Neutral-atom quantum computing moves toward an era of fault tolerance Corrective coding achieves high fault tolerance threshold
Executing quantum algorithms on error-corrected logical quantum bits is a key step in scalable quantum computing, but the necessary number of quantum bits, and the physical error rate are very demanding for current experimental hardware. Therefore, the development of error-correcting codes for specific physical noise models can help relax these requirements.
Yue Wu
The first author of the paper is Yue Wu, a Chinese national and current PhD student at Yale University. 2020 graduate of Peking University.
01An important step in fault-tolerant quantum computing - correction and deletion
Scalable, general-purpose quantum computers have the potential to outperform classical computers in a range of tasks. However, the inherent fragility of quantum states, and the limited fidelity of physical quantum bit manipulation make errors inevitable. Quantum error correction allows multiple physical quantum bits to represent a logical quantum bit - if logical quantum bit operations are implemented in an error-tolerant manner, then the logical error rate can be arbitrarily suppressed as long as the error probability during each operation is below a threshold.
The threshold error rate depends on the choice of error correction code and the nature of the noise in the physical quantum bit. For example, a quantum bit encoded with a cat state in a superconducting resonator can have a strong bias noise that leads to a significantly higher threshold.
Another type of error is corrective deletion (erasure), which indicates an error at a known location. In both classical and quantum computing devices, corrective deletion is significantly easier to correct than depolarization errors. For example, a quantum code of four quantum bits is sufficient to correct an erasure error with a surface code threshold close to 50%. Corrective errors also arise naturally in optical quantum bits: if a quantum bit is encoded in the polarization or path of a single photon, then no photon detection will signal a corrective deletion, allowing effective error correction for quantum communication and linear optical quantum computing.
In this work, the team proposes a way to perform error-tolerant quantum computing in a Reedeburg atomic array - converting most of the errors that occur naturally to correcting deletions. There are two key components to this work: First, a physical model of quantum bits encoded in a specific atom 171Yb is proposed that enables corrective censoring conversions without additional gates or auxiliary quantum bits. By encoding the quantum bits in a metastable electronic level hyperfine state, the vast majority of errors can be transferred from the computational subspace to the energy level subspace, so that the location of these errors can be revealed. At this point, a fraction of the errors can be detected in this way; the team then simulated the benefits of the corrective censoring transition at the circuit level using surface codes: compared to the pure depolarization error case, the corrective censoring transition leads to a significantly higher threshold, and the logic error rate below the threshold decreases much more quickly.
02Corrective conversion: Achieving below-threshold logic errors
A neutral-atom quantum computer captures, manipulates, and detects arrays of atomic quantum bits through light projected by a microscope objective. This experiment uses a 171Yb atom with quantum bits encoded at the energy level of F=1/26s6p3P0; at this point, the defined states |1⟩≡|mF=1/2⟩, |0⟩≡|mF=-1/2⟩. To perform a two-bit CZ gate, the state |1⟩ is experimentally coupled to a Reedeburg state |r⟩ with a Rabi frequency Ω.
The state |r⟩ can decay to a lower energy state (RD) by radiative decay or to a nearby Riedberg state (BBR) by translational decay. For such a Riedberg state, the team estimates that 61% of the decays are BBR, 34% are RD to ground state, and only 5% are RD to quantum space states. Thus, a total of 95% of the decays would occur outside of quantum space, and these errors need to be converted into corrective deletions and thus effectively detected.
Ultimately, the team concluded that the corrective-censored conversion can effectively detect a large fraction of the spontaneous decay errors.
To further check the performance of the censoring codes, the team performed Monte Carlo simulations using XZZX surface codes. In the case of the corrective censoring transformation, logical errors were significantly reduced: the logical error rate decreased with increasing distance d. The error tolerance threshold, defined as the physical error rate, increased by a factor of 4.4 from pth=0.937% to pth=4.15% during the experiment. In addition to increasing the threshold, the high percentage of error correction and deletion also leads to a rapid decrease in the logical error rate below the threshold.
Overview of a neutral-atom fault-tolerant quantum computer using censored conversion. a) Schematic diagram of a neutral-atom quantum computer; b) Physical quantum bits are single 171Yb atoms; c) XZZX surface code studied in this work; d) Quantum circuit representing a stabilizer (stabilizer) measurement on data quantum bits D1-D4 using auxiliary bit A1 with a censored conversion step. The censored conversion is performed after each gate operation, and the atoms that are censored are replaced from the storage with a removable optical tweezer as needed.
Gate error model and simulation performance. a) Possible atomic states in a two-quantum bit gate. Categorized in yellow boxes are detectable correction errors, red are undetectable errors, and green are computational subspaces. b) Gate errors as a function of gate duration.
Circuit-level error thresholds in the presence of correction errors. a) Ratio of logical error rate to physical quantum bit error rate in the presence of pure computational errors (Re=0, open circles, dashed lines) and high conversion correction errors (Re=0.98, filled circles, solid lines): error thresholds are pth=0.937(4)% and pth=4.15(2)%, respectively; b) pth is the ratio of Re function (green star highlights Re=0.98).
03Neutral atom route breakthrough: fault-tolerant computing is expected
This experiment presents a way to efficiently implement fault-tolerant quantum logic operations in an array of neutral atoms using 171Yb. By exploiting the unique hierarchical structure of this alkaline earth atom, the team transforms the spontaneous decay from the Reedeburg state, the main source of errors in double-quantum bit gates, into a directly detectable error correction and deletion. The result is a 4.4-fold increase in circuit-level thresholds for surface codes: a threshold error rate of Re = 0.98 corresponds to 95.9% double-quantum bitgate fidelity, which exceeds the current state-of-the-art.
In the future, the correction-censoring conversion will also be applicable to other codes and other physical quantum bit platforms. Not only that, but with reasonable technical improvements, the error rate is expected to be reduced by at least an order of magnitude: this will bring the neutral atom quantum bits well below the threshold and into the era of true fault tolerance.
Reference link:
https://www.nature.com/articles/s41467-022-32094-6
