Fermion spins in loop quantum gravity - Mansuroglu, Refik; Sahlmann, Hanno (Physical Review D, 2021)
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 fmd 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.
CRIS-Team WoS Importer:2021-06-04

Kinematics of arbitrary spin matter fields in loop quantum gravity - Mansuroglu, Refik; Sahlmann, Hanno (Physical Review D, 2021)
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 12 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 constraints for the quantum theory: We define and study a less ambiguous variant of the Baez-Krasnov path observables, and we 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 12 and higher. In the case of spin 12, we will also discuss extensions of it by introducing an electromagnetic field and antiparticles. We finally discuss how far the picture with matter excitations of higher spin can be obtained from classical actions for higher spin fields.
CRIS-Team Scopus Importer:2021-05-28

Large-scale simulations of Floquet physics on near-term quantum computers - Eckstein, Timo; Mansuroglu, Refik; Czarnik, Piotr; Zhu, Jian Xin; Hartmann, Michael; Cincio, Lukasz; Sornborger, Andrew T.; Holmes, Zoë (npj Quantum Information, 2024)
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.
CRIS-Team Scopus Importer:2024-09-20
Keywords: Quantum Computing; Floquet physics; NISQ

No invariant perfect qubit codes - Mansuroglu, Refik; Sahlmann, Hanno (Journal of High Energy Physics, 2023)
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].
CRIS-Team Scopus Importer:2023-02-17
Keywords: Gauge-Gravity Correspondence; Holography and Condensed Matter Physics (AdS/CMT); Models of Quantum Gravity

Problem-specific classical optimization of Hamiltonian simulation - Mansuroglu, Refik; Fischer, Felix; Hartmann, Michael (Physical Review Research, 2023)
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 preprocessing routine for variational Hamiltonian simulation that circumvents the need for 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 Trotter in simulation time and system size. Unlike previous work on classical preprocessing, 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 simulation 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 preoptimization we introduce enables simulation times that are consistently more than ten times longer for a target accuracy of 0.1%.
CRIS-Team Scopus Importer:2023-11-03

Quantum Tensor-Product Decomposition from Choi-State Tomography - Mansuroglu, Refik; Adil, Arsalan; Hartmann, Michael; Holmes, Zoë; Sornborger, Andrew T. (PRX Quantum, 2024)
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 the effect of which 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 nonlocality and 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.
CRIS-Team Scopus Importer:2024-10-11

Variational Hamiltonian simulation for translational invariant systems via classical pre-processing - Mansuroglu, Refik; Eckstein, Timo; Nützel, Ludwig; Wilkinson, Samuel; Hartmann, Michael (Quantum Science and Technology, 2023)
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 noisy intermediate scale quantum-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.
CRIS-Team Scopus Importer:2023-02-17
Keywords: Hamiltonian simulation; noisy intermediate scale quantum; time evolution; translational invariance; Trotter-Suzuki decomposition; variational algorithms