Practical Quantum Error Correction with the XZZX Code and Kerr-Cat Qubits

Darmawan, Andrew S.; Brown, Benjamin J.; Grimsmo, Arne L.; Tuckett, David K.; Puri, Shruti

doi:10.1103/prxquantum.2.030345

Cited by 89 publications

(59 citation statements)

References 73 publications

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“…This disparity between different types of qubit errors highlights the importance of qubits with biased noise. These qubits recently attracted attention in the context of quantum computing where they offer a range of advantages in the design of quantum gates [49] and in quantum error correction [48,57]. Building on these results, we proposed and analysed a possible implementation of swap-test interferometry with ancilla qubits based on Kerr cats which are strongly biased towards phase flips and thus fulfill the error requirements for approaching Heisenberg-limited phase sensitivity.…”

Section: Discussionmentioning

confidence: 99%

Swap-test interferometry with biased ancilla noise

Černotík¹,

Pietikäinen²,

Puri³

et al. 2021

Preprint

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The Mach-Zehnder interferometer is a powerful device for detecting small phase shifts between two light beams. Simple input states-such as coherent states or single photons-can reach the standard quantum limit of phase estimation while more complicated states can be used to reach Heisenberg scaling; the latter, however, require complex states at the input of the interferometer which are difficult to prepare. The quest for highly sensitive phase estimation therefore calls for interferometers with nonlinear devices which would make the preparation of these complex states more efficient.Here, we show that the Heisenberg scaling can be recovered with simple input states (including Fock and coherent states) when the linear mirrors in the interferometer are replaced with controlled-swap gates and measurements on ancilla qubits. These swap tests project the input Fock and coherent states onto NOON and entangled coherent states, respectively, leading to improved sensitivity to small phase shifts in one of the interferometer arms. We perform detailed analysis of ancilla errors, showing that biasing the ancilla towards phase flips offers a great advantage, and perform thorough numerical simulations of a possible implementation in circuit quantum electrodynamics. Our results thus present a viable approach to phase estimation approaching Heisenberg-limited sensitivity.

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Section: Discussionmentioning

confidence: 99%

Swap-test interferometry with biased ancilla noise

Černotík¹,

Pietikäinen²,

Puri³

et al. 2021

Preprint

Self Cite

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show abstract

“…Furthermore, unlike ordinary DV qubits, the Kerr-cat has an underlying continuous rotation symme- try which allows one to escape a no-go theorem that otherwise prevents creation of a cNOT gate that preserves the noise bias [3]. These two features significantly improve error-correction thresholds for circuits constructed from Kerr-cats [59,60]. It was shown in Ref.…”

Section: Introductionmentioning

confidence: 99%

Ancilla-Error-Transparent Controlled Beam Splitter Gate

Pietikäinen¹,

Černotík²,

Puri³

et al. 2021

Preprint

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In hybrid circuit QED architectures containing both ancilla qubits and bosonic modes, a controlled beam splitter gate is a powerful resource. It can be used to create (up to a controlled-parity operation) an ancilla-controlled SWAP gate acting on two bosonic modes. This is the essential element required to execute the 'swap test' for purity, prepare quantum non-Gaussian entanglement and directly measure nonlinear functionals of quantum states. It also constitutes an important gate for hybrid discrete/continuous-variable quantum computation. We propose a new realization of a hybrid cSWAP utilizing 'Kerr-cat' qubits-anharmonic oscillators subject to strong two-photon driving. The Kerr-cat is used to generate a controlled-phase beam splitter (cPBS) operation. When combined with an ordinary beam splitter one obtains a controlled beam-splitter (cBS) and from this a cSWAP. The strongly biased error channel for the Kerr-cat has phase flips which dominate over bit flips. This yields important benefits for the cSWAP gate which becomes non-destructive and transparent to the dominate error. Our proposal is straightforward to implement and, based on currently existing experimental parameters, should achieve controlled beam-splitter gates with high fidelities comparable to current ordinary beam-splitter operations available in circuit QED.

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“…While many codes have been studied in the context of the abstract model of depolarizing noise arising from the action of random Pauli operators on the qubit, the realistic error model for a given qubit platform is often more complex, which presents both opportunities and challenges. For example, qubits encoded in catcodes in superconducting resonators can have strongly biased noise [11], leading to significantly higher thresholds [12,13] given suitable bias-preserving gate operations for fault-tolerant syndrome extraction [14]. On the * jdthompson@princeton.edu other hand, many qubits also exhibit some level of leakage outside of the computational space [6,15], which requires extra gates in the form of leakage-reducing units, decreasing the threshold [16].…”

Section: Introductionmentioning

confidence: 99%

Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays

Wu,

Kolkowitz,

Puri

et al. 2022

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Executing quantum algorithms on error-corrected logical qubits is a critical step for scalable quantum computing, but the requisite numbers of qubits and physical error rates are demanding for current experimental hardware. Recently, the development of error correcting codes tailored to particular physical noise models has helped relax these requirements. In this work, we propose a qubit encoding and gate protocol for 171 Yb neutral atom qubits that converts the dominant physical errors into erasures, that is, errors in known locations. The key idea is to encode qubits in a metastable electronic level, such that gate errors predominantly result in transitions to disjoint subspaces whose populations can be continuously monitored via fluorescence. We estimate that 98% of errors can be converted into erasures. We quantify the benefit of this approach via circuit-level simulations of the surface code, finding a threshold increase from 0.937% to 4.15%. We also observe a larger code distance near the threshold, leading to a faster decrease in the logical error rate for the same number of physical qubits, which is important for near-term implementations. Erasure conversion should benefit any error correcting code, and may also be applied to design new gates and encodings in other qubit platforms.

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Practical Quantum Error Correction with the XZZX Code and Kerr-Cat Qubits

Cited by 89 publications

References 73 publications

Swap-test interferometry with biased ancilla noise

Swap-test interferometry with biased ancilla noise

Ancilla-Error-Transparent Controlled Beam Splitter Gate

Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays

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