PaperlayerView exact revision on arXiv

Source-linked AI summary

Fast universal quantum control above the fault-tolerance threshold in silicon

Akito Noiri, Kenta Takeda, Takashi Nakajima, Takashi Kobayashi, Amir Sammak, Giordano Scappucci, Seigo Tarucha

arXiv:2108.02626v2quant-phcond-mat.mes-hall

TL;DR

Controlled-rotation gates can produce unwanted off-resonant target-qubit rotations when coupling is comparable to the Rabi frequency. The paper characterizes these gates and reports reproducibly greater than 99% two-qubit primitive gate fidelity around the charge-symmetry point.

Abstract

from arXiv · show

Fault-tolerant quantum computers which can solve hard problems rely on quantum error correction. One of the most promising error correction codes is the surface code, which requires universal gate fidelities exceeding the error correction threshold of 99 per cent. Among many qubit platforms, only superconducting circuits, trapped ions, and nitrogen-vacancy centers in diamond have delivered those requirements. Electron spin qubits in silicon are particularly promising for a large-scale quantum computer due to their nanofabrication capability, but the two-qubit gate fidelity has been limited to 98 per cent due to the slow operation.Here we demonstrate a two-qubit gate fidelity of 99.5 per cent, along with single-qubit gate fidelities of 99.8 per cent, in silicon spin qubits by fast electrical control using a micromagnet-induced gradient field and a tunable two-qubit coupling. We identify the condition of qubit rotation speed and coupling strength where we robustly achieve high-fidelity gates. We realize Deutsch-Jozsa and Grover search algorithms with high success rates using our universal gate set. Our results demonstrate the universal gate fidelity beyond the fault-tolerance threshold and pave the way for scalable silicon quantum computers.

Measurement setup.

The measurement setup combined millikelvin cooling with synchronized electrical and microwave control of silicon spin qubits. Microwave sideband modulation reduced unintended spin rotation and enabled rapid frequency switching.

Measurement setup

  • The sample was cooled to a base temperature of ∼20 mK, with an electron temperature of ∼60 mK, while filtered dc voltages and P1/P2 pulses controlled the gates.The setup used a 24-channel QDAC with an 800 Hz low-pass cutoff and a Tektronix AWG5014C for gate pulses.Source: Measurement setup · p. 12
  • EDSR microwave pulses were I/Q-modulated and applied to the bottom screening gate, with sidebands from -240 to 180 MHz used to suppress leakage-induced spin rotation and switch frequencies rapidly.Typical isolation after I/Q-imbalance and dc-offset calibration was ∼50 dBc; additional pulse modulations provided isolation during initialization and measurement.Source: Measurement setup · p. 12
  • Single-qubit Rabi frequencies were controlled by adjusting the amplitudes of the I/Q modulation signals.A second arbitrary waveform generator produced the I/Q signals and was triggered by the gate-pulse generator.Source: Measurement setup · p. 12

Sample fabrication.

The quantum dots are defined in an isotopically enriched silicon quantum well beneath overlapping aluminum gates, with a titanium–cobalt micromagnet above the gates.

Sample fabrication.

  • The quantum dots are defined in a silicon quantum well 50 nm below the wafer surface, with residual 29silicon concentration of 800 parts per million.Source: Sample fabrication · p. 12
  • Three overlapping aluminum gate layers are fabricated by electron-beam lithography and lift-off, with each layer insulated by native aluminum oxide [15].Source: Sample fabrication · p. 12
  • A 5-nm titanium and 250-nm cobalt micromagnet stack sits above the gates, separated by 30 nm of aluminum oxide; its design is similar to previous reports [8,19,27,40].Source: Sample fabrication · p. 12

Sequence fidelity and gate fidelity extraction in randomized benchmarking.

The section describes how randomized benchmarking extracts single- and two-qubit sequence fidelities and converts them to primitive-gate fidelities. It also outlines an interleaved procedure for estimating CNOT fidelity and a Monte Carlo method for its uncertainty.

Sequence fidelity and gate fidelity extraction in randomized benchmarking.

  • Single-qubit randomized benchmarking fits spin-up probabilities across Clifford-sequence lengths to a depolarizing decay with state-preparation and measurement offsets, then converts Clifford fidelity to primitive-gate fidelity.The procedure averages 16 random sequences, each repeated 400 times; a Clifford contains 1.875 primitive gates on average.Source: Sequence fidelity and gate fidelity… · pp. 12–13
  • Two-qubit randomized benchmarking averages 60 random sequences, each repeated 400 times, and converts two-qubit Clifford fidelity to primitive-gate fidelity using 2.57 primitive gates per Clifford.The recovery Clifford is chosen so the ideal final state is spin-up for both qubits.Source: Sequence fidelity and gate fidelity… · p. 13
  • CNOT fidelity is estimated by comparing depolarizing parameters from randomized Clifford sequences with and without a CNOT between each pair of random Clifford gates.The no-CNOT sequence provides the reference parameter, while the interleaved sequence provides the CNOT parameter.Source: Sequence fidelity and gate fidelity… · p. 13
  • Gate-fidelity errors are estimated by Monte Carlo sampling, fitting the resulting fidelity distribution with a Gaussian, and extracting its standard deviation.Source: Sequence fidelity and gate fidelity… · p. 13

Estimation of resonance frequencies fluctuations.

