Session Y69: Progress in Practical Fault-Tolerant Quantum Error Correction

Suppressing quantum errors by scaling a surface code logical qubit

Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical qubits, where increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low in order for logical performance to improve with increasing code size. Here, we report the measurement of logical qubit performance scaling across multiple code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, both in terms of logical error probability over 25 cycles and logical error per cycle (2.914%±0.016% compared to 3.028%±0.023%). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a 1.7×10−6 logical error per round floor set by a single high-energy event (1.6×10−7 when excluding this event). We are able to accurately model our experiment, and from this model we can extract error budgets that highlight the biggest challenges for future systems. These results mark the first experimental demonstration where quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.   

Distributed quantum computation with spins in diamond

A potential path towards large-scale quantum processors is to distribute computations over a quantum network [1]. By connecting many small modules through interconnects one can sidestep the challenge of placing dense arrays of qubits on a single chip of ever-increasing complexity. Optically active spin qubits in diamond are a promising platform for such distributed quantum computations and simualtions, as they combine long-lived qubits at high operating temperatures with a coherent interaction with photons that enables optical interconnects [2]. Ultimately, moving to large-scale systems will require using error-corrected logical qubits that are operated fault tolerantly, so that reliable computation becomes possible despite noisy operations. 

 

In this talk, I will present our progress towards realizing distributed error correction and computation with diamond spin qubits within the Fujitsu – QuTech collaboration. In particular, I will discuss our recent results that demonstrate a fault-tolerantly operated logical qubit based on the five-qubit code using flag qubits [3]. Additionally, I will discuss the main challenges towards distributed quantum error correction, and ultimately larger-scale quantum computations, based on spins in diamond or similar materials.

 

[1] Nickerson et al., Phys. Rev. X 4, 041041 (2014)

[2] Pompili et al., Science 372, 259 (2021)

[3] Abobeih et al., Nature 606, 884 (2022)

    

Tailored quantum error correction for large-scale quantum computing under structured noise

Large-scaling quantum computers will require error correction in order to reliably perform computations. However, the hardware overhead for error correction remains dauntingly large, with each logical qubit potentially requiring thousands of physical qubits for reliable operation. One promising approach to reducing the overheads of error correction is to tailor quantum error correcting codes to the dominant noise in the qubit hardware.

In this talk, I’ll present two examples of recent work in tailoring quantum error correction, both based on the recently introduced XZZX surface code. In the first part of the talk, I’ll present a blueprint for building the XZZX surface code out of Kerr cat qubits, which predominantly suffer from dephasing errors. I’ll explain how to efficiently implement gates and distill magic states in the presence of dephasing noise, and derive estimates for the improved overhead offered by the XZZX surface code. In the second part, I’ll show how a cluster state derived from the XZZX surface code, the so-called XZZX cluster state, can be tailored to correct probabilistic gate failures in dual-rail linear optics. Notably, our tailored error correction allows for a threshold of over 25% using simple resource states, overcoming a key barrier for photonic quantum computing.   

The Kerr cat: spectral kissing and phase-flip robustness

Schrödinger cat states, superpositions of coherent states in an oscillator, can be stabilized by a driven effective Hamiltonian thanks to the interplay between Kerr nonlinearity and single-mode squeezing [1]. The pair of resulting degenerate Kerr-cat states form a qubit whose coherence along one Bloch sphere axis increases exponentially with the average photon number, while decreasing only linearly along the other axes. The qubit protection arises from the progressive pairwise kissing of consecutive levels as the average photon number is increased--a quantum manifestation of robust period doubling in this system. We experimentally observe the pairwise kissing via spectroscopy and the associated increase in the period-doubled coherent state lifetime, which exceeds 1 ms, a factor of 440 improvement over the bare lifetime of the constituent SNAIL-transmon circuit. Furthermore, we achieve quantum nondemolition readout fidelities > 99% and retain universal quantum control [2]. Our system experimentally realizes a hardware-efficient repitition code leaving the Kerr-cat qubit poised for use in further quantum error correction schemes.

[1] Grimm, A., Frattini, N.E., Puri, S. et al. Stabilization and operation of a Kerr-cat qubit. Nature 584, 205–209 (2020).

[2] Frattini, N.E., Cortiñas, R.G., Venkatraman, J. et al. The squeezed Kerr oscillator: spectral kissing and phase-flip robustness. Arxiv 2209.03934 (2022).   

Experimental Quantum Error Correction on Quantinuum Ion Trap

While we are currently in the NISQ era, recent advances in quantum computing hardware and software have opened up opportunities to explore increasingly complex quantum error correction (QEC) primitives. In this talk, we will discuss our recent work in advancing the study of experimental QEC that is enabled by the unique capabilities of Quantinuum’s System Model H1 machines and software. In particular, we utilize our ability to do mid-circuit measurements with low crosstalk, effective all-to-all connectivity, feedforward, conditional quantum and classical operations, and hybrid classical/quantum compute to implement QEC primitives needed to implement universal quantum computing and both determine and apply corrections during computation on up-to two distance-three logical qubits. The capabilities further provide the flexibility to explore different QEC codes, protocols, and decoding schemes. Thus, this work highlights the maturing of current quantum technology towards the goal of large-scale fault-tolerant quantum computing.