arXiv subjects

Efekan Kökcü

Publications and source records attributed to Efekan Kökcü.

At least 19 recordsLinked to original sources

arXiv2026

Efficient Calculation of Equilibrium Correlation Functions

A majority of measurable dynamic quantities of a physical system is described as an equilibrium correlation function of the form $G_{AB}(t-t') = \left $, where $t'$ represents the impact time and $t$ represents the response time. Conventional quantum algorithms to compute such quantities via Hamiltonian simulation such as the Hadamard test, variational methods, or linear-response-based algorithms share one feature in common: each time point $t-t'$ is calculated by a different quantum circuit, leading to at least $O(N_t)$ total shots, and at least $O(N_t^2)$ total quantum gates. Here, we provide a different approach: utilizing $O(\log N_t)$ ancilla qubits to store time as a quantum variable, and effectively parallelize the computation of an equilibrium correlation function by requiring only a single quantum circuit for all time points. We show that this circuit needs to be run only $O(\log N_t)$ times, which in total requires $O(N_t \log N_t)$ quantum resources in the large system size limits. We prove that this scaling is optimal, and demonstrate our algorithm calculating the Green's function of a one-dimensional spinless Hubbard model.

quant-ph↗

arXiv2026

Scalable Benchmarking Framework for Dynamic Quantum Circuits

Dynamic quantum circuits with mid-circuit measurements (MCMs) and feed-forward operations play a crucial role in various applications, such as quantum error correction and quantum algorithms. With advancements in quantum hardware enabling the implementation of MCM and feed-forward loops, the use of dynamic circuits has become increasingly prevalent. There is a significant need for a benchmarking framework specially designed for dynamic circuits to capture their unique properties, as current benchmarking tools are designed primarily for unitary circuits and cannot be trivially extended to dynamic circuits. We propose dynamarq, a scalable and hardware-agnostic benchmarking framework for dynamic circuits. We collect a set of dynamic circuit benchmarks spanning various applications and propose a broad set of circuit features to characterize the structure of these dynamic circuits. We run them on two IBM quantum processors and the Quantinuum Helios-1E emulator, and propose scalable, application-dependent fidelity scores for each benchmark based on hardware execution results. We perform statistical modeling to identify correlations between circuit features and fidelity scores, and demonstrate highly accurate fidelity prediction using our model. Our model parameters are also transferable across hardware backends and calibration cycles. Our framework facilitates the understanding of dynamic circuit structures and provides insights for designing and optimizing dynamic circuits to achieve high execution fidelity on quantum hardware.

quant-ph↗

arXiv2026

Spin models with critical ground space degeneracy from Lie algebra relations

We introduce an $\mathrm{SO}(3)$-symmetric spin model derived from the algebraic structure of $\mathfrak{so}(3)$: It is obtained as the nearest-neighbor parent Hamiltonian of a Matrix Product State (MPS) built from the generators of the Lie algebra $\mathfrak{so}(3)$ and the identity matrix, and therefore encodes the quadratic relations of the Lie algebra. We characterize the ground space structure of the resulting model and show that for open boundary conditions (OBC), it exhibits a quadratic ground space degeneracy, given by one irreducible representation (irrep) of each odd dimension (integer spin). For periodic boundary conditions (PBC), it has a linear ground space degeneracy, consisting of a singlet --- namely, the MPS underlying the model --- and a ferromagnet (the irrep with maximal spin), and thus exhibits gapless excitations. We also generalize the construction and the analysis of the OBC ground space to $\mathrm{SO}(d)$ and other compact simple Lie groups. The MPS on which the model is based is an injective MPS, and therefore, its 3-site parent Hamiltonian has a unique ground space and is gapped. The observed critical behavior thus has its origin in the small parent Hamiltonian considered. The model's algebraic ground space scaling thus provides an example distinct from that reported in (Schuch et al., 2025, arXiv:2503.10767), where it was shown that small parent Hamiltonians of injective MPS generically have unique ground states, and examples with an exponential ground space degeneracy were given.

quant-ph↗

arXiv2026

Challenges in Barren Plateau Mitigation with Dynamic Parameterized Quantum Circuits

