arXiv subjects

Fedor Šimkovic IV

Publications and source records attributed to Fedor Šimkovic IV.

18 recordsLinked to original sources

arXiv2026

Augmenting Imaginary-Time Evolution with Local Geometric Information

Imaginary-time evolution (ITE) underpins a broad family of algorithms for ground-state preparation in quantum simulation and quantum many-body physics. In these methods, convergence is governed by the energy variance of the instantaneous state, causing the flow to approach the ground state only asymptotically. We introduce an augmented imaginary-time evolution (AITE) framework that replaces the standard gradient flow on the energy landscape with a geometrically informed descent along locally optimal directions, which are identified by exploiting the higher-order statistical structure of the instantaneous energy distribution. The resulting flow strictly outperforms standard ITE throughout the entire evolution and exhibits two qualitatively distinct regimes: a superlinear convergence regime, followed by an extinction regime in which the energy error vanishes exactly at a finite value of the imaginary-time flow parameter, in contrast to the asymptotic exponential decay of ITE. Standard ITE is recovered in the zero-skewness limit of AITE, implying that the acceleration extends naturally across the broader ITE algorithmic family.

quant-ph↗

arXiv2026

Hardware-Efficient Ground-State Preparation using Variational Imaginary-Time Majorana Evolution

Compact ground-state preparation circuits are essential for early fault-tolerant quantum chemistry. We introduce Variational Imaginary-time Majorana Evolution (VIME), a classical pre-training algorithm that extends operator-projected variational quantum imaginary-time evolution (OVQITE) to molecular electronic structure using a single compiled Majorana-propagation (MP) surrogate graph. We pair VIME with a compressed tiled Unitary Product State (c-tUPS) ansatz that we develop to reduce both classical simulation and quantum state-preparation costs. In the strongly correlated ruthenium complex TLD-1411, active-space calculations requiring up to 52 qubits achieve chemical precision against DMRG reference energies, with energy errors approximately $400\times$ smaller than those from ADAPT-VQE-based variational Majorana-propagation (ADAPT-VMPE). Across the strongly multireference acene series up to heptacene (60 qubits), VIME matches or improves on the MP-reported energy accuracy of the ADAPT-VMPE comparison points with up to $26\times$ fewer CNOTs and $167\times$ lower two-qubit depth. These results establish imaginary-time classical pre-training of compressed variational ansätze as a promising route to resource-efficient molecular ground-state preparation.

quant-ph↗

arXiv2026

Quantum-Classical Auxiliary-Field Quantum Monte Carlo at the Edge of Practicability

We introduce algorithmic improvements to quantum-classical auxiliary-field quantum Monte Carlo (QC-AFQMC) that reduce the dominant per-step classical scaling from $\tilde{\mathcal{O}}(N^{5.5})$ to $\tilde{\mathcal{O}}(N^{4.5})$ as a function of the number of molecular spin-orbitals $N$. Central to this improvement is the application of Aitken's block transformation to handle singular Pfaffians arising in the estimation of overlaps between a quantum trial state and classical Slater-determinant walkers. Together with the use of algorithmic differentiation for the computation of the force bias, this yields a $248\times$ estimated runtime improvement for a system of 100 molecular orbitals. Using our workflow, we demonstrate a ground-state energy calculation for $H_8$ from quantum data collected on IQM Emerald and post-processed with a tensor-network-based error-mitigation technique. We further validate the method's scalability through noiseless simulation of hydrogen chains up to $H_{12}$, and on the lithium-air battery related rearrangement pathway of the $Li_2O_4$ lithium superoxide dimer in a (26e, 20o) active space. We estimate both quantum and classical runtimes for a potential fault-tolerant implementation of QC-AFQMC, showing that the method holds promise for the early fault-tolerant era. These results move QC-AFQMC a step closer to treating chemically relevant systems.

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arXiv2026

Barbell Codes: qLDPC Codes for Superconducting Quantum Hardware

The major challenge on the way to fault-tolerant quantum computing comes from the insufficient quality of hardware components and the difficulty of scaling their number without further compromising fidelity. Quantum Low-Density Parity-Check (qLDPC) codes offer a promising solution by encoding logical qubits with low overhead and at a comparatively high code distance. However, it remains an open question how to scalably implement efficient qLDPC codes on fixed-connectivity quantum chips without increasing hardware complexity to enable the non-local interactions in their underlying QEC cycles. We resolve this challenge for the first time by introducing a family of qLDPC "barbell" codes accompanied by a realistic chip layout that natively supports all required two-qubit interactions. Crucially, the hardware complexity required to implement barbell codes remains constant as code distance increases. We provide a detailed investigation into the feasibility of all required hardware components and simulate a specific family of barbell codes against circuit-level noise. We find that, with a modest overhead of $<30$ data qubits per logical qubit, barbell codes can preserve information at a physical noise strength of $10^{-4}$ for several trillion QEC cycles. Simulations of logical multi-Pauli measurements, performed with circuits tailored to the chip, yield similar logical performance per QEC round, indicating that entangling gates between logical qubits in barbell codes can be realized fault-tolerantly.

