arXiv subjects

Refik Mansuroglu

Publications and source records attributed to Refik Mansuroglu.

13 recordsLinked to original sources

arXiv2026

Complexity of Quadratic Bosonic Hamiltonian Simulation: $\mathsf{BQP}$-Completeness and $\mathsf{PostBQP}$-Hardness

The computational complexity of simulating the dynamics of physical quantum systems is a central question at the interface of quantum physics and computer science. In this work, we address this question for the simulation of exponentially large bosonic Hamiltonians with quadratic interactions. We present two results: First, we introduce a broad class of quadratic bosonic problems for which we prove that they are $\mathsf{BQP}$-complete. Importantly, this class includes two known $\mathsf{BQP}$-complete problems as special cases: Classical oscillator networks and continuous-time quantum walks. Second, we show that extending the aforementioned class to even more general quadratic Hamiltonians results in a $\mathsf{PostBQP}$-hard problem. This reveals a sharp transition in the complexity of simulating large quantum systems on a quantum computer, as well as in the difference in complexity between their simulation on classical and quantum computers.

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arXiv2025

Direct Equivalence between Dynamics of Quantum Walks and Coupled Classical Oscillators

Continuous time quantum walks on exponentially large, sparse graphs form a powerful paradigm for quantum computing: On the one hand, they can be efficiently simulated on a quantum computer. On the other hand, they are themselves BQP-complete, providing an alternative framework for thinking about quantum computing -- a perspective which has indeed led to a number of novel algorithms and oracle problems. Recently, simulating the dynamics of a system of harmonic oscillators (that is, masses and springs) was set forth as another BQP-complete problem defined on exponentially large, sparse graphs. In this work, we establish a direct and transparent mapping between these two classes of problems. As compared to linking the two classes of problems via their BQP-completeness, our mapping has several desirable features: It is transparent, in that it respects the structure of the problem, including the geometry of the underlying graph, initialization, read-out, and efficient oracle access, resulting in low overhead in terms of both space and time; it allows to map also between restricted subsets of instances of both problems which are not BQP-complete; it provides a recipe to directly translate any quantum algorithm designed in the quantum walk paradigm to harmonic oscillators (and vice versa); and finally, it provides an alternative, transparent way to prove BQP-completeness of the harmonic oscillator problem by mapping it to BQP-completeness construction for the quantum walk problem (or vice versa).

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arXiv2025

Hyperinvariant Spin Network States -- An AdS/CFT Model from First Principles

We study the existence and limitations of hyperinvariant tensor networks incorporating a local SU(2) symmetry. As discrete implementations of the anti de-Sitter/conformal field theory (AdS/CFT) correspondence, such networks have created bridges between the fields of quantum information theory and quantum gravity. Adding SU(2) symmetry to the tensor network allows a direct connection to spin network states, a basis of the kinematic Hilbert space of loop quantum gravity (LQG). We consider a particular situation where the states can be interpreted as kinematic quantum states for three-dimensional quantum gravity. We show that important aspects of the AdS/CFT correspondence are realized in certain quantum states of the gravitational field in LQG, thus justifying, from first principles, a class of models introduced by [F. Pastawski et al., JHEP 06, 149 (2015)]. We provide examples of hyperinvariant tensor networks, but also prove constraints on their existence in the form of no-go theorems that exclude absolutely maximally entangled states as well as general holographic codes from local SU(2)-invariance. We calculate surface areas as expectation values of the LQG area operator and discuss further possible constraints as a consequence of a decay of correlations on the boundary.

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arXiv2025

Preparation Circuits for Matrix Product States by Classical Variational Disentanglement

We study the classical compilation of quantum circuits for the preparation of matrix product states (MPS), which are quantum states of low entanglement with an efficient classical description. Our algorithm represents a near-term alternative to previous sequential approaches by reverse application of a disentangler, which can be found by minimizing bipartite entanglement measures after the application of a layer of parameterized disentangling gates. Since a successful disentangler is expected to decrease the bond dimension on average, such a layer-by-layer optimization remains classically efficient even for deep circuits. Additionally, as the Schmidt coefficients of all bonds are locally accessible through the canonical $\Gamma$-$\Lambda$ form of an MPS, the optimization algorithm can be heavily parallelized. We discuss guarantees and limitations to trainability and show numerical results for ground states of one-dimensional, local Hamiltonians as well as artificially spread out entanglement among multiple qubits using error correcting codes.