Variational quantum algorithms (VQAs) are a promising paradigm for quantum advantage, yet their trainability is severely hampered by barren plateaus (BPs). Several recent works have proposed dynamic parameterized quantum circuits (DPQCs), which interleave unitary layers with parameterized CPTP maps, such as engineered dissipation, feedforward gadgets, and periodic resets, as a possible strategy for mitigating BPs. We unify this class of circuits into a formalization for DPQCs.We identify constraints on the nature and the structure of DPQCs if they are to prevent a significant number of parameters from becoming untrainable. Using purification and Pauli-path analysis, we further identify a mechanism by which the cost function can remain anti-concentrated even when many parameters remain untrainable. Our analysis reveals ways to design DPQCs that do not have an exponentially concentrated cost function, and our results suggest that BP mitigation via DPQCs is at least as hard as designing BP-free unitaries.

quant-ph↗

arXiv2026

Efficient Quantum Implementation of Dynamical Mean Field Theory for Correlated Materials

The accurate theoretical description of materials with strongly correlated electrons is a formidable challenge in condensed matter physics and computational chemistry. Dynamical Mean Field Theory (DMFT) is a successful approach that predicts behaviors of such systems by incorporating some of the correlated behavior using an impurity model, but it is limited by the need to calculate the impurity Green's function. This work proposes a framework for DMFT calculations on quantum computers, focusing on near-term applications. It leverages the structure of the impurity problem, combining a low-rank Gaussian subspace representation of the ground state and a compressed, short-depth quantum circuit that joins state preparation with time evolution to compute Green's functions. We demonstrate the convergence of the DMFT algorithm using the Gaussian subspace in a noise-free setting, and show the hardware viability of circuit compression by extracting the impurity Green's function on IBM quantum processors for a single impurity coupled to three bath orbitals (8 qubits, 1 ancilla). We discuss potential paths toward realizing this quantum computing use case in materials science.

quant-ph↗

arXiv2026

Global approximations to correlation functions of strongly interacting quantum field theories

We introduce a method for constructing global approximations to correlation functions of strongly interacting quantum field theories, starting from perturbative results. The key idea is to employ interpolation method, such as the two-point Padé expansion, to interpolate the weak and strong coupling expansions of correlation function. We benchmark this many-body interpolation approach on two prototypical models: the lattice $ϕ^4$ field theory and the 2D Hubbard model. For the $ϕ^4$ theory, the resulting two point Padé approximants exhibit uniform and global convergence to the exact correlation function. For the Hubbard model, we show that even at second order, the Padé appproximant already provides reasonable characterization of the Matsubara Green's function for a wide range of parameters. Finally, we offer a heuristic explanation for these convergence properties based on analytic function theory.

cond-mat.str-el↗

arXiv2026

Strong-coupling expansion and two-point Padé approximation for lattice $ϕ^4$ field theory

Reliable approximations for correlation functions at intermediate and strong coupling remain hard to obtain for general quantum field theories. Perturbative expansions are often asymptotic or have a finite radius of convergence, which limits their applicability beyond weak coupling. Here we combine weak- and strong-coupling expansions and propose to use two-point Padé schemes to construct approximants. For lattice $ϕ^4$ theory, we show that this two-point interpolation strategy yields accurate global approximations to the two-point correlation function across broad coupling regimes and compares favorably with standard one-point resummation methods. We also provide heuristic explanations for the observed convergence behavior and discuss the practical range of validity of the approach.

hep-lat↗

arXiv2025

RedCarD: A Quantum Assisted Algorithm for Fixed-Depth Unitary Synthesis via Cartan Decomposition

A critical step in developing circuits for quantum simulation is to synthesize a desired unitary operator using the circuit building blocks. Studying unitaries and their generators from the Lie algebraic perspective has given rise to several algorithms for synthesis based on a Cartan decomposition of the dynamical Lie algebra. For unitaries of the form $e^{-itH}$, such as time-independent Hamiltonian simulation, the resulting circuits have depth that does not depend on simulation time $t$. However, finding such circuits has a large classical overhead in the cost function evaluation and the high dimensional optimization problem. In this work, by further partitioning the dynamical Lie algebra, we break down the optimization problem into smaller independent subproblems. Moreover, the resulting algebraic structure allows us to easily shift the evaluation of the cost function to the quantum computer, further cutting the classical overhead of the algorithm. As an application of the new hybrid algorithm, we synthesize the time evolution unitary for the 4-site transverse field Ising model on several IBM devices and Quantinuum's H1-1 quantum computer.

