Handling leakage with subsystem codes

Brown, Natalie C.; Newman, Michael; Brown, Kenneth R.

doi:10.1088/1367-2630/ab3372

Cited by 32 publications

(29 citation statements)

References 100 publications

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“…We also point out that in general, topological codes without leakage reduction units [58] are not robust against leakage errors that occur when a bare qubit state is excited and falls out of its desired two-level subspace [58][59][60][61]. In the case of the surface-GKP code, leakage errors do occur as well because each bosonic mode may not be in the desired two-level GKP code subspace.…”

Section: Resultsmentioning

confidence: 99%

Fault-tolerant bosonic quantum error correction with the surface–Gottesman-Kitaev-Preskill code

Noh

Chamberland²

2020

Phys. Rev. A

154

194

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Bosonic quantum error correction is a viable option for realizing error-corrected quantum information processing in continuous-variable bosonic systems. Various single-mode bosonic quantum error-correcting codes such as cat, binomial, and GKP codes have been implemented experimentally in circuit QED and trapped ion systems. Moreover, there have been many theoretical proposals to scale up such single-mode bosonic codes to realize large-scale fault-tolerant quantum computation. Here, we consider the concatenation of the single-mode GKP code with the surface code, namely, the surface-GKP code. In particular, we thoroughly investigate the performance of the surface-GKP code by assuming realistic GKP states with a finite squeezing and noisy circuit elements due to photon losses. By using a minimum-weight perfect matching decoding algorithm on a 3D space-time graph, we show that fault-tolerant quantum error correction is possible with the surface-GKP code if the squeezing of the GKP states is higher than 11.2dB in the case where the GKP states are the only noisy elements. We also show that the squeezing threshold changes to 18.6dB when both the GKP states and circuit elements are comparably noisy. At this threshold, each circuit component fails with probability 0.69%. Finally, if the GKP states are noiseless, fault-tolerant quantum error correction with the surface-GKP code is possible if each circuit element fails with probability less than 0.81%. We stress that our decoding scheme uses the additional information from GKPstabilizer measurements and we provide a simple method to compute renormalized edge weights of the matching graphs. Furthermore, our noise model is general as it includes full circuit-level noise.

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Section: Resultsmentioning

confidence: 99%

Fault-tolerant bosonic quantum error correction with the surface–Gottesman-Kitaev-Preskill code

Noh

Chamberland²

2020

Phys. Rev. A

154

194

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“…Lastly, in Ref. [43] it was shown how some families of subsystem codes achieve better error correcting capabilities compared to the surface code in the presence of leakage errors. An interesting direction for future work would be to analyze the performance of codes defined on low degree graphs in the presence of leakage errors to see if such codes also have favorable error correcting capabilities compared to more standard implementations such as in the surface code.…”

Section: Discussionmentioning

confidence: 99%

Topological and Subsystem Codes on Low-Degree Graphs with Flag Qubits

Chamberland¹,

Zhu²,

Yoder³

et al. 2020

Phys. Rev. X

212

211

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In this work we introduce two code families, which we call the heavy hexagon code and heavy square code. Both code families are implemented by assigning physical data and ancilla qubits to both vertices and edges of low degree graphs. Such a layout is particularly suitable for superconducting qubit architectures to minimize frequency collision and crosstalk. In some cases, frequency collisions can be reduced by several orders of magnitude. The heavy hexagon code is a hybrid surface/Bacon-Shor code mapped onto a (heavy) hexagonal lattice whereas the heavy square code is the surface code mapped onto a (heavy) square lattice. In both cases, the lattice includes all the ancilla qubits required for fault-tolerant error-correction. Naively, the limited qubit connectivity might be thought to limit the error-correcting capability of the code to less than its full distance. Therefore, essential to our construction is the use of flag qubits. We modify minimum weight perfect matching decoding to effciently and scalably incorporate information from measurements of the flag qubits and correct up to the full code distance while respecting the limited connectivity. Simulations show that high threshold values for both codes can be obtained using our decoding protocol. Further, our decoding scheme can be adapted to other topological code families.

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“…Furthermore, leakage can last over many QEC cycles, despite having a finite duration set by the relaxation time 36 . Hence, leakage represents a menacing error source in the context of quantum error correction 17,[36][37][38][39][40][41][42][43] , despite leakage probabilities per operation being smaller than readout, control or decoherence error probabilities 6,8,9,44 .…”

Section: Introductionmentioning

confidence: 99%

Leakage detection for a transmon-based surface code

et al. 2020

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Leakage outside of the qubit computational subspace, present in many leading experimental platforms, constitutes a threatening error for quantum error correction (QEC) for qubits. We develop a leakage-detection scheme via Hidden Markov models (HMMs) for transmon-based implementations of the surface code. By performing realistic density-matrix simulations of the distance-3 surface code (Surface-17), we observe that leakage is sharply projected and leads to an increase in the surface-code defect probability of neighboring stabilizers. Together with the analog readout of the ancilla qubits, this increase enables the accurate detection of the time and location of leakage. We restore the logical error rate below the memory break-even point by post-selecting out leakage, discarding less than half of the data for the given noise parameters. Leakage detection via HMMs opens the prospect for near-term QEC demonstrations, targeted leakage reduction and leakage-aware decoding and is applicable to other experimental platforms.

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Handling leakage with subsystem codes

Cited by 32 publications

References 100 publications

Fault-tolerant bosonic quantum error correction with the surface–Gottesman-Kitaev-Preskill code

Fault-tolerant bosonic quantum error correction with the surface–Gottesman-Kitaev-Preskill code

Topological and Subsystem Codes on Low-Degree Graphs with Flag Qubits

Leakage detection for a transmon-based surface code

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