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arXiv:2512.13044

Imaginary-time-enhanced feedback-based quantum algorithms for universal ground-state preparation

Thanh Nguyen Van Long, Lan Nguyen Tran, Le Bin Ho

quant-phcond-mat.str-elSubmitted Dec 15, 2025• Announced Dec 16, 2025• 0 citations• Revised Oct 22, 2026 (v2)
v1 · Dec 15, 2025v2 · Oct 22, 2026
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Abstract

Preparing ground states of strongly correlated quantum systems is a central goal in quantum simulation and optimization. The feedback-based quantum algorithm (FALQON) provides an attractive alternative to variational methods with a fully quantum feedback rule, but it fails in the presence of spectral degeneracies, where the feedback signal collapses and the evolution cannot reach the ground state. Using the Fermi-Hubbard model on lattices up to 3x3, we show that this breakdown appears at half-filling on the 2x2 lattice and extends to both half-filled and doped configurations on the 3x3 lattice. We then introduce an imaginary-time-enhanced FALQON ($i$FALQON) scheme, which inserts short imaginary-time evolution steps into the feedback loop. This proposed method suppresses excited-state components, escapes degenerate subspaces, restores monotonic energy descent and improves ground-state convergence across the tested fillings. We further benchmark its performance against existing methods, showing improved results for iFALQON, demonstrating the potential of hybrid real-imaginary-time feedback dynamics for ground-state preparation in strongly correlated quantum systems.

Journal reference
Physical Review Research (2026)
DOI
10.1103/cbcv-fnm2
Comments
11 pages, 7 figures

