of the dilution refrigerator.
While single-shot detection of silicon spin qubits is now a laboratory routine, the need for quantum error correction in a large-scale quantum computing device demands a quantum non-demolition (QND) implementation. Unlike conventional counterparts, the QND spin readout imposes minimal disturbance to the probed spin polarization and can therefore be repeated to extinguish measurement errors. Here, we show that an electron spin qubit in silicon can be measured in a highly non-demolition manner by probing another electron spin in a neighboring dot Ising-coupled to the qubit spin. The high non-demolition fidelity (99% on average) enables over 20 readout repetitions of a single spin state, yielding an overall average measurement fidelity of up to 95% within 1.2 ms. We further demonstrate that our repetitive QND readout protocol can realize heralded high-fidelity (>99.6%) ground-state preparation. Our QND-based measurement and preparation, mediated by a second qubit of the same kind, will allow for a wide class of quantum information protocols with electron spins in silicon without compromising the architectural homogeneity.
Electron spins in silicon quantum dots are a promising platform for fault-tolerant quantum computing. Low-frequency noise, including nuclear spin fluctuations and charge noise, is a primary factor limiting gate fidelities. Suppressing this noise is crucial for high-fidelity qubit operations. Here, we report on a two-qubit quantum device in natural silicon with universal qubit control, designed to investigate the upper limits of gate fidelities in a non-purified Si/SiGe quantum dot device. By employing advanced device structures, qubit manipulation techniques, and optimization methods, we have achieved single-qubit gate fidelities exceeding 99% and a two-qubit controlled-Z (CZ) gate fidelity of 91%. Decoupled CZ gates are used to prepare Bell states with an average fidelity of 91%, typically exceeding previously reported values in natural silicon devices. These results underscore that even natural silicon has the potential to achieve high-fidelity gate operations, particularly with further optimization methods to suppress low-frequency noise.