quant-ph↗

arXiv2026

Near-Term Fermionic Simulation with Subspace Noise Tailored Quantum Error Mitigation

Quantum error mitigation (QEM) has emerged as a powerful tool for the extraction of useful quantum information from quantum devices. Here, we introduce the Subspace Noise Tailoring (SNT) algorithm, which efficiently combines the cheap cost of Symmetry Verification (SV) and low bias of Probabilistic Error Cancellation (PEC) QEM techniques. We study the performance of our method by simulating the Trotterized time evolution of the spin-1/2 Fermi-Hubbard model (FHM) using a variety of local fermion-to-qubit encodings, which define a computational subspace through a set of stabilizers, the measurement of which can be used to post-select noisy quantum data. We study different combinations of QEM and encodings and uncover a rich state diagram of optimal combinations, depending on the hardware performance, system size and available shot budget. We then demonstrate how SNT extends the reach of current noisy quantum computers in terms of the number of fermionic lattice sites and the number of Trotter steps, and quantify the required hardware performance beyond which a noisy device may compete with current state-of-the-art classical computational methods.

quant-ph↗

arXiv2025

Quantum Assisted Ghost Gutzwiller Ansatz

The ghost Gutzwiller ansatz (gGut) embedding technique was shown to achieve comparable accuracy to the gold standard dynamical mean-field theory method in simulating real material properties, yet at a much lower computational cost. Despite that, gGut is limited by the algorithmic bottleneck of computing the density matrix of the underlying effective embedding model, a quantity which must be converged within a self-consistent embedding loop. We develop a hybrid quantum-classical gGut technique which computes the ground state properties of embedding Hamiltonians with the help of a quantum computer, using the sample-based quantum-selected configuration interaction (QSCI) algorithm. We study the applicability of SCI-based methods to the evaluation of the density of states for single-band Anderson impurity models within gGut and find that such ground states of interest become sufficiently sparse in the CI basis as the number of ghost orbitals is increased. Further, we investigate the performance of QSCI using local unitary cluster Jastrow (LUCJ) variational quantum states in combination with a circuit cutting technique, prepared on IQM's quantum hardware for system sizes of up to 11 ghost orbitals, equivalent to 24 qubits. We report converged gGut calculations which correctly capture the metal-to-insulator phase transition in the Fermi-Hubbard model on the Bethe lattice by using quantum samples to build an SCI basis with as little as $1\%$ of the total CI basis states.

quant-ph↗

arXiv2025

Fermion-to-qubit encodings with arbitrary code distance

We introduce a framework which allows to systematically and arbitrarily scale the code distance of local fermion-to-qubit encodings in one and two dimensions without growing the weights of stabilizers. This is achieved by embedding low-distance encodings into the surface code in the form of topological defects. We introduce a family of Ladder Encodings (LE), which is optimal in the sense that the code distance is equal to the weights of density and nearest-neighbor hopping operators of a one-dimensional Fermi-Hubbard model. In two dimensions, we show how to scale the code distance of LE as well as other low-distance encodings such as Verstraete-Cirac and Derby-Klassen. We further introduce Perforated Encodings, which locally encode two fermionic spin modes within the same surface code structure. We show that our strategy is also extendable to other topological codes by explicitly embedding the LE into a 6.6.6 color code.

quant-ph↗

arXiv2024

Magnetic phase diagram of the three-dimensional doped Hubbard model

We establish the phase diagram of the Hubbard model on a cubic lattice for a wide range of temperatures, dopings and interaction strengths, considering both commensurate and incommensurate magnetic orders. We use the dynamical mean-field theory together with an efficient method to compute the free energy which enable the determination of the correct ordering vectors. Besides an antiferromagnetic state close to half-filling, we identify a number of different magnetic spiral phases with ordering vectors $(q,π,π)$, $(q,q,π)$ and $(q,q,q)$ as well as a region with close competition between them, hinting at spatial phase separation or at the onset of a stripe phase. Additionally, we extensively study several thermodynamic properties with direct relevance to cold-atom experiments: the entropy, energy and double-occupancy.

