Abstract
Fault-tolerant quantum computing requires initializing the quantum register in a well-defined fiducial state. In solid-state systems, this is typically achieved through thermalization to a cold reservoir, such that the initialization fidelity is fundamentally limited by temperature. Here, we present a method of preparing a fiducial quantum state with a confidence beyond the thermal limit. It is based on real-time monitoring of the qubit through a negative-result measurement—the equivalent of a “Maxwell’s demon” that triggers the experiment only upon the appearance of a qubit in the lowest-energy state. We experimentally apply it to initialize an electron spin qubit in silicon, achieving a ground-state initialization fidelity of 98.9(4)%, corresponding to a reduction in initialization error compared to the unmonitored system. A fidelity approaching 99.9% could be achieved with realistic improvements in the bandwidth of the amplifier chain or by slowing down the rate of electron tunneling from the reservoir. We use a nuclear spin ancilla, measured in quantum nondemolition mode, to prove the value of the electron initialization fidelity far beyond the intrinsic fidelity of the electron readout. However, the method itself does not require an ancilla for its execution, saving the need for additional resources. The quantitative analysis of the initialization fidelity reveals that a simple picture of spin-dependent electron tunneling does not correctly describe the data. Our digital Maxwell’s demon can be applied to a wide range of quantum systems, with minimal demands on control and detection hardware.
- Received 20 December 2021
- Revised 31 May 2022
- Accepted 19 September 2022
DOI:https://doi.org/10.1103/PhysRevX.12.041008
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Quantum computers promise to solve certain tasks that are otherwise intractable on a classical computer, on the condition that they have sufficiently low error rates to admit fault-tolerant operation. For many types of semiconductor and superconductor qubits, “state preparation and measurement” errors are the greatest hindrance to meeting these requirements. Here, we demonstrate a drastic improvement in qubit initialization fidelity by borrowing ideas from the classic Maxwell’s demon paradox.
Maxwell’s demon is an imagined, omniscient being that appears to beat the second law of thermodynamics by using its knowledge to separate the cold particles from the hot ones in a gas. Here, we start with an electron drawn from a cold charge reservoir via energy-dependent tunneling. The nonzero reservoir temperature would normally cause a 20% probability of drawing an electron in the wrong, high-energy initial state. We then apply our “demon”—a real-time electronic triggering system that monitors the signal from a detector, set up to give a click if the drawn electron is in a high-energy spin state. In the absence of a click, the demon becomes increasingly confident that the chosen electron is in the low-energy state and decides to accept it as a qubit in the “0” state, from which further quantum logic can be reliably performed.
Our method achieves an initialization fidelity of 99%, compatible with fault-tolerant quantum operations, while starting from a native, thermally limited fidelity of 80%. This represents a 20-fold reduction in qubit preparation error, without requiring additional quantum resources such as auxiliary qubits. The method delivers a high-confidence 0 state in real time and in every run, eliminating the need to weed out wrong initial states through postselection data analysis.
We anticipate that this electronic Maxwell’s demon will greatly facilitate the achievement of fault-tolerant quantum computing in the near term.
