Preparing algebraically correlated ground states of quantum many-body systems is an important, yet challenging task for quantum simulation. We introduce a protocol that employs local projective measurements and unitary feedback for frustration-free gapless systems. Our approach prepares a priori unknown ground states in time that scales polynomially with system size. We analytically show the performance of our protocol for the dynamics of a single particle; we argue the same mechanism generalizes to many-body systems based on the physics of quasiparticles. Our theory predicts that the transient cooling dynamics directly reveals the system's universal critical properties. In particular, the state preparation time is linear in the inverse of the finite-size gap (up to log correction) when the system's dynamical critical exponent is larger than or equal to the effective spatial dimension explored by the quasiparticles. We verify these predictions in numerical simulations of ferromagnetic Heisenberg models in one and two dimensions, a Fredkin spin chain, and a two-dimensional model of resonating valence bond states. Our protocol stabilizes gapless many-body ground states fully digitally without requiring analog rotations, enabling access to high-fidelity states beyond conventional adiabatic approaches in near-term experiments.
Preparing algebraically correlated ground states of quantum many-body systems is an important, yet challenging task for quantum simulation. We introduce a protocol that employs local projective measurements and unitary feedback for frustration-free gapless systems. Our approach prepares a priori unknown ground states in time that scales polynomially with system size. We analytically show the performance of our protocol for the dynamics of a single particle; we argue the same mechanism generalizes to many-body systems based on the physics of quasiparticles. Our theory predicts that the transient cooling dynamics directly reveals the system's universal critical properties. In particular, the state preparation time is linear in the inverse of the finite-size gap (up to log correction) when the system's dynamical critical exponent is larger than or equal to the effective spatial dimension explored by the quasiparticles. We verify these predictions in numerical simulations of ferromagnetic Heisenberg models in one and two dimensions, a Fredkin spin chain, and a two-dimensional model of resonating valence bond states. Our protocol stabilizes gapless many-body ground states fully digitally without requiring analog rotations, enabling access to high-fidelity states beyond conventional adiabatic approaches in near-term experiments.
Preparing algebraically correlated ground states of quantum many-body systems is an important, yet challenging task for quantum simulation. We introduce a protocol that employs local projective measurements and unitary feedback for frustration-free gapless systems. Our approach prepares a priori unknown ground states in time that scales polynomially with system size. We analytically show the performance our protocol for the dynamics of a single-particle; we argue the same mechanism generalizes to many-body systems based on the physics of quasiparticles. Our theory predicts that a transient cooling dynamics directly reveals the system's universal critical properties. In particular, the state preparation time is linear in the inverse of the finite-size gap (up to log correction) when the system's dynamical critical exponent is larger or equal the effective spatial dimension explored by the quasiparticles. We verify these predictions in numerical simulations of ferromagnetic Heisenberg models in one- and two dimensions, a Fredkin spin chain, and a two-dimensional model of resonating valence bond states. Our protocol stabilizes gapless many-body ground states fully digitally without requiring analog rotations, enabling access to high-fidelity states beyond conventional adiabatic approaches in near-term experiments.
We introduce frustration-free control, a measurement-feedback framework for quantum state preparation that extends frustration-free Hamiltonians to monitored stochastic dynamics. The protocol drives many-body systems into highly entangled target states, common dark states of all measurement projectors, through minimal local unitary corrections that realize an absorbing-state dynamics without postselection. We show that relaxation to the target state is governed by emergent transport of nonlocal charges, such as singlet excitations in SU(2)-symmetric dynamics. While measurement feedback annihilates compatible charge configurations, both measurement and scrambling unitaries induce charge transport and thus determine the convergence time. Mapping a baseline model of SU(N) SWAP measurements with local corrections to a solvable absorbing random walk yields a run-time scaling t∼L^{z} with transport exponent z=2. Simulations of Motzkin and Fredkin chains reveal subdiffusive scaling z≥8/3, confirming absorbing-state transport as a general organizing principle for deterministic entangled-state preparation and transport diagnostics in monitored quantum dynamics.
Dissipative state preparation engineers quantum many-body states as steady states of an open-system dynamics. The spatial range of the required dissipation sets both the feasibility of analog implementations and the connectivity and control complexity of digital ones. Yet how this locality quantitatively constrains preparation times remains largely unknown. Here, we establish an exact locality-preparation time relation for quadratic fermionic systems and develop a construction that optimizes the locality of the dissipative dynamics while preserving the target state. Applied to the Kitaev chain, our framework reveals sharply different locality-preparation time tradeoffs in critical and gapped regimes. At criticality, suppressing the algebraic tails of the jump operators necessarily forces the preparation time to grow algebraically with system size. By contrast, both trivial and topological gapped phases admit exponentially localized dissipation with a finite preparation time in the thermodynamic limit. Our results identify when fast dissipative preparation is compatible with local control and when criticality imposes an unavoidable dynamical cost.
Probing correlated states of many-body systems is one of the central tasks for quantum simulators and processors. A promising approach to state preparation is to realize desired correlated states as steady states of engineered dissipative evolution. A recent experiment with a Google superconducting quantum processor [X. Mi , Science 383, 1332 (2024)] demonstrated a cooling algorithm utilizing auxiliary degrees of freedom that are periodically reset to remove quasiparticles from the system, thereby driving it towards its ground state. In this work, we develop a kinetic-theory framework to describe quasiparticle cooling dynamics, and employ it to compare the efficiency of different cooling algorithms. In particular, we introduce a protocol where coupling to auxiliaries is modulated in time to minimize heating processes, and demonstrate that it allows a high-fidelity preparation of ground states in different quantum phases. We verify the validity of the kinetic-theory description by an extensive comparison with numerical simulations for the examples of a one-dimensional transverse-field Ising model, the transverse-field Ising model with an additional integrability-breaking field, and a nonintegrable antiferromagnetic Heisenberg spin ladder. In all cases, we are able to efficiently cool into the many-body ground state. The effects of noise, which limits efficiency of variational quantum algorithms in near-term quantum processors, are investigated through the lens of the kinetic theory: we show how the steady-state quasiparticle populations depend on the noise rate, and we establish maximum noise values for achieving high-fidelity ground states. This work establishes quasiparticle cooling algorithms as a practical, robust method for many-body state preparation on near-term quantum processors.
Inspired by natural cooling processes, dissipation has become a promising approach for preparing low-energy states of quantum systems. However, the potential of dissipative protocols remains unclear beyond certain commuting Hamiltonians. This work provides significant analytical and numerical insights into the power of dissipation for preparing the ground state of noncommuting Hamiltonians. For quasi-free dissipative dynamics, including certain 1D spin systems with boundary dissipation, our results reveal a new connection between the mixing time in trace distance and the spectral properties of a non-Hermitian Hamiltonian, leading to an explicit and sharp bound on the mixing time that scales polynomially with system size. For more general spin systems, we develop a tensor network-based algorithm for constructing the Lindblad jump operator and for simulating the dynamics. Using this algorithm, we demonstrate numerically that dissipative ground state preparation protocols can achieve rapid mixing for certain 1D local Hamiltonians under bulk dissipation, with a mixing time that scales logarithmically with the system size. We then prove the rapid mixing result for certain weakly interacting spin and fermionic systems in arbitrary dimensions, extending recent results for high-temperature quantum Gibbs samplers to the zero-temperature regime. Together, these results show that dissipation can be a powerful tool for ground state preparation, with potential applications across condensed matter physics, quantum materials science, and beyond.
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 N-qubit Hilbert space the characteristic convergence time scales linearly with N 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.