RECORD
Practical quantum error correction with the XZZX code and Kerr-cat qubits
Quantum Physics · Submitted 19 Apr 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our simulations show that our system is scalable below a threshold gate infidelity of $p_\mathrm{CX} \sim 6.5\%$ within a physically reasonable parameter regime, where $p_\mathrm{CX}$ is the infidelity of the noisiest gate of our system; the controlled-not gate.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
The development of robust architectures capable of large-scale fault-tolerant quantum computation should consider both their quantum error-correcting codes, and the underlying physical qubits upon which they are built, in tandem. Following this design principle we demonstrate remarkable error correction performance by concatenating the XZZX surface code with Kerr-cat qubits. We contrast several variants of fault-tolerant systems undergoing different circuit noise models that reflect the physics of Kerr-cat qubits. Our simulations show that our system is scalable below a threshold gate infidelity of $p_\mathrm{CX} \sim 6.5\%$ within a physically reasonable parameter regime, where $p_\mathrm{CX}$ is the infidelity of the noisiest gate of our system; the controlled-not gate. This threshold can be reached in a superconducting circuit architecture with a Kerr-nonlinearity of $10$MHz, a $\sim 6.25$ photon cat qubit, single-photon lifetime of $\gtrsim 64\mu$s, and thermal photon population $\lesssim 8\%$. Such parameters are routinely achieved in superconducting circuits.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The development of robust architectures capable of large-scale fault-tolerant quantum computation should consider both their quantum error-correcting codes, and the underlying physical qubits upon which they are built, in tandem. | background 1.00 | 0.06 | 0.05 | hedged possibility 0.59 |
| s1 | Following this design principle we demonstrate remarkable error correction performance by concatenating the XZZX surface code with Kerr-cat qubits. | contribution 0.87 | 0.93 | 0.67 | asserted 1.00 |
| s2 | We contrast several variants of fault-tolerant systems undergoing different circuit noise models that reflect the physics of Kerr-cat qubits. | method 0.87 | 0.87 | 0.03 | asserted 0.92 |
| s3 | Our simulations show that our system is scalable below a threshold gate infidelity of $p_\mathrm{CX} \sim 6.5\%$ within a physically reasonable parameter regime, where $p_\mathrm{CX}$ is the infidelity of the noisiest gate of our system; the controlled-not gate. | result 1.00 | 0.95 | 0.58 | asserted 1.00 |
| s4 | This threshold can be reached in a superconducting circuit architecture with a Kerr-nonlinearity of $10$MHz, a $\sim 6.25$ photon cat qubit, single-photon lifetime of $\gtrsim 64\mu$s, and thermal photon population $\lesssim 8\%$. | result 0.86 | 0.71 | 0.18 | asserted 0.80 |
| s5 | Such parameters are routinely achieved in superconducting circuits. | interpretation 0.92 | 0.12 | 0.04 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
The development of robust architectures capable of large-scale fault-tolerant quantum computation should consider both their quantum error-correcting codes, and the underlying physical qubits upon which they are built, in tandem. Following this design principle we demonstrate remarkable error correction performance by concatenating the XZZX surface code with Kerr-cat qubits. We contrast several variants of fault-tolerant systems undergoing different circuit noise models that reflect the physics of Kerr-cat qubits. Our simulations show that our system is scalable below a threshold gate infidelity of $p_\mathrm{CX} \sim 6.5\%$ within a physically reasonable parameter regime, where $p_\mathrm{CX}$ is the infidelity of the noisiest gate of our system; the controlled-not gate. This threshold can be reached in a superconducting circuit architecture with a Kerr-nonlinearity of $10$MHz, a $\sim 6.25$ photon cat qubit, single-photon lifetime of $\gtrsim 64\mu$s, and thermal photon population $\lesssim 8\%$. Such parameters are routinely achieved in superconducting circuits.
Human review
References
How later papers used it
78 later papers cite it
1 later paper by other authors is listed below: 1 used its method or tool.
Uses its method or tool 1 of 2 papers with this label
-
Followed this paper in first considering the resonator-assisted interaction Hamiltonian.
Bias-Preserving Gates and Quantum Error Correction With Dual-Rail Cat Codes (2026) · 0.93 · paraphrased: the licence does not allow quoting
How the literature uses it
12 arXiv papers cite this in 29 sentences
Papers citing it · 20 sentences without a confident label
Builds on it 1 paper
-
One could imagine a possible hardware implementation in superconducting circuits as an extension of the proposals in Refs. [ref] , stacking the proposed two-dimensional layouts in a vertical direction in an alternating ABAB pattern as illustrated in fig:architecture_sketch.