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Preparing ground states of strongly correlated quantum systems is a central goal in quantum simulation and optimization. The feedback-based quantum algorithm (FALQON) provides an attractive alternative to variational methods with a fully quantum feedback rule, but it fails in the presence of spectral degeneracies, where the feedback signal collapses and the evolution cannot reach the ground state. Using the Fermi-Hubbard model on lattices up to 3x3, we show that this breakdown appears at half-filling on the 2x2 lattice and extends to both half-filled and doped configurations on the 3x3 lattice. We then introduce an imaginary-time-enhanced FALQON (iiiFALQON) scheme, which inserts short imaginary-time evolution steps into the feedback loop. This proposed method suppresses excited-state components, escapes degenerate subspaces, restores monotonic energy descent and improves ground-state convergence across the tested fillings. We further benchmark its performance against existing methods, showing improved results for iFALQON, demonstrating the potential of hybrid real-imaginary-time feedback dynamics for ground-state preparation in strongly correlated quantum systems.
The efficient preparation of correlated thermal states, such as the Thermofield Double (TFD) state, is a fundamental prerequisite for simulating quantum gravity models and many-body thermodynamics on quantum processors. In this work, we investigate the ground state preparation of the Two Coupled Sachdev-Ye-Kitaev model, known as the Maldacena-Qi model, which is dual to a traversable wormhole in AdS2AdS_2AdS2​, utilizing feedback-based quantum algorithms. We demonstrate that the standard feedback-based quantum algorithm (FALQON) and its time-rescaled variant (TR-FALQON) face severe kinetic limitations in this system, failing to converge to the highly entangled ground state when initialized in trivial product states. To overcome these barriers, we propose the hybrid ITE-TR-FALQON protocol, which integrates the imaginary-time evolution present in imaginary-time-enhanced FALQON (ITE-FALQON) with the time-rescaling mechanism. Our numerical results indicate that the introduction of non-unitary dynamics is strictly necessary to break symmetry traps and filter out excited states, while time-rescaling drastically accelerates algorithm convergence. The proposed method achieves fidelities close to unity and reproduces the von Neumann and Rényi entropy spectra of the exact TFD state with high precision.
Explicitly correlated methods, which represent dominant short-range correlations by a diagonal Jastrow-type correlator, are designed to accurately describe systems of strongly correlated electrons, such as the fully periodic 2D Fermi--Hubbard model. However, as the reference state is compact in momentum space whereas the correlator acts naturally in real space, there is a fundamental mismatch of bases that classical algorithms resolve only by restricting the reference or the correlator. Here we propose a hybrid algorithm in which a quantum processor prepares a low-entanglement momentum-space matrix product state (MPS), precomputed classically by the transcorrelated method at the cost of a nonvariational energy, rotates it to real space, and measures in bases fixed by the Hamiltonian. Because the measurement bases are independent of the correlator, the correlator can be variationally optimized entirely in classical post-processing with no quantum-classical feedback loop. We demonstrate our algorithm on 32 qubits of Quantinuum's H2-2 with a bond-dimension-4 MPS for the half-filled 4×44 \times 44×4 lattice and achieve a relative ground-state energy error of 16±4%16 \pm 4\%16±4% after postselection, reduced to 3.5±0.5%3.5 \pm 0.5\%3.5±0.5% by calibration using low-order moments from the MPS. Compared with other feedback-free hybrid algorithms, even under generous assumptions, our method requires fewer samples than quantum-selected configuration interaction and fewer two-qubit gates than quantum Krylov methods.
This work investigates the impact of time rescaling on the performance of Feedback-Based Quantum Algorithms (FQAs) and their variant for optimization tasks, Feedback-Based Algorithm for Quantum Optimization (FALQON). We introduce the Time-Rescaled Feedback-Based Quantum Algorithm (TR-FQA) and Time-Rescaled Feedback-Based Algorithm for Quantum Optimization (TR-FALQON), time-rescaled versions of FQA and FALQON, respectively. The method is applied to two representative problems: the MaxCut combinatorial optimization problem and ground-state preparation in the axial next-nearest neighbor Ising (ANNNI) model. The results show that TR-FALQON accelerates convergence toward the optimal solution in the circuit's early layers and outperforms the standard version in low-depth regimes. In the context of state preparation, TR-FQA requires fewer layers than the original algorithm. These findings suggest that time rescaling can reduce the number of layers needed to reach a high-quality solution, even if the exact ground state is not obtained.
Ground-state preparation of quantum many-body systems is a fundamental challenge across quantum science, with implications for quantum simulation, quantum computing, and the study of complex quantum matter. The exponential growth of Hilbert space and the complexity of entangled eigenstates motivate the development of new approaches that go beyond conventional strategies based on adiabatic evolution, variational optimization, imaginary-time methods, and engineered dissipative processes. Here, we demonstrate that the recently proposed quantum Landau-Lifshitz-Gilbert (QLLG) dynamics [Phys. Rev. Lett. {\bf 133}, 266704 (2024)] provides an intrinsic nonlinear dissipative mechanism for real-time ground-state preparation. Unlike engineered dissipative schemes, QLLG encodes relaxation directly into the quantum equation of motion while preserving the underlying quantum structure of the evolution. The QLLG evolution selectively suppresses excited-state contributions, driving the system toward the lowest-energy eigenstate within the accessible symmetry sector. We show that the dynamics admits a monotonic energy functional and a stable ground-state fixed point, and that for generic initial states in an NNN-qubit Hilbert space the characteristic convergence time scales linearly with NNN and inversely with the spectral gap. Numerical simulations of an interacting spin chain confirm our analytical predictions. These results establish nonlinear dissipative QLLG dynamics as a new avenue for quantum state preparation, opening a new route for quantum simulation, computation, and state engineering.
Feedback-based quantum algorithms have recently emerged as potential methods for approximating the ground states of Hamiltonians . One such algorithm, the feedback-based algorithm for quantum optimization (FALQON), is specifically designed to solve quadratic unconstrained binary optimization problems. Its extension, the feedback-based algorithm for quantum optimization with constraints (FALQON-C), was introduced to handle constrained optimization problems with equality and inequality constraints . In this work, we extend the feedback-based quantum algorithms framework to address a broader class of constraints known as invalid configuration (IC) constraints, which explicitly prohibit specific configurations of decision variables. We first present a transformation technique that converts the constrained optimization problem with invalid configuration constraints into an equivalent unconstrained problem by incorporating a penalizing term into the cost function. Then, leaning upon control theory, we propose an alternative method tailored for feedback-based quantum algorithms that directly tackles IC constraints without requiring slack variables. Our approach introduces a new operator that encodes the optimal feasible solution of the constrained optimization problem as its ground state. Then, a controlled quantum system based on the Lyapunov control technique is designed to ensure convergence to the ground state of this operator. Two approaches are introduced in the design of this operator to address IC constraints: the folded spectrum approach and the deflation approach. These methods eliminate the need for slack variables, significantly reducing the quantum circuit depth and the number of qubits required. We show the effectiveness of our proposed algorithms through numerical simulations.
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