cond-mat.str-el↗

arXiv2024

Low-depth simulations of fermionic systems on square-grid quantum hardware

We present a general strategy for mapping fermionic systems to quantum hardware with square qubit connectivity which yields low-depth quantum circuits, counted in the number of native two-qubit fSIM gates. We achieve this by leveraging novel operator decomposition and circuit compression techniques paired with specifically chosen low-depth fermion-to-qubit mappings and allow for a high degree of gate cancellations and parallelism. Our mappings retain the flexibility to simultaneously optimize for qubit counts or qubit operator weights and can be used to investigate arbitrary fermionic lattice geometries. We showcase our approach by investigating the tight-binding model, the Fermi-Hubbard model as well as the multi-orbital Hubbard-Kanamori model. We report unprecedentedly low circuit depths per single Trotter layer with up to a $70 \%$ improvement upon previous state-of-the-art. Our compression technique also results in significant reduction of two-qubit gates. We find the lowest gate-counts when applying the XYZ-formalism to the DK mapping. Additionally, we show that our decomposition and compression formalism produces favourable circuits even when no native parameterized two-qubit gates are available.

quant-ph↗

arXiv2024

On-Premises Superconducting Quantum Computer for Education and Research

With a growing interest in quantum technology globally, there is an increasing need for accessing relevant physical systems for education and research. In this paper we introduce a commercially available on-site quantum computer utilizing superconducting technology, offering insights into its fundamental hardware and software components. We show how this system can be used in education to teach quantum concepts and deepen understanding of quantum theory and quantum computing. It offers learning opportunities for future talent and contributes to technological progress. Additionally, we demonstrate its use in research by replicating some notable recent achievements.

quant-ph↗

arXiv2024

Small Quantum Codes from Algebraic Extensions of Generalized Bicycle Codes

Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from the surface code, which has a vanishing encoding rate, to very promising codes with constant encoding rate and linear distance. In this work, motivated by current small-scale experimental quantum processing units, we devise small quantum codes that are inspired by a subset of quantum LDPC codes, known as generalized bicycle (GB) codes. We introduce a code construction based on algebraic manipulation of the parity-check matrix of GB codes, rather than manipulation of Tanner graphs. Our construction leads to families of quantum LDPC codes of small size, and we demonstrate numerically that their performance scales comparably to the performance of surface codes for similar sizes under a phenomenological noise model. The advantage of our code family is that they encode many logical qubits in one code, at the expense of non-local connectivity. We then explore three variants of the code construction focusing on reducing the long-range connectivity by bringing it closer to the current experimental capabilities of short-range connectivity devices.

quant-ph↗

arXiv2023

Optimal, hardware native decomposition of parameterized multi-qubit Pauli gates

We show how to efficiently decompose a parameterized multi-qubit Pauli (PMQP) gate into native parameterized two-qubit Pauli (P2QP) gates minimizing both the circuit depth and the number of P2QP gates. Given a realistic quantum computational model, we argue that the technique is optimal in terms of the number of hardware native gates and the overall depth of the decomposition. Starting from PMQP gate decompositions for the path and star hardware graph, we generalize the procedure to any generic hardware graph and provide exact expressions for the depth and number of P2QP gates of the decomposition. Furthermore, we show how to efficiently combine the decomposition of multiple PMQP gates to further reduce the depth as well as the number of P2QP gates for a combinatorial optimization problem using the Lechner-Hauke-Zoller (LHZ) mapping.

quant-ph↗

arXiv2021

Mott insulating states with competing orders in the triangular lattice Hubbard model

The physics of the triangular lattice Hubbard model exhibits a rich phenomenology, ranging from a metal-insulator transition, intriguing thermodynamic behavior, and a putative spin liquid phase at intermediate coupling, ultimately becoming a magnetic insulator at strong coupling. In this multimethod study, we combine a finite-temperature tensor network method, minimally entangled thermal typical states (METTS), with two Green-function-based methods, connected-determinant diagrammatic Monte Carlo and cellular dynamical mean-field theory, to establish several aspects of this model. We elucidate the evolution from the metallic to the insulating regime from the complementary perspectives brought by these different methods. We compute the full thermodynamics of the model on a width-four cylinder using METTS in the intermediate to strong coupling regime. We find that the insulating state hosts a large entropy at intermediate temperatures, which increases with the strength of the coupling. Correspondingly, and consistently with a thermodynamic Maxwell relation, the double occupancy has a minimum as a function of temperature which is the manifestation of the Pomeranchuk effect of increased localization upon heating. The intermediate coupling regime is found to exhibit both pronounced chiral as well as stripy antiferromagnetic spin correlations. We propose a scenario in which time-reversal symmetry-broken states compete with stripy-spin states at lowest temperatures.

cond-mat.str-el↗

arXiv2021

The Weak, the Strong and the Long Correlation Regimes of the Two-Dimensional Hubbard Model at Finite Temperature

