Quantum computers could be used to solve certain problems exponentially faster than classical computers, but are challenging to build because of their increased susceptibility to errors. However, it is possible to detect and correct errors without destroying coherence, by using quantum error correcting codes. The simplest of these are three-quantum-bit (three-qubit) codes, which map a one-qubit state to an entangled three-qubit state; they can correct any single phase-flip or bit-flip error on one of the three qubits, depending on the code used. Here we demonstrate such phase- and bit-flip error correcting codes in a superconducting circuit. We encode a quantum state, induce errors on the qubits and decode the error syndrome--a quantum state indicating which error has occurred--by reversing the encoding process. This syndrome is then used as the input to a three-qubit gate that corrects the primary qubit if it was flipped. As the code can recover from a single error on any qubit, the fidelity of this process should decrease only quadratically with error probability. We implement the correcting three-qubit gate (known as a conditional-conditional NOT, or Toffoli, gate) in 63 nanoseconds, using an interaction with the third excited state of a single qubit. We find 85 ± 1 per cent fidelity to the expected classical action of this gate, and 78 ± 1 per cent fidelity to the ideal quantum process matrix. Using this gate, we perform a single pass of both quantum bit- and phase-flip error correction and demonstrate the predicted first-order insensitivity to errors. Concatenation of these two codes in a nine-qubit device would correct arbitrary single-qubit errors. In combination with recent advances in superconducting qubit coherence times, this could lead to scalable quantum technology.
Traditionally, quantum entanglement has played a central role in foundational discussions of quantum mechanics. The measurement of correlations between entangled particles can exhibit results at odds with classical behavior. These discrepancies increase exponentially with the number of entangled particles 1 . When entanglement is extended from just two quantum bits (qubits) to three, the incompatibilities between classical and quantum correlation properties can change from a violation of inequalities 2 involving statistical averages to sign differences in deterministic observations 3 . With the ample confirmation of quantum mechanical predictions by experiments 4-7 , entanglement has evolved from a philosophical conundrum to a key resource for quantum-based technologies, like quantum cryptography and computation 8 . In particular, maximal entanglement of more than two qubits is crucial to the implementation of quantum error correction protocols. While entanglement of up to 3, 5, and 8 qubits has been demonstrated among spins 9 , photons 7 , and ions 10 , respectively, entanglement in engineered solid-state systems has been limited to two qubits [11][12][13][14][15] . Here, we demonstrate three-qubit entanglement in a superconducting circuit, creating Greenberger-HorneZeilinger (GHZ) states with fidelity of 88%, measured with quantum state tomography.Several entanglement witnesses show violation of biseparable bounds by 830 ± 80%. Our entangling sequence realizes the first step of basic quantum error correction, namely the encoding of a logical qubit into a manifold of GHZ-like states using a repetition code. The integration of encoding, decoding and error-correcting steps in a feedback loop will be the next milestone for quantum computing with integrated circuits.With steady improvements in qubit coherence, control, and readout over a decade, superconducting quantum circuits 16 have recently attained two milestones for solidstate two-qubit entanglement. The first is the violation of Bell inequalities without a detection loophole, realized with phase qubits by minimizing cross-talk between high-fidelity individual qubit readouts 14 . Second is the realization of simple quantum algorithms 13 , achieved through improved two-qubit gates and coherence in cir- (inset) to Q4] inside a meandering coplanar waveguide resonator. Local flux-bias lines allow qubit tuning on nanosecond timescales with room-temperature voltages Vi. Microwave pulses at qubit transition frequencies f1, f2, and f3 realize single-qubit x-and y-rotations in 8 ns. Q4 (operational but unused) is biased at its maximal frequency of 12.27 GHz to minimize its interaction with the qubits employed. Pulsed measurement of cavity homodyne voltage VH (at the bare cavity frequency fc = 9.070 GHz) allows joint qubit readout. A detailed schematic of the measurement setup is shown in Supplementary Fig. S2. b, Grey-scale images of cavity transmission and qubit spectroscopy versus local tuning of Q1 show avoided crossings with Q2 (66 MHz splitting), with Q3 (128 ...
Quantum error correction (QEC) is required for a practical quantum computer because of the fragile nature of quantum information [1]. In QEC, information is redundantly stored in a large Hilbert space and one or more observables must be monitored to reveal the occurrence of an error, without disturbing the information encoded in an unknown quantum state. Such observables, typically multi-qubit parities such as σ , must correspond to a special symmetry property inherent to the encoding scheme. Measurements of these observables, or error syndromes, must also be performed in a quantum non-demolition (QND) way and faster than the rate at which errors occur. Previously, QND measurements of quantum jumps between energy eigenstates have been performed in systems such as trapped ions [2][3][4], electrons [5], cavity quantum electrodynamics (QED) [6, 7], nitrogen-vacancy (NV) centers [8,9], and superconducting qubits [10,11]. So far, however, no fast and repeated monitoring of an error syndrome has been realized. Here, we track the quantum jumps of a possible error syndrome, the photon number parity of a microwave cavity, by mapping this property onto an ancilla qubit. This quantity is just the error syndrome required in a recently proposed scheme for a hardware-efficient protected quantum memory using Schrödinger cat states in a harmonic oscillator [12]. We demonstrate the projective nature of this measurement onto a parity eigenspace by observing the collapse of a coherent state onto even or odd cat states. The measurement is fast compared to the cavity lifetime, has a high single-shot fidelity, and has a 99.8% probability per single measurement of leaving the parity unchanged. In combination with the deterministic encoding of * current address: Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, P. R. China † current address: Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria; Institut für Quantenoptik und Quanteninformation,Österreichische Akademie der Wissenschaften, Otto-Hittmair-Platz 1, A-6020 Innsbruck, Austria quantum information in cat states realized earlier [13,14], our demonstrated QND parity tracking represents a significant step towards implementing an active system that extends the lifetime of a quantum bit.Besides their necessity in quantum error correction and quantum information, QND measurements play a central role in quantum mechanics. The application of an ideal projective QND measurement yields a result corresponding to an eigenvalue of the measured operator, and projects the system onto the eigenstate associated with that eigenvalue. Moreover, the measurement must leave the system in that state, so that subsequent measure- Experimental device and parity measurement protocol (P) of a photon state. (a) Bottom half of the device containing a transmon qubit located in a trench and coupled to two waveguide cavities. The low frequency cavity, with ωs/2π = 7.216 GHz and a lifetime of τ0 = 5...
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