arXiv subjects

Elie Assémat

Publications and source records attributed to Elie Assémat.

6 recordsLinked to original sources

arXiv2018

Optimized cross-resonance gate for coupled transmon systems

The cross-resonant gate is an entangling gate for fixed frequency superconducting qubits introduced for untunable qubits. While being simple and extensible, it suffers from long duration and limited fidelity. Using two different optimal control algorithms, we probe the quantum speed limit for a CNOT gate in this system. We show that the ability to approach this limit depends strongly on the ansatz used to describe the optimal control pulse. A piecewise constant ansatz with a single carrier leads to an experimentally feasible pulse shape, shorter than the one currently used in experiments, but that remains relatively far from the speed limit. On the other hand, an ansatz based on the two dominant frequencies involved in the optimal control problem allows to generate an optimal solution more than twice as fast, in under $30$ns. This comes close to the theoretical quantum speed limit, which we estimate at $15$ns for typical circuit-QED parameters, which is more than an order of magnitude faster than current experimental microwave-driven realizations, and more than twice as fast as tunable direct-coupling experimental realizations.

quant-ph↗

arXiv2018

Gradient optimization of analytic controls: the route to high accuracy quantum optimal control

Quantum computation places very stringent demands on gate fidelities, and experimental implementations require both the controls and the resultant dynamics to conform to hardware-specific constraints. Superconducting qubits present the additional requirement that pulses must have simple parameterizations, so they can be further calibrated in the experiment, to compensate for uncertainties in system parameters. Other quantum technologies, such as sensing, require extremely high fidelities. We present a novel, conceptually simple and easy-to-implement gradient-based optimal control technique named Gradient Optimization of Analytic conTrols (GOAT), which satisfies all the above requirements, unlike previous approaches. To demonstrate GOAT's capabilities, with emphasis on flexibility and ease of subsequent calibration, we optimize fast coherence-limited pulses for two leading superconducting qubits architectures - flux-tunable transmons and fixed-frequency transmons with tunable couplers.

quant-ph↗

arXiv2016

Quantum Dynamics in Phase space using the Biorthogonal von Neumann bases: Algorithmic Considerations

The von Neumann lattice refers to a discrete basis of Gaussians located on a lattice in phase space. It provides an attractive approach for solving quantum mechanical problems, allowing the pruning of tensor-product basis sets using phase space considerations. In a series of recent articles Shimshovitz et al. [Phys. Rev. Lett. 109 7 (2012)], Takemoto et al. [Journal of Chemical Physics 137 1 (2012)] Machnes et al. [Journal of Chemical Physics, accepted (2016)]), we have introduced two key new elements into the method: a formalism for converging the basis and for efficient pruning by use of the biorthogonal basis. In this paper we review the key components of the theory and then present new, efficient and parallelizable iterative algorithms for solving the time-independent and time-dependent Schrödinger equations. The algorithms dynamically determine the active reduced basis iteratively without resorting to classical analogs. These algorithmic developments, combined with the previous formal developments, allow quantum dynamics to be performed directly and economically in phase space. We provide two illustrative examples: double-well tunneling and double ionization of helium.

quant-ph↗

arXiv2016

Quantum Dynamics in Phase Space using Projected von Neumann Bases

We describe the mathematical underpinnings of the biorthogonal von Neumann method for quantum mechanical simulations (PvB). In particular, we present a detailed discussion of the important issue of non-orthogonal projection onto subspaces of biorthogonal bases, and how this differs from orthogonal projection. We present various representations of the Schrödinger equation in the reduced basis and discuss their relative merits. We conclude with illustrative examples and a discussion of the outlook and challenges ahead for the PvB representation.

quant-ph↗

arXiv2015

Double ionization of Helium from a phase space perspective

The aim of this paper is two-fold. First, we present a phase space perspective on long range double ionization in a one dimensional model of helium. The dynamics is simulated with the periodic von Neumann (PvB) method, an exact quantum method based on a lattice of phase space Gaussians. Second, we benchmark the method by comparing to the Multiconfiguration Time-dependent Hartree method. The PvB approach is found to be faster than the standard MCTDH code for the dynamics calculations and to give better accuracy control.

quant-ph↗

arXiv2014

On the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space

We analyze the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space and a discrete spectrum. Based on recent mathematical results, we rigorously show under which conditions such a system can be approximated in a finite dimensional Hilbert space. For a given threshold error, we estimate this finite dimension in terms of the used control field. As illustrative examples, we consider the cases of a rigid rotor and of a harmonic oscillator.

math.OC↗