Analog information decoding of bosonic quantum LDPC codes · Conceptional architecture · 0.99
Uses its method or tool 2 papers
-
We incorporate our initialization protocol into a quantum-computing architecture based on the XZZX code [ref] ; a surface code that is tailored to correct biased noise.
High-Fidelity Magic-State Preparation with a Biased-Noise Architecture · Introduction · 0.96
-
Using Eqs. [ref]–[ref], the projected interaction becomes [equation] Thus, the resonator response depends on the logical state of the DRCC-1 qubit and can be detected via homodyne measurement [ref] .
Bias-Preserving Gates and Quantum Error Correction With Dual-Rail Cat Codes · Computational basis measurement · 0.86
Compares with it 1 paper
-
Our scheme fundamentally differs from the previous proposals based on two-photon dissipation [ref] as we only require single-photon loss.
Stabilizing a Bosonic Qubit using Colored Dissipation · Introduction · 0.99
Cites it as support 1 paper
-
Due to the ability to preserve bias, cat codes concatenated with particular stabilizer codes yield substantial increases in performance for systems whose noise is substantially biased [ref] .
Bosonic coding: introduction and use cases · Noise-bias preservation · 1.00
Cites it as background 1 paper
-
To date, most studies of bosonic codes have focused on their concatenation with repetition codes [ref] or two-dimensional topological codes [ref] .
Analog information decoding of bosonic quantum LDPC codes · Introduction · 0.92
What it cites · 141 sentences without a confident label
Uses the method or tool of 6 papers
-
We assume that at the beginning of the computation, each SNAIL (data and ancilla) has been pumped into the cat-qubit basis by the adiabatic pumping technique described in Refs. [ref] .
The Kerr-Cat Qubit: Stabilization, Readout, and Gates · Logical Cat Operations and Noise Channels · 1.00
-
We assume that at the beginning of the computation, each SNAIL (data and ancilla) has been pumped into the cat-qubit basis by the adiabatic pumping technique described in Refs. [ref] .
Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving · Logical Cat Operations and Noise Channels · 1.00
-
It is implemented by turning off the parametric drive and evolving the cats freely under the self-Kerr nonlinearity for time $π/2K$ [ref] .
Stabilized Cat in Driven Nonlinear Cavity: A Fault-Tolerant Error Syndrome Detector · $ℳ_X, 𝒫_|+⟩$ · 0.94
Uses data or values from 2 papers
-
So far, the strength of the two-photon dissipation induced this way has been limited to $10-100$ KHz, leading to slow gate operations ($≳1 μs$) [ref] .
Coherent oscillations inside a quantum manifold stabilized by dissipation · Kerr cats and dissipative cats · 0.82
-
We assume a homodyne measurement efficiency of $60%$ [ref] .
Gated conditional displacement readout of superconducting qubits · Kerr-cat noise thresholds · 0.93
Compares with 1 paper
-
In our small-scale simulations we compare the XZZX code on this layout to the tailored surface code (TSC) [ref] on the same layout and to the one-dimensional repetition code with $n=9$ qubits.
Tailoring surface codes for highly biased noise · Small codes · 0.89
Cites as support 1 paper
-
This was demonstrated using a phenomenological noise model in Ref. [ref] .
The XZZX Surface Code · Decoding · 0.97
Cites as background 19 papers
-
Here we describe the Kerr cat [ref] which, in our proposal, forms the elementary qubit from which the XZZX code is built.
Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving · Cat qubits and bias preserving gates · 0.89
-
Here we describe the Kerr cat [ref] which, in our proposal, forms the elementary qubit from which the XZZX code is built.
The Kerr-Cat Qubit: Stabilization, Readout, and Gates · Cat qubits and bias preserving gates · 0.89
-
While we cannot expect to reduce qubit noise arbitrarily with laboratory engineering alone, the theory of quantum error correction [ref] has shown that we can produce logical qubits that experience next-to-no noise by using a redundancy of high-quality physical qubits, provided the noise strength on the physical qubits as they perform computational operations is below some threshold value [ref] .
Quantum memories at finite temperature · Introduction · 0.81
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.