Extending the lifetime of a quantum bit with error correction in superconducting circuits

Abstract

Quantum error correction (QEC) can overcome the errors experienced by qubits and is therefore an essential component of a future quantum computer. To implement QEC, a qubit is redundantly encoded in a higher-dimensional space using quantum states with carefully tailored symmetry properties. Projective measurements of these parity-type observables provide error syndrome information, with which errors can be corrected via simple operations. The 'break-even' point of QEC--at which the lifetime of a qubit exceeds the lifetime of the constituents of the system--has so far remained out of reach. Although previous works have demonstrated elements of QEC, they primarily illustrate the signatures or scaling properties of QEC codes rather than test the capacity of the system to preserve a qubit 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 Schrödinger-cat states of a superconducting resonator. We implement a full QEC protocol by using real-time feedback to encode, monitor naturally occurring errors, decode and correct. As measured by full process tomography, without any post-selection, the corrected qubit lifetime is 320 microseconds, which is longer than the lifetime of any of the parts of the system: 20 times longer than the lifetime of the transmon, about 2.2 times longer than the lifetime of an uncorrected logical encoding and about 1.1 longer than the lifetime of the best physical qubit (the |0〉f and |1〉f Fock states of the resonator). Our results illustrate the benefit of using hardware-efficient qubit encodings rather than traditional QEC schemes. Furthermore, they advance the field of experimental error correction from confirming basic concepts to exploring the metrics that drive system performance and the challenges in realizing a fault-tolerant system.

Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

“…Similar analysis for a Josephson junction based traveling-wave parametric amplifier could help the current experimental and theoretical effort [65][66][67][68][69]. Finally, while higher-order corrections hinder the performance of the JPA for squeezing and amplification, it can become a feature for other applications of the JPA such as robust cat state preparation and stabilization [70] which can be used for quantum computation [71] and quantum annealing [72]. For this work to be self-contained, we present the standard solution to the equation of motions of the DPA discussed in Sec.…”

Microwave Quantum States Beat the Heat

“…Here, the state of the first qubit is mapped to the first cavity as c g jgi 1 þ c e jei 1 → c g jþi 1 þ c e j−i 1 , where the cavity logical basis jAEi j ¼ ðj0i j AE ffiffi ffi 2 p j2i j þ j4i j Þ=2 has even photon parity. This unitary transformation can be realized with optimal control pulses driving the qubit and the cavity while using the dispersive shift between the qubit and the cavity mode as nonlinear element [53]. Waveguide losses, with rates κ f , can be modeled with a beam splitter with transmission probability expð−κ f τÞ, whereas the rate of cavity losses is denoted κ 0 .…”

“…Instead of encoding the qubits in the Fock states j0i and j1i, we use multiphoton states, with the requirement that the loss or addition of a photon projects them onto a new subspace where the error can be detected and corrected. A possibility is to use a basis of cat states, i.e., superposition of coherent states [51,52], where a photon loss only induces a change of parity of the photon number [53]. While we present the efficiency of QST with cat states in Ref.…”

Hardware for dynamic quantum computing

“…This active control may manifest as: continuous entropy removal from the system via active reset 5 , active error correction after decoding syndrome measurements, Pauli frame updates for subsequent pulses after state injection 6,7 , or non-deterministic "repeat-until-success" 8 gates. The community is now tackling the challenge of dynamically steering an experiment within the coherence time of the qubits [9][10][11][12] . For superconducting qubits this coherence time-although continuously improving-is currently 50-100 µs.…”