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

# Publications

*Logical-qubit operations in an error-detecting surface code*

J. F. Marques, B. M. Varbanov, M. S. Moreira, H. Ali, N. Muthusubramanian, C. Zachariadis, F. Battistel, M. Beekman, N. Haider, W. Vlothuizen, A. Bruno, B. M. Terhal, L. DiCarlo

We realize a suite of logical operations on a distance-two logical qubit stabilized using repeated error detection cycles. Logical operations include initialization into arbitrary states, measurement in the cardinal bases of the Bloch sphere, and a universal set of single-qubit gates. For each type of operation, we observe higher performance for fault-tolerant variants over non-fault-tolerant variants, and quantify the difference through detailed characterization. In particular, we demonstrate process tomography of logical gates, using the notion of a logical Pauli transfer matrix. This integration of high-fidelity logical operations with a scalable scheme for repeated stabilization is a milestone on the road to quantum error correction with higher-distance superconducting surface codes.

*A hardware-efficient leakage-reduction scheme for quantum error correction with superconducting transmon qubits*

F.Battistel, B. M. Varbanov, B. M. Terhal

Leakage outside of the qubit computational subspace poses a threatening challenge to quantum error correction (QEC). We propose a scheme using two leakage-reduction units (LRUs) that mitigate these issues for a transmon-based surface code, without requiring an overhead in terms of hardware or QEC-cycle time as in previous proposals. For data qubits we consider a microwave drive to transfer leakage to the readout resonator, where it quickly decays, ensuring that this negligibly affects the coherence within the computational subspace for realistic system parameters. For ancilla qubits we apply a |1⟩↔|2⟩ π pulse conditioned on the measurement outcome. Using density-matrix simulations of the distance-3 surface code we show that the average leakage lifetime is reduced to almost 1 QEC cycle, even when the LRUs are implemented with limited fidelity. Furthermore, we show that this leads to a significant reduction of the logical error rate. This LRU scheme opens the prospect for near-term scalable QEC demonstrations.

*High-fidelity controlled-Z gate with maximal intermediate leakage operating at the speed limit in a superconducting quantum processor*

V. Negîrneac, H. Ali, N. Muthusubramanian, F. Battistel, R. Sagastizabal, M. S. Moreira, J. F. Marques, W. J. Vlothuizen, M. Beekman, C. Zachariadis, N. Haider, A. Bruno, L. DiCarlo

Physical Review Letters

arXiv:2008.07411

We introduce the sudden variant (SNZ) of the Net Zero scheme realizing controlled-Z (CZ) gates by baseband flux control of transmon frequency. SNZ CZ gates operate at the speed limit of transverse coupling between computational and non-computational states by maximizing intermediate leakage. The key advantage of SNZ is tuneup simplicity, owing to the regular structure of conditional phase and leakage as a function of two control parameters. We realize SNZ CZ gates in a multi-transmon processor, achieving 99.93±0.24% fidelity and 0.10±0.02% leakage. SNZ is compatible with scalable schemes for quantum error correction and adaptable to generalized conditional-phase gates useful in intermediate-scale applications.

*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

Nature Partner Journal Quantum Information

arXiv:2002.07119

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.

*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.

*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.

# 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)