quant-ph↗

arXiv2025

QTurbo: A Robust and Efficient Compiler for Analog Quantum Simulation

Analog quantum simulation leverages native hardware dynamics to emulate complex quantum systems with great efficiency by bypassing the quantum circuit abstraction. However, conventional compilation methods for analog simulators are typically labor-intensive, prone to errors, and computationally demanding. This paper introduces QTurbo, a powerful analog quantum simulation compiler designed to significantly enhance compilation efficiency and optimize hardware execution time. By generating precise and noiseresilient pulse schedules, our approach ensures greater accuracy and reliability, outperforming the existing state-of-theart approach.

quant-ph↗

arXiv2025

Algebraic Compression of Free Fermionic Quantum Circuits: Particle Creation, Arbitrary Lattices and Controlled Evolution

Recently we developed a local and constructive algorithm based on Lie algebraic methods for compressing Trotterized evolution under Hamiltonians that can be mapped to free fermions. The compression algorithm yields a circuit which scales linearly in the number of qubits, has a depth independent of evolution time and compresses time-dependent Hamiltonians. The algorithm is limited to simple nearest-neighbor spin interactions and fermionic hopping. In this work, we extend our methods to compress evolution with long-range fermionic hopping, thereby enabling the embedding of arbitrary lattices onto a chain of qubits for fermion models. Moreover, we show that controlled time evolution, as well as fermion creation and annihilation operators can also be compressed. We demonstrate our results by adiabatically preparing the ground state for a half-filled fermionic chain, simulating a $4 \times 4$ tight binding model on ibmq washington, and calculating the topological Zak phase on a Quantinuum H1-1 trapped-ion quantum computer. With these new developments, our results enable the simulation of a wider range of models of interest and the efficient compression of subcircuits.

quant-ph↗

arXiv2025

A Practical Framework for Assessing the Performance of Observable Estimation in Quantum Simulation

Simulating dynamics of physical systems is a key application of quantum computing, with potential impact in fields such as condensed matter physics and quantum chemistry. However, current quantum algorithms for Hamiltonian simulation yield results that are inadequate for real use cases and suffer from lengthy execution times when implemented on near-term quantum hardware. In this work, we introduce a framework for evaluating the performance of quantum simulation algorithms, focusing on the computation of observables, such as energy expectation values. Our framework provides end-to-end demonstrations of algorithmic optimizations that utilize Pauli term groups based on k-commutativity, generate customized Clifford measurement circuits, and implement weighted shot distribution strategies across these groups. These demonstrations span multiple quantum execution environments, allowing us to identify critical factors influencing runtime and solution accuracy. We integrate enhancements into the QED-C Application-Oriented Benchmark suite, utilizing problem instances from the open-source HamLib collection. Our results demonstrate a 27.1% error reduction through Pauli grouping methods, with an additional 37.6% improvement from the optimized shot distribution strategy. Our framework provides an essential tool for advancing quantum simulation performance using algorithmic optimization techniques, enabling systematic evaluation of improvements that could maximize near-term quantum computers' capabilities and advance practical quantum utility as hardware evolves.

quant-ph↗

arXiv2024

Classification of dynamical Lie algebras generated by spin interactions on undirected graphs

We provide a classification of all dynamical Lie algebras generated by 2-local spin interactions on undirected graphs. Building on our previous work where we provided such a classification for spin chains, here we consider the more general case of undirected graphs. As it turns out, the one-dimensional case is special; for any other graph, the dynamical Lie algebra solely depends on whether the graph is bipartite or not. An important consequence of this result is that the cases where the dynamical Lie algebra is polynomial in size are special and restricted to one dimension.

quant-ph↗

arXiv2023

Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension

Much is understood about 1-dimensional spin chains in terms of entanglement properties, physical phases, and integrability. However, the Lie algebraic properties of the Hamiltonians describing these systems remain largely unexplored. In this work, we provide a classification of all Lie algebras generated by translation-invariant 2-local spin chain Hamiltonians, or so-called dynamical Lie algebras. We consider chains with open and periodic boundary conditions and find 17 unique dynamical Lie algebras. Our classification covers some well-known models such as the transverse-field Ising model and the Heisenberg chain, and we also find more exotic classes of Hamiltonians that cannot be identified easily. In addition to the closed and open spin chains, we consider systems with a fully connected topology, which may be relevant for quantum machine learning approaches. We discuss the practical implications of our work in the context of quantum control, variational quantum computing, and the spin chain literature.