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arXiv2025

Efficient Quantum Cooling Algorithm for Fermionic Systems

We present a cooling algorithm for ground state preparation of fermionic Hamiltonians. Our algorithm makes use of the Hamiltonian simulation of the considered system coupled to an ancillary fridge, which is regularly reset to its known ground state. We derive suitable interaction Hamiltonians that originate from ladder operators of the free theory and initiate resonant gaps between system and fridge. We further propose a spectroscopic scan to find the relevant eigenenergies of the system using energy measurements on the fridge. With these insights, we design a ground state cooling algorithm for fermionic systems that is efficient, i.e. its runtime is polynomial in the system size, as long as the initial state is prepared in a low-energy sector of polynomial size. We achieve the latter via a pseudo-adiabatic sweep from a parameter regime whose ground state can be easily prepared. We estimate that our algorithm has a polynomial runtime for systems where the spectral gap decreases at most polynomially in system size, and is faster than the adiabatic algorithm for a large range of settings. We generalize the algorithm to prepare thermal states and demonstrate our findings on the Fermi-Hubbard model.

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arXiv2024

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 $ω$ but also a linear advantage in simulation time $t$ compared to~Trotterization.

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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.

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arXiv2024

Quantum Tensor Product Decomposition from Choi State Tomography

The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt, or tensor product decomposition. While quantum technological implementations of the former are thoroughly studied, entangling properties on the operator level are harder to extract in the quantum computational framework because of the exponential nature of sample complexity. Here we present an algorithm for unbalanced partitions into a small subsystem and a large one (the environment) to compute the tensor product decomposition of a unitary whose effect on the small subsystem is captured in classical memory while the effect on the environment is accessible as a quantum resource. This quantum algorithm may be used to make predictions about operator non-locality, effective open quantum dynamics on a subsystem, as well as for finding low-rank approximations and low-depth compilations of quantum circuit unitaries. We demonstrate the method and its applications on a time-evolution unitary of an isotropic Heisenberg model in two dimensions.

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arXiv2023

Problem specific classical optimization of Hamiltonian simulation

Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and sampling problems. Here, we present a classical pre-processing routine for variational Hamiltonian simulation that circumvents the need of a quantum optimization by expanding rigorous error bounds in a perturbative regime for suitable time steps. The resulting cost function is efficiently computable on a classical computer. We show that there always exists potential for optimization with respect to a Trotter sequence of the same order and that the cost value has the same scaling as for Trotter in simulation time and system size. Unlike previous work on classical pre-processing, the method is applicable to any Hamiltonian system independent of locality and interaction lengths. Via numerical experiments for spin-lattice models, we find that our approach significantly improves digital quantum simulations capabilities with respect to Trotter sequences for the same resources. For short times, we find accuracy improvements of more than three orders of magnitude for our method as compared to Trotter sequences of the same gate number. Moreover, for a given gate number and accuracy target, we find that the pre-optimization we introduce enables simulation times that are consistently more than 10 times longer for a target accuracy of 0.1%.

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arXiv2023

No invariant perfect qubit codes

Perfect tensors describe highly entangled quantum states that have attracted particular attention in the fields of quantum information theory and quantum gravity. In loop quantum gravity, the natural question arises whether SU(2) invariant tensors, which are fundamental ingredients of the basis states of spacetime, can also be perfect. In this work, we present a number of general constraints for the layout of such invariant perfect tensors (IPTs) and further describe a systematic and constructive approach to check the existence of an IPT of given valence. We apply our algorithm to show that no qubit encoding of valence 6 can be described by an IPT and close a gap to prove a no-go theorem for invariant perfect qubit encodings. We also provide two alternative proofs for the non-existence of 4-valent qubit IPTs which has been shown in [1,2].

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arXiv2023

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.

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arXiv2021

Kinematics of arbitrary spin matter fields in loop quantum gravity

Loop quantum gravity envisions a small scale structure of spacetime that is markedly different from that of the classical spacetime continuum. This has ramifications for the excitation of matter fields and for their coupling to gravity. There is a general understanding of how to formulate scalar fields, spin $\frac{1}{2}$ fields and gauge fields in the framework of loop quantum gravity. The goal of the present work is to investigate kinematical aspects of this coupling. We will study implications of the Gauß and diffeomorphism constraint for the quantum theory: We define and study a less ambiguous variant of the Baez-Krasnov path observables, and investigate symmetry properties of spin network states imposed by diffeomorphism group averaging. We will do this in a setting which allows for matter excitations of spin $\frac{1}{2}$ and higher. In the case of spin $\frac{1}{2}$, we will also discuss extensions of it by introducing an electromagnetic field and antiparticles. We finally discuss in how far the picture with matter excitations of higher spin can be obtained from classical actions for higher spin fields.

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arXiv2021

Fermion spins in loop quantum gravity

We define and study kinematical observables involving fermion spin, such as the total spin of a collection of particles, in loop quantum gravity. Due to the requirement of gauge invariance, the relevant quantum states contain strong entanglement between gravity and fermionic degrees of freedom. Interestingly we find that properties and spectra of the observables are nevertheless similar to their counterparts from quantum mechanics. However, there are also new effects. Due to the entanglement between gravity and fermionic degrees of freedom, alignment of quantum spins has consequences for quantized geometry. We sketch a particular effect of this kind that may in principle be observable.

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