Publications of Gabriel Jauma

We have analyzed and proposed coupling mechanisms between Three Josephson Junction Flux Qubits (3JJQ). For this, we have developed a numerical method to extract the effective Hamiltonian of a system of coupled qubits via the Schrieffer-Wolff transformation (SWT). We then give a comprehensive introduction to the 3JJQ, and study it analytically by approximating its potential with a Harmonic well. With a clear understanding of the 3JJQs, we use the SWT to gain intuition about their effective dipolar interaction with the electromagnetic field, and use that intuition to propose and study analytically and numerically the capacitive coupling of two 3JJQs via a non-tunable capacitor, and the inductive coupling of two 3JJQs via a tunable Josephson Junction (dc-SQUID), showing that we are able to reproduce non-stoquastic Hamiltonians in the strong-coupling regime.

We study the spin-glass transition in several Ising models of relevance for quantum annealers. We extract the spin-glass critical temperature by extrapolating the pseudo-critical properties obtained with Replica-Exchange Monte-Carlo for finite-size systems. We find a spin-glass phase for some random lattices (random-regular and small-world graphs) in good agreement with previous results. However, our results for the quasi-two-dimensional graphs implemented in the D-Wave annealers (Chimera, Zephyr, and Pegasus) indicate only a zero-temperature spin-glass state, as their pseudo-critical temperature drifts towards smaller values. This implies that the asymptotic runtime to find the low-energy configuration of those graphs is likely to be polynomial in system size, nevertheless, this scaling may only be reached for very large system sizes — much larger than existing annealers — as we observe an abrupt increase in the computational cost of the simulations around the pseudo-critical temperatures. Thus, two-dimensional systems with local crossings can display enough complexity to make unfeasible the search with classical methods of low-energy configurations.

Variational algorithms have received significant attention in recent years due to their potential to solve practical problems using noisy intermediate-scale quantum (NISQ) devices. A fundamental step of these algorithms is the evaluation of the expected value of Hamiltonians, and hence efficient schemes to perform this task are required. The standard approach employs local measurements of Pauli operators and requires a large number of circuits. An alternative is to make use of entangled measurements, which might introduce additional gates between physically disconnected qubits that harm the performance. As a solution to this problem, we propose hardware-efficient entangled measurements (HEEM), that is, measurements that permit only entanglement between physically connected qubits. We show that this strategy enhances the evaluation of molecular Hamiltonians in NISQ devices by reducing the number of circuits required without increasing their depth. We provide quantitative metrics of how this approach offers better results than local measurements and arbitrarily entangled measurements. We estimate the ground-state energy of the H$_2$O molecule with classical simulators and quantum hardware using the variational quantum eigensolver with HEEM.

A flux qubit can interact strongly when it is capacitively coupled to other circuit elements. This interaction can be separated in two parts, one acting on the qubit subspaces and one in which excited states mediate the interaction. The first term dominates the interaction between the flux qubit and an LC-resonator, leading to ultrastrong couplings of the form $\sigma^y(a+a^\dagger),$ which complement the inductive $\sigma^xi(a^\dagger-a)$ coupling. However, when coupling two flux qubits capacitively, all terms need to be taken into account, leading to complex non-stoquastic ultrastrong interaction of the $\sigma^y\sigma^y$, $\sigma^z\sigma^z$ and $\sigma^x\sigma^x$ type. Our theory explains all these interactions, describing them in terms of general circuit properties—coupling capacitances, qubit gaps, inductive, Josephson and capactive energies—, that apply to a wide variety of circuits and flux qubit designs.

We analyze the coupling of two flux qubits with a general many-body projector into the low-energy subspace. Specifically, we extract the effective Hamiltonians that controls the dynamics of two qubits when they are coupled via a capacitor and/or via a Josephson junction. While the capacitor induces a static charge coupling tunable by design, the Josephson junction produces a magnetic-like interaction easily tunable by replacing the junction with a SQUID. Those two elements allow to engineer qubits Hamiltonians with $XX$, $YY$ and $ZZ$ interactions, including ultra-strongly coupled ones. We present an exhaustive numerical study for two three-Josephson junctions flux qubit that can be directly used in experimental work. The method developed here, namely the numerical tool to extract qubit effective Hamiltonians at strong coupling, can be applied to replicate our analysis for general systems of many qubits and any type of coupling.