quant-ph↗

arXiv2023

Mapping the metal-insulator phase diagram by algebraically fast-forwarding dynamics on a cloud quantum computer

Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model and thus gives an approximate solution of the Hubbard model from the solution of simpler quantum impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models by preparing and evolving the ground state under the impurity Hamiltonian on a quantum computer that is assumed to have the scalability and accuracy far beyond the current state-of-the-art quantum hardware. As a proof of principle demonstration targeting the Anderson impurity model we close the DMFT loop with current noisy hardware. With a highly optimized fast-forwarding quantum circuit and a noise resilient spectral analysis we observe a Mott phase transition. Based on a Cartan decomposition, our algorithm gives a fixed depth, fast-forwarding, quantum circuit that can evolve the initial state over arbitrarily long times without time-discretization errors typical of other product decomposition formulas such as Trotter decomposition. By exploiting the structure of the fast-forwarding circuits we reduce the gate count (to 77 CNOTs after optimization), simulate the dynamics, and extract frequencies from the Anderson impurity model on noisy quantum hardware. We then demonstrate the Mott transition by mapping the full metal-insulator phase-diagram. Near the Mott phase transition, our method maintains accuracy where Trotter error would otherwise dominate due to the long-time evolution required to resolve quasiparticle resonance frequency extremely close to zero. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware, made viable by a highly optimized computation in terms of gate depth, simulation error, and runtime on quantum hardware.

quant-ph↗

arXiv2023

A linear response framework for simulating bosonic and fermionic correlation functions illustrated on quantum computers

Response functions are a fundamental aspect of physics; they represent the link between experimental observations and the underlying quantum many-body state. However, this link is often under-appreciated, as the Lehmann formalism for obtaining response functions in linear response has no direct link to experiment. Within the context of quantum computing, and by using a linear response framework, we restore this link by making the experiment an inextricable part of the quantum simulation. This method can be frequency- and momentum-selective, avoids limitations on operators that can be directly measured, and is ancilla-free. As prototypical examples of response functions, we demonstrate that both bosonic and fermionic Green's functions can be obtained, and apply these ideas to the study of a charge-density-wave material on ibm_auckland. The linear response method provides a robust framework for using quantum computers to study systems in physics and chemistry. It also provides new paradigms for computing response functions on classical computers.

quant-ph↗

arXiv2022

Subspace Diagonalization on Quantum Computers using Eigenvector Continuation

Quantum subspace diagonalization (QSD) methods are quantum-classical hybrid methods, commonly used to find ground and excited state energies by projecting the Hamiltonian to a smaller subspace. In applying these, the choice of subspace basis is critical from the perspectives of basis completeness and efficiency of implementation on quantum computers. In this work, we present Eigenvector Continuation (EC) as a QSD method, where low-energy states of the Hamiltonian at different points in parameter space are chosen as the subspace basis. This unique choice enables rapid evaluation of low-energy spectra, including ground and nearby excited states, with minimal hardware effort. As a particular advantage, EC is able to capture the spectrum across ground state crossovers corresponding to different symmetry sectors of the problem. We demonstrate this method for interacting spin models and molecules.

quant-ph↗

arXiv2022

Fixed Depth Hamiltonian Simulation via Cartan Decomposition

Simulating quantum dynamics on classical computers is challenging for large systems due to the significant memory requirements. Simulation on quantum computers is a promising alternative, but fully optimizing quantum circuits to minimize limited quantum resources remains an open problem. We tackle this problem presenting a constructive algorithm, based on Cartan decomposition of the Lie algebra generated by the Hamiltonian, that generates quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model, where a O(n^2)-gate circuits naturally emerge. Compared to product formulas with significantly larger gate counts, our algorithm drastically improves simulation precision. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.

quant-ph↗

arXiv2021

Algebraic Compression of Quantum Circuits for Hamiltonian Evolution

Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as Trotterization, which leads to circuits whose depth scales with the number of steps. When the circuit elements are limited to a subset of SU(4) -- or equivalently, when the Hamiltonian may be mapped onto free fermionic models -- several identities exist that combine and simplify the circuit. Based on this, we present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians. We explicitly show how this algorithm works for several spin models, and demonstrate its use for adiabatic state preparation of the transverse field Ising model.

quant-ph↗