arXiv subjects

Mathias Mikkelsen

Publications and source records attributed to Mathias Mikkelsen.

9 recordsLinked to original sources

arXiv2025

First and second quantized digital quantum simulations of bosonic systems

We compare the basic resource requirements for first and second quantized bosonic mappings in a system consisting of $N$ particles in $M$ modes. In addition to the standard binary first quantized mapping, we investigate the unary first quantized mapping. Our comparison focuses on the $k$-body reduced density matrix ($k$-RDM) and two standard bosonic Hamiltonians. The first quantized mappings use less resources for off-diagonal terms of the $k$-RDM by a factor of $ \sim N^k$, compared to the second quantized mappings. The number of gates for the first quantized binary mapping increases faster with $M$ compared to the other mappings. Nevertheless, a detailed numeric analysis reveals that the binary first quantized mapping still requires fewer gates than the binary and unary second quantized ones for realistic combinations of $N$ and $M$, while requiring exponentially fewer qubits than the unary mappings. Additionally, the number of CNOT and $R_z(\phi)$ gates necessary to express a single Trotter step of the Hamiltonian in the binary first quantized mapping is comparable to the (most efficient for a single Trotter step) unary first quantized one when $M = 2^n$ for both the Bose-Hubbard model and the harmonic trap with short-range interactions. Additionally the binary mapping leads to lower one-norms than the unary mapping making it the overall most efficient choice for qubitization-based quantum phase estimation.

quant-ph↗

arXiv2025

Entanglement-enhanced correlation propagation in the one-dimensional SU($N$) Fermi-Hubbard model

We investigate the dynamics of correlation propagation in the one-dimensional Fermi-Hubbard model with SU($N$) symmetry when the repulsive-interaction strength is quenched from a large value, at which the ground state is a Mott-insulator with $1/N$ filling, to an intermediate value. From approximate analytical insights based on a simple model that captures the essential physics of the doublon excitations, we show that entanglement in the initial state leads to collective enhancement of the propagation velocity $v_{\text{SU}(N)}$ when $N>2$, becoming equal to the velocity of the Bose-Hubbard model in the large-$N$ limit. These results are supported by numerical calculations of the density-density correlation in the quench dynamics for $N=2,3,4,$ and $6$.

cond-mat.quant-gas↗

arXiv2024

Quantum-selected configuration interaction with time-evolved state

Quantum-selected configuration interaction (QSCI) utilizes an input quantum state on a quantum device to select important bases (electron configurations in quantum chemistry) that define a subspace in which to diagonalize a target Hamiltonian, i.e., perform selected configuration interaction, on classical computers. Previous proposals for preparing a good input state, which is crucial for the quality of QSCI, based on optimization of quantum circuits may suffer from optimization difficulty and require many runs of the quantum device. Here, we propose using a time-evolved state by the target Hamiltonian (for some initial state) as an input of QSCI. Our proposal is based on the intuition that the time evolution by the Hamiltonian creates electron excitations of various orders when applied to the initial state. We numerically investigate the accuracy of the energy obtained by the proposed method for quantum chemistry Hamiltonians describing electronic states of small molecules. Numerical results reveal that our method can yield sufficiently accurate ground-state energies for the investigated molecules. Systematic analysis when increasing the number of qubits in a hydrogen chain shows that the subspace size required for sufficiently accurate results is reasonable at system sizes that cannot be solved by naive classical diagonalization. Our proposal provides a systematic and optimization-free method to prepare the input state of QSCI and could contribute to practical applications of quantum computers in quantum chemistry calculations.

quant-ph↗

arXiv2023

Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU$(N)$ Hubbard models

It is well established that the noise correlations measured by time-of-flight imaging in cold-atom experiments, which correspond to the density-density correlations in the momentum space of trapped atomic gases, can probe the spin structure factor deep in the Mott-insulating regime of SU(2) Hubbard models. We explicitly derive the mathematical relation between the noise correlations and the spin structure factor in the strong-interaction limit of SU$(N)$ Hubbard models at any integer filling $\rho$. By calculating the ground states of one-dimensional SU$(N)$ Fermi-Hubbard models for $2\leq N\leq 6$ with use of the density-matrix renormalization-group method, we confirm the relation numerically in the regime of strong interactions $U \gg t$, where $U$ and $t$ denote the onsite interaction and the hopping energy. We show that the deviation between the actual noise correlations and those obtained from the spin structure factor scales as approximately $(t/U)^2$ for $\rho=1$ at intermediate and large lattice sizes on the basis of numeric and semi-analytic arguments.

