Abstract Fault-tolerant quantum computing requires many qubits with long lifetimes and accurate quantum gate operations. However, external noise limits the computing time and hampers accurate quantum gate operations. Quantum error correction (QEC) codes may extend such limits, but imperfect gate operations during QEC cause errors, which could cancel out QEC. We used density matrix simulations to examine the performance of QEC codes with five qubits. In current quantum devices, less than ten qubits are needed to conduct sufficient gate operations within their lifetime so that it is feasible to implement QEC codes. We analyzed the maximum tolerable error rate and error correction effect of individual QEC codes according to the qubit arrangement and gate accuracy. Assuming a 0.1% gate error probability, a logical ∣ 1 〉 state encoded by a five-qubit QEC code is expected to have a 0.25 higher fidelity than its physical counterpart.Abstract Fault-tolerant quantum computing requires many qubits with long lifetimes and accurate quantum gate operations. However, external noise limits the computing time and hampers accurate quantum gate operations. Quantum error correction (QEC) codes may extend such limits, but imperfect gate operations during QEC cause errors, which could cancel out QEC. We used density matrix simulations to examine the performance of QEC codes with five qubits. In current quantum devices, less than ten qubits are needed to conduct sufficient gate operations within their lifetime so that it is feasible to implement QEC codes. We analyzed the maximum tolerable error rate and error correction effect of individual QEC codes according to the qubit arrangement and gate accuracy. Assuming a 0.1% gate error probability, a logical ∣ 1 〉 state encoded by a five-qubit QEC code is expected to have a 0.25 higher fidelity than its physical counterpart.

Quantum Science and TechnologyNov 18, 201911 citations

Bosonic Error Correction with Fluxonium

Shantanu R. Jha, Shoumik D. Chowdhury, Gabriele Rolleri +22 more

Bosonic quantum error correction (QEC) offers a hardware-efficient route to fault-tolerant quantum computing. To date, however, superconducting circuit implementations of bosonic codes have utilized centimeter-scale 3D microwave cavities controlled by fixed-frequency transmon qubits, with logical lifetimes limited by transmon bit-flip errors. Here, we realize bosonic QEC in a fully planar architecture by pairing a heavy fluxonium, whose $451 \pm 70~μ\mathrm{s}$ bit-flip lifetime exceeds that of any control qubit in previous demonstrations, with an on-chip Archimedean spiral resonator several orders of magnitude smaller in mode volume than prior 3D cavities. We prepare finite-energy Gottesman-Kitaev-Preskill (GKP) states and stabilize them using measurement-free error correction with rapid fluxonium reset, extending the logical lifetime by a factor of $1.59 \pm 0.05$ . These results provide the first demonstration of resonator control using a weakly coupled fluxonium and, with it, the first realization of standalone bosonic QEC in a fully planar superconducting circuit architecture.Bosonic quantum error correction (QEC) offers a hardware-efficient route to fault-tolerant quantum computing. To date, however, superconducting circuit implementations of bosonic codes have utilized centimeter-scale 3D microwave cavities controlled by fixed-frequency transmon qubits, with logical lifetimes limited by transmon bit-flip errors. Here, we realize bosonic QEC in a fully planar architecture by pairing a heavy fluxonium, whose $451 \pm 70~μ\mathrm{s}$ bit-flip lifetime exceeds that of any control qubit in previous demonstrations, with an on-chip Archimedean spiral resonator several orders of magnitude smaller in mode volume than prior 3D cavities. We prepare finite-energy Gottesman-Kitaev-Preskill (GKP) states and stabilize them using measurement-free error correction with rapid fluxonium reset, extending the logical lifetime by a factor of $1.59 \pm 0.05$. These results provide the first demonstration of resonator control using a weakly coupled fluxonium and, with it, the first realization of standalone bosonic QEC in a fully planar superconducting circuit architecture.

quant-pharXiv:2609.26880Sep 24, 20260 citations

Quantum error correction beyond qubits

Takao Aoki, Go Takahashi, Tadashi Kajiya +4 more

arXiv:0811.3734Nature PhysicsJun 28, 2009144 citations

Demonstrating Quantum Error Correction that Extends the Lifetime of Quantum Information

