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arXiv:2601.16180

Studying energy-resolved transport with wavepacket dynamics on quantum computers

Melody Lee, Roland C. Farrell

quant-phcond-mat.dis-nnSubmitted Jan 22, 2026• Announced Jan 23, 2026• 0 citations
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Abstract

Probing energy-dependent transport in quantum simulators requires preparing states with tunable energy and small energy variance. Existing approaches often study quench dynamics of simple initial states, such as computational basis states, which are far from energy eigenstates and therefore limit the achievable energy resolution. In this work, we propose using wavepackets to probe transport properties with improved energy resolution. To demonstrate the utility of this approach, we prepare and evolve wavepackets on Quantinuum's H2-2 quantum computer and identify an energy-dependent localization transition in the Anderson model on an 8x7 lattice--a finite-size mobility edge. We observe that a wavepacket initialized at low energy remains spatially localized under time evolution, while a high-energy wavepacket delocalizes, consistent with the presence of a mobility edge. Crucial to our experiments is an error mitigation strategy that infers the noiseless output bit string distribution using maximum-likelihood estimation. Compared to post-selection, this method removes systematic errors and reduces statistical uncertainty by up to a factor of 5. We extend our methods to the many-particle regime by developing a quantum algorithm for preparing quasiparticle wavepackets in a one-dimensional model of interacting fermions. This technique has modest quantum resource requirements, making wavepacket-based studies of transport in many-body systems a promising application for near-term quantum computers.

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21 pages, 11 figures, 4 tables

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Probing energy-dependent transport in quantum simulators requires preparing states with tunable energy and small energy variance. Existing approaches often study quench dynamics of simple initial states, such as computational basis states, which are far from energy eigenstates and therefore limit the achievable energy resolution. In this work, we propose using wavepackets to probe transport properties with improved energy resolution. To demonstrate the utility of this approach, we prepare and evolve wavepackets on Quantinuum's H2-2 quantum computer and identify an energy-dependent localization transition in the Anderson model on an 8x7 lattice--a finite-size mobility edge. We observe that a wavepacket initialized at low energy remains spatially localized under time evolution, while a high-energy wavepacket delocalizes, consistent with the presence of a mobility edge. Crucial to our experiments is an error mitigation strategy that infers the noiseless output bit string distribution using maximum-likelihood estimation. Compared to post-selection, this method removes systematic errors and reduces statistical uncertainty by up to a factor of 5. We extend our methods to the many-particle regime by developing a quantum algorithm for preparing quasiparticle wavepackets in a one-dimensional model of interacting fermions. This technique has modest quantum resource requirements, making wavepacket-based studies of transport in many-body systems a promising application for near-term quantum computers.
The many-body localization (MBL) transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from “extended/ergodic" (exhibiting extensive entanglement entropies and fluctuations) to “localized" (exhibiting area-law scaling of entanglement and fluctuations). The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder – if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using “quantum-quench spectroscopy", namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.
We introduce a method called resolution refinement that allows one to bootstrap eigenstate preparation on a quantum computer. We first prepare an eigenstate of a low-resolution Hamiltonian using any method of choice. The eigenstate is then lifted to higher resolution and adiabatically evolved to produce the corresponding eigenstate of a higher-fidelity Hamiltonian. We give examples of resolution refinement applied to both single-particle basis states as well as a spatial lattice grid. For basis refinement, we compute few-body ground states of the Busch model for interacting particles in a harmonic trap in one dimension. For lattice refinement, we compute Hartree-Fock nuclear states for a central Woods-Saxon potential in three dimensions, and we compute bound states and continuum states in a multi-species Hubbard model of fermions in one dimension. In all cases, the method is efficient and requires an adiabatic evolution time that scales with the inverse of the energy gap times the square root of the system size. We show that this very favorable scaling arises from the fact that resolution refinement does not make large changes to the structure or energies of the low-energy eigenstates.
Hadron wave packets are prepared and time evolved in the Schwinger model using 112 qubits of IBM's 133-qubit Heron quantum computer ibm_torino. The initialization of the hadron wave packet is performed in two steps. First, the vacuum is prepared across the whole lattice using the recently developed SC-ADAPT-VQE algorithm and workflow. SC-ADAPT-VQE is then extended to the preparation of localized states, and used to establish a hadron wave packet on top of the vacuum. This is done by adaptively constructing low-depth circuits that maximize the overlap with an adiabatically prepared hadron wave packet. Due to the localized nature of the wavepacket, these circuits can be determined on a sequence of small lattices using classical computers, and then robustly scaled to prepare wave packets on large lattices for simulations using quantum computers. Time evolution is implemented with a second-order Trotterization. To reduce both the required qubit connectivity and circuit depth, an approximate quasilocal interaction is introduced. This approximation is made possible by the emergence of confinement at long distances, and converges exponentially with increasing distance of the interactions. Using multiple error-mitigation strategies, up to 14 Trotter steps of time evolution are performed, employing 13,858 two-qubit gates (with a CNOT depth of 370). The propagation of hadrons is clearly identified, with results that compare favorably with Matrix Product State simulations. Prospects for a near-term quantum advantage in simulations of hadron scattering are discussed.
Accurately determining ground-state properties of quantum many-body systems remains one of the major challenges of quantum simulation. In this work, we present a protocol for estimating the ground-state energy using only global time evolution under a target Hamiltonian. This avoids the need for controlled operations that are typically required in conventional quantum phase estimation and extends the algorithm applicability to analog simulators. Our method extracts energy differences from measurements of the Loschmidt echo over an initial ground-state approximation, combines them with direct energy measurements, and solves a set of equations to infer the individual eigenenergies. We benchmark this protocol on free-fermion systems, showing orders-of-magnitude precision gains over direct energy measurements on the initial state, with accuracy improving rapidly with initial-state fidelity and persisting for hundreds of modes. We further demonstrate applicability to the 2D Ising and Fermi-Hubbard models and show that the approach extends naturally to other observables such as order parameters. Finally, we analyze the effect of experimental imperfections and propose error-mitigation strategies. These results establish a practical route to compute physically relevant quantities with high precision using globally controlled quantum simulators.
Motivated by recent experiments on interacting bosons in a quasi-one-dimensional optical lattice [M. Rispoli et al., Nature (London) 573, 385 (2019)], we analyze theoretically properties of the system in the crossover between delocalized and localized regimes. Comparison of time dynamics for uniform and density-wave-like initial states enables a demonstration of the existence of the mobility edge. To this end we define a different observable, the mean speed of transport at long times. It gives us an efficient estimate of the critical disorder for the crossover. We also show that the mean velocity growth of occupation fluctuations close to the edges of the system carries similar information. Using the quantum quench procedure, we show that it is possible to probe the mobility edge for different energies.
The existence of many-body mobility edges in closed quantum systems has been the focus of intense debate after the emergence of the description of the many-body localization phenomenon. Here we propose that this issue can be settled in experiments by investigating the time evolution of local degrees of freedom, tailored for specific energies and initial states. An interacting model of spinless fermions with exponentially long-ranged tunneling amplitudes, whose noninteracting version is known to display single-particle mobility edges, is used as the starting point upon which nearest-neighbor interactions are included. We verify the manifestation of many-body mobility edges by using numerous probes, suggesting that one cannot explain their appearance as merely being a result of finite-size effects. Lastly, our scheme of following the quantum time evolution at different energies is generic and can be promptly used in a variety of models.