cond-mat.quant-gas↗

arXiv2023

Quantum chaos in interacting Bose-Bose mixtures

The appearance of chaotic quantum dynamics significantly depends on the symmetry properties of the system, and in cold atomic systems many of these can be experimentally controlled. In this work, we systematically study the emergence of quantum chaos in a minimal system describing one-dimensional harmonically trapped Bose-Bose mixtures by tuning the particle-particle interactions. Using an advanced exact diagonalization scheme, we examine the transition from integrability to chaos when the inter-component interaction changes from weak to strong. Our study is based on the analysis of the level spacing distribution and the distribution of the matrix elements of observables in terms of the eigenstate thermalization hypothesis and their dynamics. We show that one can obtain strong signatures of chaos by increasing the inter-component interaction strength and breaking the symmetry of intra-component interactions.

quant-ph↗

arXiv2022

Resonant superfluidity in the Rabi-coupled spin-dependent Fermi-Hubbard model

We investigate the ground-state phase diagram of the one-dimensional attractive Fermi-Hubbard model with spin-dependent hoppings and an on-site Rabi coupling using the density matrix renormalization group method. In particular, we show that even in the limit of one component being immobile the pair superfluidity can be resonantly enhanced when the Rabi coupling is on the order of the interaction strength just before the system starts to strongly polarize. We derive an effective spin-1/2 XXZ model in order to understand the ground-state properties in the strong attraction limit.

cond-mat.quant-gas↗

arXiv2022

Piezo-Electric Shear Rheometry: Further developments in experimental implementation and data extraction

The Piezo-electric Shear Gauge (PSG) [Christensen & Olsen, Rev. Sci. Instrum. 66, 5019, 1995] is a rheometric technique developed to measure the complex shear modulus of viscous liquids near their glass transition temperature. We report recent advances to the PSG technique: 1) The data extraction procedure is optimized which extends the upper limit of the frequency range of the method to between 50 and 70 kHz. 2) The measuring cell is simplified to use only one piezo-electric ceramic disc instead of three. We present an implementation of this design intended for liquid samples. Data obtained with this design revealed that a soft extra spacer is necessary to allow for thermal contraction of the sample in the axial direction. Model calculations show that flow in the radial direction is hindered by the confined geometry of the cell when the liquid becomes viscous upon cooling. The method is especially well-suited for -- but not limited to -- glassy materials.

cond-mat.soft↗

arXiv2020

Connecting scrambling and work statistics for short-range interactions in the harmonic oscillator

We investigate the relationship between information scrambling and work statistics after a quench for the paradigmatic example of short-range interacting particles in a one-dimensional harmonic trap, considering up to five particles numerically. In particular, we find that scrambling requires finite interactions, in the presence of which the long-time average of the squared commutator for the individual canonical operators is directly proportional to the variance of the work probability distribution. In addition to the numerical results, we outline the mathematical structure of the N-body system which leads to this outcome. We thereby establish a connection between the scrambling properties and the induced work fluctuations, with the latter being an experimental observable that is directly accessible in modern cold atom experiments.

quant-ph↗

arXiv2018

Static and dynamic phases of a Tonks-Girardeau gas in an optical lattice

We investigate the properties of a Tonks-Girardeau gas in the presence of a one-dimensional lattice potential. Such a system is known to exhibit a pinning transition when the lattice is commensurate with the particle density, leading to the formation of an insulating state even at infinitesimally small lattice depths. Here we examine the properties of the gas at all lattices depths and, in addition to the static properties, also consider the non-adiabatic dynamics induced by the sudden motion of the lattice potential with a constant speed. Our work provides a continuum counterpart to the work done in discrete lattice models.

cond-mat.quant-gas↗