Quantum Error Correction with Only Two Extra Qubits

Chao, Rui; Reichardt, Ben W.

doi:10.1103/physrevlett.121.050502

Cited by 193 publications

(245 citation statements)

References 30 publications

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“…In this section, we briefly introduce the flag-based error syndrome extraction for stabiliser codes. For more details, we refer the readers to [13][14][15][16]20]. Figure 1 shows the circuits for measuring a weight-4 Z-stabiliser (or check), similar circuits can be derived for measuring other Pauli operators.…”

Section: Flag-based Quantum Error Correctionmentioning

confidence: 99%

“…One of the main constraints is the degree of qubit connectivity, that is, one qubit can only interact with a limited number of other qubits. It is challenging to map existing flag circuits onto connectivity-constrained quantum processors [14,16] for (a) measuring two weight-4 Z-checks in parallel using three ancillas and (b) measuring three weight-4 Z-checks in parallel using four ancillas.…”

Section: Flag-based Quantum Error Correctionmentioning

confidence: 99%

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Fault-tolerant quantum error correction on near-term quantum processors using flag and bridge qubits

Lao

Almudéver

2020

Phys. Rev. A

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Fault-tolerant (FT) computation by using quantum error correction (QEC) is essential for realizing large-scale quantum algorithms. Devices are expected to have enough qubits to demonstrate aspects of fault tolerance in the near future. However, these near-term quantum processors will only contain a small amount of noisy qubits and allow limited qubit connectivity. Fault-tolerant schemes that not only have low qubit overhead but also comply with geometrical interaction constraints are therefore necessary. In this work, we combine flag fault tolerance with quantum circuit mapping, to enable an efficient flag-bridge approach to implement FT QEC on near-term devices. We further show an example of performing the Steane code error correction on two current superconducting processors and numerically analyze their performance with circuit level noise. The simulation results show that the QEC circuits that measure more stabilisers in parallel have lower logical error rates. We also observe that the Steane code can outperform the distance-3 surface code using flag-bridge error correction. In addition, we foresee potential applications of the flag-bridge approach such as FT computation using lattice surgery and code deformation techniques. arXiv:1909.07628v1 [quant-ph]

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Section: Flag-based Quantum Error Correctionmentioning

confidence: 99%

Section: Flag-based Quantum Error Correctionmentioning

confidence: 99%

Fault-tolerant quantum error correction on near-term quantum processors using flag and bridge qubits

Lao

Almudéver

2020

Phys. Rev. A

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“…To avoid this degradation of the code distance, we take a similar approach to [32][33][34][35][36] by adding a small number of additional ancilla qubits, so called 'flag qubits', to detect hook errors. For our chosen color code with 5 The syndrome increment is usually…”

Section: Flag Qubitsmentioning

confidence: 99%

Neural network decoder for topological color codes with circuit level noise

et al. 2019

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A quantum computer needs the assistance of a classical algorithm to detect and identify errors that affect encoded quantum information. At this interface of classical and quantum computing the technique of machine learning has appeared as a way to tailor such an algorithm to the specific error processes of an experiment-without the need for a priori knowledge of the error model. Here, we apply this technique to topological color codes. We demonstrate that a recurrent neural network with long short-term memory cells can be trained to reduce the error rate ò L of the encoded logical qubit to values much below the error rate ò phys of the physical qubits-fitting the expected power law scaling   µ + ( ) d L phys 1 2 , with d the code distance. The neural network incorporates the information from 'flag qubits' to avoid reduction in the effective code distance caused by the circuit. As a test, we apply the neural network decoder to a density-matrix based simulation of a superconducting quantum computer, demonstrating that the logical qubit has a longer life-time than the constituting physical qubits with near-term experimental parameters.

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“…This amounts to performing the simplest Shor-style extraction, without verification or decoding. Typical mechanisms for fault-tolerance involve preparing and verifying entangled ancilla states [80][81][82][83] or the use of flags [84,85]. Unfortunately, as a leakage event can manifest many Pauli errors, it can often fool such verification schemes.…”

Section: Surface Codes With Unverified Cat Statesmentioning

confidence: 99%

Handling leakage with subsystem codes

2019

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Leakage is a particularly damaging error that occurs when a qubit state falls out of its two-level computational subspace. Compared to independent depolarizing noise, leaked qubits may produce many more configurations of harmful correlated errors during error-correction. In this work, we investigate different local codes in the low-error regime of a leakage gate error model. When restricting to bare-ancilla extraction, we observe that subsystem codes are good candidates for handling leakage, as their locality can limit damaging correlated errors. As a case study, we compare subspace surface codes to the subsystem surface codes introduced by Bravyi et al. In contrast to depolarizing noise, subsystem surface codes outperform same-distance subspace surface codes below error rates as high as 7.5×10 −4 while offering better per-qubit distance protection. Furthermore, we show that at low to intermediate distances, Bacon-Shor codes offer better per-qubit error protection against leakage in an ion-trap motivated error model below error rates as high as 1.2×10 −3 . For restricted leakage models, this advantage can be extended to higher distances by relaxing to unverified two-qubit cat state extraction in the surface code. These results highlight an intrinsic benefit of subsystem code locality to error-corrective performance.

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Quantum Error Correction with Only Two Extra Qubits

Cited by 193 publications

References 30 publications

Fault-tolerant quantum error correction on near-term quantum processors using flag and bridge qubits

Fault-tolerant quantum error correction on near-term quantum processors using flag and bridge qubits

Neural network decoder for topological color codes with circuit level noise

Handling leakage with subsystem codes

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