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arXiv:2312.15493 · Physical review. B./Physical review. B

Measurement-based entanglement of semiconductor spin qubits

Remy L. Delva, Jonas Mielke, Guido Burkard, J. R. Petta

Published Jul 16, 2024• 3 citations
arXivHTMLPDF

Abstract

Measurement-based entanglement (MBE) is a method for entangling quantum systems through the state projection that accompanies a parity measurement. We derive a stochastic master equation describing measurement-based entanglement of a pair of silicon double-dot flopping-mode spin qubits, develop numerical simulations to model this process, and explore what modifications could enable an experimental implementation of such a protocol. With device parameters corresponding to current qubit and cavity designs, we predict an overlap of the final state of the MBE protocol with the target Bell state $|{\mathrm{\ensuremath{\Psi}}}_{+}\ensuremath{\rangle}$ of $\ensuremath{\approx}61%$. By increasing the cavity outcoupling rate by a factor of 10, we are able to obtain an improvement of this metric to $\ensuremath{\approx}81%$ while maintaining a yield of 33%.

DOI
10.1103/physrevb.110.035304

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A measurement-based quantum feedback protocol is developed for spin-state initialization in a gate-defined double quantum dot spin qubit coupled to a superconducting cavity. The protocol improves qubit state initialization as it is able to robustly prepare the spin in shorter time and reach a higher fidelity, which can be preset. Being able to preset the fidelity aimed at is a highly desired feature enabling qubit initialization to be more deterministic. The protocol developed herein is also effective at high temperatures, which is critical for the current efforts toward scaling up the number of qubits in quantum computers.
We present efficient methods to reliably characterize and tune gate-defined semiconductor spin qubits. Our methods are developed for double quantum dots in GaAs heterostructures, but they can easily be adapted to other quantum-dot-based qubit systems. These tuning procedures include the characterization of the interdot tunnel coupling, the tunnel coupling to the surrounding leads, and the identification of various fast initialization points for the operation of the qubit. Since semiconductor-based spin qubits are compatible with standard semiconductor process technology and hence promise good prospects of scalability, the challenge of efficiently tuning the dot’s parameters will only grow in the near future, once the multiqubit stage is reached. With the anticipation of being used as the basis for future automated tuning protocols, all measurements presented here are fast-to-execute and easy-to-analyze characterization methods. They result in quantitative measures of the relevant qubit parameters within a couple of seconds and require almost no human interference.
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Universal quantum computation requires single-qubit control together with at least one entangling two-qubit gate. CNOT and CROT gates are two famous examples of such gates, wherein the state of one qubit (control) dictates the transformation applied to the other (target). By using a simple derivation motivated by symmetry, we show that current device architectures of semiconductor-based quantum dot devices prevent efficient implementation of a CNOT and other asymmetric control-target gates via Heisenberg exchange, Coulomb repulsion, or other interaction that is invariant under spin exchange. Guided by this general principle, we propose a heterogeneous blueprint of double quantum dot devices that enables efficient implementation of the CNOT by breaking the spin exchange symmetry. Crucially, our numerical simulations predict that this novel device blueprint can enable a single-pulse fault-tolerant 100-ns CNOT gate in isotopically purified silicon.
Quantum computers leverage entanglement to achieve superior computational power. However, verifying that the entangled state does not follow the principle of local causality has proven difficult for spin qubits in gate-defined quantum dots, as it requires simultaneously high concurrence values and readout fidelities to break the classical bound imposed by Bell’s inequality. While low error rates for state preparation, control, and measurement have been independently demonstrated, a simultaneous demonstration remained challenging. We employ advanced protocols like heralded initialization and calibration via gate set tomography (GST), to push fidelities of the full 2-qubit gate set above 99%, including state preparation and measurement (SPAM). We demonstrate a 97.17% Bell state fidelity without correcting for readout errors and violate Bell’s inequality using direct parity readout with a Bell signal of S = 2.731. Our measurements exceed the classical limit even at 1.1 K or entanglement lifetimes of 100 μs. Violating Bell’s inequality in a silicon quantum dot qubit system is a key milestone, as it proves quantum entanglement, fundamental to achieving quantum advantage. Silicon-based spin qubits are promising candidates for a scalable quantum computer. Here the authors demonstrate the violation of Bell’s inequality in gate-defined quantum dots in silicon, marking a significant advancement that showcases the maturity of this platform.