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Preparation and Measurement of Three-Qubit Entanglement in a Superconducting Circuit
L. DiCarlo, M. D. Reed, L. Sun, B. R. Johnson, J. M. Chow, J. M. Gambetta, L. Frunzio, S. M. Girvin, M. H. Devoret, R. J. Schoelkopf
TL;DR
Verified GHZ-class entanglement in engineered solid-state circuits remained undemonstrated, despite prior unverified W-class tripartite production. This paper uses conditional-phase gates and joint readout to produce and detect three-qubit GHZ states, reporting 88% fidelity by quantum state tomography.
Problem
Verified GHZ-class entanglement remained undemonstrated in engineered solid-state circuits, despite prior deterministic but unverified W-class tripartite production.
Source: p. 2Method
The authors extend conditional-phase gates and joint qubit readout in cQED to generate and detect GHZ-class entanglement between three superconducting qubits.
Source: pp. 2, 4Results
88% fidelity to |GHZ⟩ in the measured Pauli set demonstrates GHZ-type entanglement between three engineered solid-state qubits.
Source: p. 4Takeaways & Limitations
The entangling sequence encodes one logical qubit in an entangled state of three physical qubits using a repetition code, realizing the first step of basic quantum error correction.
Source: p. 5A feedback loop for error correction remains future work, with an error-syndrome detecting circuit still to be realized.
Source: p. 5
Abstract
from arXiv · showhide
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. 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 involving statistical averages to sign differences in deterministic observations. With the ample confirmation of quantum mechanical predictions by experiments, entanglement has evolved from a philosophical conundrum to a key resource for quantum-based technologies, like quantum cryptography and computation. 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, photons, and ions, respectively, entanglement in engineered solid-state systems has been limited to two qubits. Here, we demonstrate three-qubit entanglement in a superconducting circuit, creating Greenberger-Horne-Zeilinger (GHZ) states with fidelity of 88%, measured with quantum state tomography. Several entanglement witnesses show violation of bi-separable bounds by 830\pm80%. 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.
I. METHODS
The methods characterize transmons with a flux-dependent generalized Tavis–Cummings model, measure qubit coherence, and calibrate joint-readout measurement weights.
Hamiltonian parameters
- The transmon-generalized Tavis–Cummings Hamiltonian was fitted to spectroscopy and transmission data after numerical diagonalization with four qubit levels and four cavity photons.The fitted parameters include ωc/2π = 9.070 GHz, Jq/h = {42, 29, 47, 57} GHz for Q1–Q4, g/2π ≈ 220 MHz, and ECq/h ≈ 330 MHz. Flux control enters through the transmon Josephson energy; cross-talk up to ∼40% was corrected by orthogonalization.Source: §I · pp. 5–6
Coherence times
- At point I, measured T1 values for Q1–Q3 were (1.2, 1.0, 0.6) µs and T*2 values were (0.3, 0.6, 0.5) µs; T1 was consistent with Purcell-effect relaxation and non-radiative loss (quality factor ∼55,000), while T*2 was consistent with 1/f flux noise.Source: §I · p. 6
Joint readout
- For joint readout, the weighting coefficients β in the measurement operator were calibrated in every tomography measurement.Source: §I · p. 6
Supplementary Material for ‘Preparation and Measurement of Three-Qubit Entanglement in a Superconducting
The supplementary figures characterize the avoided crossing used as a C-Phase gate primitive, document the three-qubit control and readout setup, and specify GHZ preparation and tomography timing.
Figure S1
- 73 MHz splitting at the |110⟩↔|020⟩ crossing provides the Q1–Q2 C-Phase primitive, with a 14 ns coherent oscillation setting the two-qubit gate time.The levels become resonant at local bias point II.Source: Figure S1 · p. 7
Figure S2
- The wiring supports full control of three qubits and biasing of a fourth, with microwave drives, fast flux pulses, and homodyne cavity readout.Quiescent bias from dc sources improves frequency stability away from the flux sweet spot; the output chain has about 70 dB gain and about 10 K noise temperature at 4–8 GHz.Source: Figure S2 · p. 8
Figures S3–S4
- The GHZ-state sequence, including tomography pre-rotations, takes 81 ns, followed by a 1 µs measurement pulse.The microwave rotations use Gaussian envelopes with σ = 2 ns, truncated at ±2σ, and 3 ns buffers between pulses. Reconstructed density matrices are shown as real and imaginary cityscape plots; maximum-likelihood estimation does not constrain them to be positive semidefinite.Source: Figure S3 · p. 9, Figure S4 · p. 9