Repeated Ramsey measurements tracked the four resonance frequencies over time. The resulting analysis indicates that single-qubit frequency noise, rather than fluctuations in J, mostly limits dephasing times.

Estimation of resonance frequencies fluctuations.

  • Four resonance frequencies were estimated from 10,000 repeated Ramsey-measurement cycles using Bayesian estimation, with each cycle taking 1.706 s.Ramsey evolution times ranged from 0.04 µs to 4.0 µs in 0.04 µs steps; the frequency fluctuations were used to derive ΔJ/2 and the single-qubit frequency fluctuations Δf1 and Δf2.Source: Estimation of resonance frequencies… · pp. 13–14
  • Single-qubit frequency noise mostly limits dephasing times, because Δf_m is larger than ΔJ/2; J fluctuations therefore have no significant impact.The passage attributes this conclusion to the fluctuation of each resonance frequency being Δf_m,σ = Δf_m ± ΔJ/2.Source: Estimation of resonance frequencies… · p. 14

Theoretical description of controlled-rotation.

Controlled rotation arises from off-diagonal terms when one of four resonance frequencies is selected. The account identifies unwanted off-resonant target-qubit rotation when coupling J is comparable to the Rabi frequency f_R, and gives a frequency choice to avoid it.

Theoretical description of controlled-rotation.

  • Selecting one of f1,↓, f1,↑, f2,↓, or f2,↑ makes the off-diagonal terms produce a CROT gate.Terms oscillating much faster than f_R are averaged out during the π/2 CROT time t_hp = 1/(4f_R).Source: Theoretical description of… · p. 14
  • When J is comparable to f_R, terms oscillating at frequency J cause unwanted off-resonant rotation of the target qubit.The unwanted rotation occurs during the π/2 CROT time t_hp = 1/(4f_R).Source: Theoretical description of… · p. 14
  • f_R = J/√(16k^2 − 1), with integer k, is the chosen Rabi frequency.The passage cites [16,30] for this choice.Source: Theoretical description of… · p. 14

Simulation of two-qubit gate infidelity by quasi-static noise in resonance frequencies.

The section simulates two-qubit primitive-gate infidelity under quasi-static resonance-frequency noise and reports low infidelity around the optimal f_R = 4–5 MHz condition.

Simulation of two-qubit gate infidelity by quasi-static noise in resonance frequencies.

  • The simulation treats resonance-frequency noise as quasi-static during each 100 µs measurement but changing between measurements.It uses measured time dependence of ΔJ, ΔdẼZ = Δf2 − Δf1, and ΔEZ = (Δf1 + Δf2)/2.Source: Simulation of two-qubit gate… · p. 14
  • The authors extract primitive-gate infidelity by averaging 60 random Clifford sequences, each repeated 100 times with different noise values.In the simulation, J is fixed at √15 f_R.Source: Simulation of two-qubit gate… · p. 14
  • The simulated two-qubit primitive-gate infidelity is low around the optimal gate condition f_R = 4–5 MHz.The supplied passage does not include the numerical infidelity value.Source: Simulation of two-qubit gate… · p. 14, Figure 5b · p. 15

Additional information

The additional characterization shows that two-qubit primitive fidelity remains above 99% around charge symmetry but falls sharply at large detuning, mainly because of fast Rabi decay. It also documents qubit relaxation, gate-fidelity extraction, and algorithm output-state measurements.

Detuning dependence of EDSR spectra

  • At the charge-symmetry point, the EDSR-frequency detuning slope is finite due to the micromagnet-induced gradient field.Source: Additional information · p. 19

Qubits characterizations

Single-tone single-qubit gate performance

  • Single-tone single-qubit gate fidelities are best at fR = 2–5 MHz and are consistent with the fidelities obtained in Fig. 2c.The Rabi-frequency dependence was assessed at fixed J = 32.0 MHz.Source: Figure 3 · p. 22, Additional information · p. 22

Two-qubit gate fidelity extraction

  • The alternate sequence-fidelity extraction gives Ft(271) = −0.007 and agrees with the standard protocol using data up to n = 62.The alternate method uses a final ideal spin-down state for both qubits; the standard extraction relies on saturation of P↑↑ at large n.Source: Figure 4 · p. 23, Additional information · p. 23

Estimation of two-qubit primitive gate infidelity by resonance frequency noise

  • Two-qubit primitive gate infidelity was estimated from resonance-frequency noise, with Δf1 and Δf2 larger than exchange noise ΔJ/2 at J = 18.85 MHz.Simulations also examined inserting idle time to remove controlled-phase accumulation during CROT when switching J on and off.Source: Figure 5 · p. 24, Additional information · p. 24

Detuning dependence of the two-qubit gate performance

  • Around charge symmetry, two-qubit primitive gate fidelity reproducibly exceeds 99%; at large positive and negative detuning, it sharply drops mainly due to fast Rabi decay.The charge-symmetry point is at detuning = 0 mV, where J = 18.85 MHz.Source: Figure 6 · p. 25, Additional information · p. 25

Output state of Deutsch–Jozsa algorithm and Grover search algorithm

  • The measured algorithm output-state density matrices have imaginary-part element magnitudes below 0.055, 0.056, 0.040, 0.111, 0.072, and 0.081 for f0, f1, f3, f10, f01, and f00, respectively.Source: Figure 8 · p. 27, Additional information · p. 27

Related papers

Loading 2108.02626v2…