I put here some of the work that I did and that I’m doing. I’m happy to receive any feedback.
A fast, low-leakage, high-fidelity two-qubit gate for a programmable superconducting quantum computer
M. A. Rol, F. Battistel, F. K. Malinowski, C. C. Bultink, B. M. Tarasinski, R. Vollmer, N. Haider, N. Muthusubramanian, A. Bruno, B. M. Terhal, L. DiCarlo
A common approach to realize conditional-phase (CZ) gates in transmon qubits relies on flux control of the qubit frequency to make computational states interact with non-computational ones using a fast-adiabatic trajectory to minimize leakage. We develop a bipolar flux-pulsing method with two key advantages over the traditional unipolar variant. First, the action of the bipolar pulse is robust to long-timescale linear-dynamical distortions in the flux-control line, facilitating tuneup and ensuring atomic repeatability. Second, the flux symmetry of the transmon Hamiltonian makes the conditional phase and the single-qubit phase of the pulsed qubit first-order insensitive to low-frequency flux noise, increasing fidelity. By harnessing destructive interference to minimize leakage, the bipolar pulse can approach the speed limit set by the exchange coupling. We demonstrate a repeatable, high-fidelity (99.1%), low-leakage (0.1%), and fast (40 ns) CZ gate in a circuit QED quantum processor. Detailed numerical simulations with excellent match to experiment show that leakage is dominated by remaining short-timescale distortions and fidelity is limited by high-frequency flux noise.
Spectral Quantum Tomography
J. Helsen, F. Battistel, B. M. Terhal
We introduce spectral quantum tomography, a simple method to extract the eigenvalues of a noisy few-qubit gate, represented by a trace-preserving superoperator, in a SPAM-resistant fashion, using low resources in terms of gate sequence length. The eigenvalues provide detailed gate information, supplementary to known gate-quality measures such as the gate fidelity, and can be used as a gate diagnostic tool. We apply our method to one- and two-qubit gates on two different superconducting systems available in the cloud, namely the QuTech Quantum Infinity and the IBM Quantum Experience. We discuss how cross-talk, leakage and non-Markovian errors affect the eigenvalue data.
Abstract: The Multi-Scale Entanglement Renormalization Ansatz (MERA), introduced by Vidal in 2005, is a tensor network which has proven to be useful to represent many-body states where the entanglement is gradually introduced at different scales, in a local way at each scale. In particular, a MERA can be viewed as the encoding circuit for a family of quantum error correcting codes.
Our motivation for studying such codes comes, on the one hand, from the fact that there are interesting codes which have a MERA representation, like the toric code, and, on the other hand, from a recent work by Kim & Kastoryano, in which the authors exploit the causal structure of entanglement renormalization to derive bounds on the ability of MERA codes to correct against erasure errors.
After an introduction to Quantum Error Correction and MERA, in this work we discuss the validity of the Kim & Kastoryano assumptions and results, and we generalize their bounds to some more general classes of noise models, using some results on approximate error correction obtained by Bény & Oreshkov. Moreover, we study 1D stabilizer MERA codes and find interesting examples for which we have numerical evidence (although not very strong) of a high threshold probability, with the drawback that such codes involve non-local interactions between qubits. We also could not find a “good” recovery algorithm which can be executed in polynomial time, but the possibility that one exists is still open.
IMPRS-TopMath Spring School on “Quantum Entropy and its Use”
“Black hole entropy and thermodynamics”. Trieste, July 2015.
Full text (in Italian)