I put here some of the work that I did and that I’m doing. I’m happy to receive any feedback.

# Publications

### Fast, High-Fidelity Conditional-Phase Gate Exploiting Leakage Interference in Weakly Anharmonic Superconducting Qubits

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

Physical Review Letters

arXiv:1903.02492

Conditional-phase (CZ) gates in transmons can be realized by flux pulsing computational states towards resonance with noncomputational ones. We present a 40 ns CZ gate based on a bipolar flux pulse suppressing leakage (0.1%) by interference and approaching the speed limit set by exchange coupling. This pulse harnesses a built-in echo to enhance fidelity (99.1%) and is robust to long-timescale distortion in the flux-control line, ensuring repeatability. Numerical simulations matching experiment show that fidelity is limited by high-frequency dephasing and leakage by short-timescale distortion.

*Spectral Quantum Tomography*

J. Helsen, F. Battistel, B. M. Terhal

Nature Partner Journal Quantum Information

arXiv:1904.00177

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.

*Leakage detection for a transmon-based surface code*

B. M. Varbanov, F. Battistel, B. M. Tarasinski, V. P. Ostroukh, T. E. O’Brien, L. DiCarlo, B. M. Terhal

Leakage outside of the qubit computational subspace, present in many leading experimental platforms, constitutes a threatening error for quantum error correction (QEC) for qubits. We develop a leakage-detection scheme via Hidden Markov models (HMMs) for transmon-based implementations of the surface code. By performing realistic density-matrix simulations of the distance-3 surface code (Surface-17), we observe that leakage is sharply projected and leads to an increase in the surface-code defect probability of neighboring stabilizers. Together with the analog readout of the ancilla qubits, this increase enables the accurate detection of the time and location of leakage. We restore the logical error rate below the memory break-even point by post-selecting out leakage, discarding about 47% of the data. Leakage detection via HMMs opens the prospect for near-term QEC demonstrations, targeted leakage reduction and leakage-aware decoding and is applicable to other experimental platforms.

# Unpublished work

**Master Thesis**

“General Quantum Error Correction for MERA Codes”. Munich, September 2017.

Full text & Slides

*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”

Talk on “Quantum Capacity of a Quantum Channel”. Bavaria, March 2017.

Script & Slides

### Bachelor Thesis

“Black hole entropy and thermodynamics”. Trieste, July 2015.

Full text (in Italian)