Nissim Ofek, Andrei Petrenko, Reinier Heeres +10 more

The remarkable discovery of Quantum Error Correction (QEC), which can overcome the errors experienced by a bit of quantum information (qubit), was a critical advance that gives hope for eventually realizing practical quantum computers. In principle, a system that implements QEC can actually pass a "break-even" point and preserve quantum information for longer than the lifetime of its constituent parts. Reaching the break-even point, however, has thus far remained an outstanding and challenging goal. Several previous works have demonstrated elements of QEC in NMR, ions, nitrogen vacancy (NV) centers, photons, and superconducting transmons. However, these works primarily illustrate the signatures or scaling properties of QEC codes rather than test the capacity of the system to extend the lifetime of quantum information over time. Here we demonstrate a QEC system that reaches the break-even point by suppressing the natural errors due to energy loss for a qubit logically encoded in superpositions of coherent states, or cat states of a superconducting resonator. Moreover, the experiment implements a full QEC protocol by using real-time feedback to encode, monitor naturally occurring errors, decode, and correct. As measured by full process tomography, the enhanced lifetime of the encoded information is 320 microseconds without any post-selection. This is 20 times greater than that of the system's transmon, over twice as long as an uncorrected logical encoding, and 10% longer than the highest quality element of the system (the resonator's 0, 1 Fock states). Our results illustrate the power of novel, hardware efficient qubit encodings over traditional QEC schemes. Furthermore, they advance the field of experimental error correction from confirming the basic concepts to exploring the metrics that drive system performance and the challenges in implementing a fault-tolerant system.The remarkable discovery of Quantum Error Correction (QEC), which can overcome the errors experienced by a bit of quantum information (qubit), was a critical advance that gives hope for eventually realizing practical quantum computers. In principle, a system that implements QEC can actually pass a "break-even" point and preserve quantum information for longer than the lifetime of its constituent parts. Reaching the break-even point, however, has thus far remained an outstanding and challenging goal. Several previous works have demonstrated elements of QEC in NMR, ions, nitrogen vacancy (NV) centers, photons, and superconducting transmons. However, these works primarily illustrate the signatures or scaling properties of QEC codes rather than test the capacity of the system to extend the lifetime of quantum information over time. Here we demonstrate a QEC system that reaches the break-even point by suppressing the natural errors due to energy loss for a qubit logically encoded in superpositions of coherent states, or cat states of a superconducting resonator. Moreover, the experiment implements a full QEC protocol by using real-time feedback to encode, monitor naturally occurring errors, decode, and correct. As measured by full process tomography, the enhanced lifetime of the encoded information is 320 microseconds without any post-selection. This is 20 times greater than that of the system's transmon, over twice as long as an uncorrected logical encoding, and 10% longer than the highest quality element of the system (the resonator's 0, 1 Fock states). Our results illustrate the power of novel, hardware efficient qubit encodings over traditional QEC schemes. Furthermore, they advance the field of experimental error correction from confirming the basic concepts to exploring the metrics that drive system performance and the challenges in implementing a fault-tolerant system.

arXiv:1602.04768Feb 15, 201619 citations

Protecting a bosonic qubit with autonomous quantum error correction

Jeffrey M. Gertler, Brian Baker, Juliang Li +3 more

arXiv:2004.09322NatureFeb 10, 2021159 citations

451 \pm 70~μ\mathrm{s}

bit-flip lifetime exceeds that of any control qubit in previous demonstrations, with an on-chip Archimedean spiral resonator several orders of magnitude smaller in mode volume than prior 3D cavities. We prepare finite-energy Gottesman-Kitaev-Preskill (GKP) states and stabilize them using measurement-free error correction with rapid fluxonium reset, extending the logical lifetime by a factor of

1.59 \pm 0.05

. These results provide the first demonstration of resonator control using a weakly coupled fluxonium and, with it, the first realization of standalone bosonic QEC in a fully planar superconducting circuit architecture.