We investigate the momentum-resolved spin and charge susceptibilities, as well as the chemical potential and double occupancy in the two-dimensional Hubbard model as functions of doping, temperature and interaction strength. Through these quantities, we identify a weak-coupling regime, a strong-coupling regime with short-range correlations and an intermediate-coupling regime with long magnetic correlation lengths. In the spin channel, we observe an additional crossover from commensurate to incommensurate correlations. In contrast, we find charge correlations to be only short ranged for all studied temperatures, which suggests that the spin and charge responses are decoupled. These findings were obtained by a novel connected determinant diagrammatic Monte Carlo algorithm for the computation of double expansions, which we introduce in this paper. This permits us to obtain numerically exact results at unprecedentedly low temperatures $T\geq 0.067$ for interactions up to $U\leq 8$, while working on arbitrarily large lattices. Our method also allows us to gain physical insights from investigating the analytic structure of perturbative series. We connect to previous work by studying smaller lattice geometries and report substantial finite-size effects.

cond-mat.str-el↗

arXiv2021

Superfluid ground state phase diagram of the two-dimensional Hubbard model in the emergent Bardeen-Cooper-Schrieffer regime

In nonperturbative regimes, the superfluid instability in the two-dimensional Hubbard model can be described by an emergent BCS theory with small effective pairing constants. We compute the effective couplings using a controlled bold-line diagrammatic Monte Carlo approach, which stochastically sums all skeleton Feynman diagrams dressed in the one- and two-particle channels to high expansion orders, and map out the resulting superfluid ground-state phase diagram in a range of next-nearest-neighbor hopping $0 \leq t^{\prime} \leq 0.3t$, interaction strength $0 \leq U \leq 3t$, and lattice filling $0 \leq n \leq 2$. The phase diagram is dramatically transformed in the hole-doped region and becomes particularly rich at larger doping and $t'$. At $t'=0.3$, the weak-coupling picture with the dominant triplet pairing sharply peaked at $n \approx 0.73$ due to the Van Hove singularity is replaced by a plateau of the singlet $d_{x^2-y^2}$ paring, while for $U \gtrsim 3t$ the effective couplings are consistent with the $d_{x^2-y^2}$ high-temperature superconductivity in the hole-doped region near cuprates' optimal doping.

cond-mat.str-el↗

arXiv2021

Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model

The Hubbard model represents the fundamental model for interacting quantum systems and electronic correlations. Using the two-dimensional half-filled Hubbard model at weak coupling as a testing ground, we perform a comparative study of a comprehensive set of state of the art quantum many-body methods. Upon cooling into its insulating antiferromagnetic ground-state, the model hosts a rich sequence of distinct physical regimes with crossovers between a high-temperature incoherent regime, an intermediate temperature metallic regime and a low-temperature insulating regime with a pseudogap created by antiferromagnetic fluctuations. We assess the ability of each method to properly address these physical regimes and crossovers through the computation of several observables probing both quasiparticle properties and magnetic correlations, with two numerically exact methods (diagrammatic and determinantal quantum Monte Carlo) serving as a benchmark. By combining computational results and analytical insights, we elucidate the nature and role of spin fluctuations in each of these regimes. Based on this analysis, we explain how quasiparticles can coexist with increasingly long-range antiferromagnetic correlations, and why dynamical mean-field theory is found to provide a remarkably accurate approximation of local quantities in the metallic regime. We also critically discuss whether imaginary time methods are able to capture the non-Fermi liquid singularities of this fully nested system.

cond-mat.str-el↗

arXiv2020

Efficient One-Loop-Renormalized Vertex Expansions with Connected Determinant Diagrammatic Monte Carlo

We present a technique that enables the evaluation of perturbative expansions based on one-loop-renormalized vertices up to large expansion orders. Specifically, we show how to compute large-order corrections to the random phase approximation in either the particle-hole or particle-particle channels. The algorithm's efficiency is achieved by the summation over contributions of all symmetrized Feynman diagram topologies using determinants, and by integrating out analytically the two-body long-range interactions in order to yield an effective zero-range interaction. Notably, the exponential scaling of the algorithm as a function of perturbation order leads to a polynomial scaling of the approximation error with computational time for a convergent series. To assess the performance of our approach, we apply it to the non-perturbative regime of the square-lattice fermionic Hubbard model away from half-filling and report, as compared to the bare interaction expansion algorithm, significant improvements of the Monte Carlo variance as well as the convergence properties of the resulting perturbative series.

cond-mat.str-el↗

arXiv2020

Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model

The ground state of the Hubbard model with nearest-neighbor hopping on the square lattice at half filling is known to be that of an antiferromagnetic (AFM) band insulator for any on-site repulsion. At finite temperature, the absence of long-range order makes the question of how the interaction-driven insulator is realized nontrivial. We address this problem with controlled accuracy in the thermodynamic limit using self-energy diagrammatic determinant Monte Carlo and dynamical cluster approximation methods and show that development of long-range AFM correlations drives an extended crossover from Fermi liquid to insulating behavior in the parameter regime that precludes a metal-to-insulator transition. The intermediate crossover state is best described as a non-Fermi liquid with a partially gapped Fermi surface.

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