arXiv subjects

Timo Eckstein

Publications and source records attributed to Timo Eckstein.

7 recordsLinked to original sources

arXiv2025

Optimizing Superconducting Three-Qubit Gates for Surface-Code Error Correction

Quantum error correction (QEC) is one of the crucial building blocks for developing quantum computers that have significant potential for reaching a quantum advantage in applications. Prominent candidates for QEC are stabilizer codes for which periodic readout of stabilizer operators is typically implemented via successive two-qubit entangling gates, and is repeated many times during a computation. To improve QEC performance, it is thus beneficial to make the stabilizer readout faster and less prone to fault-tolerance-breaking errors. Here we design a 3-qubit CZZ gate for superconducting transmon qubits that maps the parity of two data qubits onto one measurement qubit in a single step. We find that the gate can be executed in a duration of $35\,$ns with a fidelity of F$=99.96 \, \%$. To optimize the gate, we use an error model obtained from the microscopic gate simulation to systematically suppress Pauli errors that are particularly harmful to the QEC protocol. Using this error model, we investigate the implementation of this 3-qubit gate in a surface code syndrome readout schedule. We find that for the rotated surface code, the implementation of CZZ gates increases the error threshold by nearly 50\% to $\approx 1.2\,\%$ and decreases the logical error rate, in the experimental relevant regime, by up to one order of magnitude, compared to the standard CZ readout protocol. We also show that for the unrotated surface code, strictly fault-tolerant readout schedules can be found. This opens a new perspective for below-threshold surface-code error correction, where it can be advantageous to use multi-qubit gates instead of two-qubit gates to obtain a better QEC performance.

quant-ph↗

arXiv2024

Shot-noise reduction for lattice Hamiltonians

Efficiently estimating energy expectation values of quantum lattice systems on quantum computers is a crucial subroutine for various quantum algorithms, which can lead to significant overhead due to the high measurement shot numbers required. We introduce a measurement strategy tailored to quantum lattice systems and (noisy) energy eigenstates. It is based on a geometric partitioning of the Hamiltonian into local patches, and performing the measurements in the eigenbases of those patches. The resulting energy estimator has a smaller variance than the ones of Pauli grouping schemes, which leads to a reduction of the total number of shots. We provide rigorous guarantees for this variance improvement for energy eigentstates, also in the presence of depolarizing noise. As one can choose the subsystem size, one can ensure that measurement circuits remain within implementable depths. In numerical experiments, we demonstrate the shot count reduction for various 2D lattice models, including the transverse field XY and Ising models, as well as the Fermi-Hubbard model. We find sampling improvements of several orders of magnitude already for plaquettes of two by two qubits, where the required readout circuits remain very moderate in depth.

quant-ph↗

arXiv2024

Solving an Industrially Relevant Quantum Chemistry Problem on Quantum Hardware

Quantum chemical calculations are among the most promising applications for quantum computing. Implementations of dedicated quantum algorithms on available quantum hardware were so far, however, mostly limited to comparatively simple systems without strong correlations. As such, they can also be addressed by classically efficient single-reference methods. In this work, we calculate the lowest energy eigenvalue of active space Hamiltonians of industrially relevant and strongly correlated metal chelates on trapped ion quantum hardware, and integrate the results into a typical industrial quantum chemical workflow to arrive at chemically meaningful properties. We are able to achieve chemical accuracy by training a variational quantum algorithm on quantum hardware, followed by a classical diagonalization in the subspace of states measured as outputs of the quantum circuit. This approach is particularly measurement-efficient, requiring 600 single-shot measurements per cost function evaluation on a ten qubit system, and allows for efficient post-processing to handle erroneous runs.

quant-ph↗

arXiv2023

Large-scale simulations of Floquet physics on near-term quantum computers

Periodically driven quantum systems exhibit a diverse set of phenomena but are more challenging to simulate than their equilibrium counterparts. Here, we introduce the Quantum High-Frequency Floquet Simulation (QHiFFS) algorithm as a method to simulate fast-driven quantum systems on quantum hardware. Central to QHiFFS is the concept of a kick operator which transforms the system into a basis where the dynamics is governed by a time-independent effective Hamiltonian. This allows prior methods for time-independent simulation to be lifted to simulate Floquet systems. We use the periodically driven biaxial next-nearest neighbor Ising (BNNNI) model, a natural test bed for quantum frustrated magnetism and criticality, as a case study to illustrate our algorithm. We implemented a 20-qubit simulation of the driven two-dimensional BNNNI model on Quantinuum's trapped ion quantum computer. Our error analysis shows that QHiFFS exhibits not only a cubic advantage in driving frequency $\omega$ but also a linear advantage in simulation time $t$ compared to~Trotterization.

quant-ph↗

arXiv2021

Electronic coherence and coherent dephasing in the optical control of electrons in graphene

Electronic coherence is of utmost importance for the access and control of quantum-mechanical solid-state properties. Using a purely electronic observable, the photocurrent, we measure an electronic coherence time of 22 +/- 4 fs in graphene. The photocurrent is ideally suited to measure electronic coherence as it is a direct result of quantum path interference, controlled by the delay between two ultrashort two-color laser pulses. The maximum delay for which interference between the population amplitude injected by the first pulse interferes with that generated by the second pulse determines the electronic coherence time. In particular, numerical simulations reveal that the experimental data yield a lower boundary on the electronic coherence time and that coherent dephasing masks a lower coherence time. We expect that our results will significantly advance the understanding of coherent quantum-control in solid-state systems ranging from excitation with weak fields to strongly driven systems.

cond-mat.mes-hall↗

arXiv2021

Variational Hamiltonian simulation for translational invariant systems via classical pre-processing

The simulation of time evolution of large quantum systems is a classically challenging and in general intractable task, making it a promising application for quantum computation. A Trotter-Suzuki approximation yields an implementation thereof, where a higher approximation accuracy can be traded for an increased gate count. In this work, we introduce a variational algorithm which uses solutions of classical optimizations to predict efficient quantum circuits for time evolution of translationally invariant quantum systems. Our strategy can improve upon the Trotter-Suzuki accuracy by several orders of magnitude. It translates into a reduction in gate count and hence gain in overall fidelity at the same algorithmic accuracy. This is important in NISQ-applications where the fidelity of the output state decays exponentially with the number of gates. The performance advantage of our classical assisted strategy can be extended to open boundaries with translational symmetry in the bulk. We can extrapolate our method to beyond classically simulatable system sizes, maintaining its total fidelity advantage over a Trotter-Suzuki approximation making it an interesting candidate for beyond classical time evolution.

quant-ph↗

arXiv2019

Inelastic ponderomotive scattering of electrons at a high-intensity optical travelling wave in vacuum

In the early days of quantum mechanics Kapitza and Dirac predicted that matter waves would scatter off the optical intensity grating formed by two counter-propagating light waves [1]. This interaction, driven by the ponderomotive potential of the optical standing wave, was both studied theoretically and demonstrated experimentally for atoms [2] and electrons [3-5]. In the original version of the experiment [1,5], only the transverse momentum of particles was varied, but their energy and longitudinal momentum remained unchanged after the interaction. Here, we report on the generalization of the Kapitza-Dirac effect. We demonstrate that the energy of sub-relativistic electrons is strongly modulated on the few-femtosecond time scale via the interaction with a travelling wave created in vacuum by two colliding laser pulses at different frequencies. This effect extends the possibilities of temporal control of freely propagating particles with coherent light and can serve the attosecond ballistic bunching of electrons [6], or for the acceleration of neutral atoms or molecules by light.

physics.optics↗