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.
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6 pages, 3 figures in main text; 14 pages, 4 figures in supplemental material
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.
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.
Can the ground state of a local Hamiltonian be prepared by local dissipation? We address this question for free-fermion Hamiltonians, using a quadratic Lindbladian with linear jump operators for the dissipative ground-state preparation. For translation-invariant targets, Fourier correspondence relates spatial locality to momentum-space analyticity, allowing us to derive a complete spectral criterion for the existence of exponentially local linear jump operators that prepare the ground state. This criterion leads to a no-go theorem that, sign-changing Fermi-level crossings exclude exponentially local linear jump operators for preparing the ground state. While these crossings are the complete obstruction in one dimension, additional obstructions generally arise in higher dimensions. We illustrate these additional obstructions using two quadratic-band-touching models with algebraically decaying ground-state correlations. We further show that short-range ground-state correlations, although not necessary, are sufficient for local dissipative preparation even without translation invariance. Our results establish how the spectral structure of the target Hamiltonian governs the locality of dissipative ground-state preparation.
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.
We propose a dynamical approach to identifying ground-state quantum phases through short-time dissipative cooling. Rather than determining the phase by preparing highly accurate approximations to ground states, we prepare a representative state of a candidate phase and monitor the early-time response of phase-sensitive observables under cooling dynamics tailored to the target Hamiltonian. For a class of phase-decision problems in which the relevant observables can be inferred from the low-energy manifold, and with jump operators implementable using only short-time Hamiltonian simulation, the dissipative evolution rapidly suppresses high-energy components and drives the system into a low-energy manifold whose observables already reveal the underlying ground-state phase, well before mixing to the steady state. We demonstrate this strategy for the frustrated J1--J2 Heisenberg chain, the Kitaev honeycomb model, and the XXZ chain, including Berezinskii--Kosterlitz--Thouless and topological phase transitions. In particular, coarse filter resolutions and short evolution times suffice to recover phase-sensitive quantities such as the Luttinger parameter and topological diagnostics. We further provide theoretical justification that cooling dynamics with such jump operators can rigorously prepare low-energy manifolds for free-fermionic and free-bosonic systems, and investigate this mechanism for interacting fermionic systems. Our results suggest that phase decision is a plausible target for future utility-scale studies on early fault-tolerant quantum devices.
Ground-state preparation is a fundamental challenge in quantum many-body physics, chemistry and materials science. Dissipative state-preparation techniques engineer a Lindbladian coupling to a bath that drives the system to its ground state, needing no initial overlap. Their cost is dominated by the Hamiltonian simulations inside the filtered jump operators, since each jump is a weighted sum of Heisenberg-evolved copies, or branches, of a coupling operator. We reduce this cost by following three simple observations to their logical end. First, on a fixed time grid, linear programming optimises the branch weights, trading the heating response against the circuit cost. Second, Lieb--Robinson bounds let each branch evolve on a patch whose radius grows with its duration. Third, if the dynamics converges quickly and truncation changes the jumps only slightly, the stationary state stays near the ground state even on patches smaller than the light cone. We validate our approach numerically. On a grid of 81 evolution times, the optimised filter reduces the worst-case heating response, or leakage, more than 116-fold at equal cost. Across fifteen molecules and six chains, the cost falls by 27 to 56\% at matched design-grid leakage; at matched cost, the molecular leakage falls by a factor of 2.9 to 2×103. Density-matrix simulations show high ground-state fidelity for both filters, and on Ising and Hubbard chains the cheaper filter keeps a ground-state population of at least 0.89 on patches of three or four sites. The same patches fail on a Heisenberg chain whose truncation error falls more slowly with patch size and whose Lindbladian gap is 12 times smaller than the Ising chain's, pointing to a role for the gap in how far patches can be truncated. At fixed radius the per-branch cost becomes independent of system size, reducing the cost of dissipative state preparation.
Dissipative algorithms for preparing thermal and ground states typically require a total Hamiltonian simulation time that grows at least linearly with system size N, even when their mixing time grows only polylogarithmically. We achieve sublinear simulation time for free fermions by engineering local interactions with a bath whose size grows in proportion to the system size. Starting from arbitrary initial states, our thermal state preparation algorithm achieves trace-norm error ε in total simulation time O(N/ε) at fixed inverse temperature and bounded single-particle bandwidth, while ground state preparation of gapped systems requires only polylog(N/ε) time. We further establish lower bounds for thermal state preparation within the bath protocols considered, identifying two obstacles to faster preparation, namely fourth-order deviations from the target thermal state and fluctuations induced by a random frequency shared by all bath qubits. Our results demonstrate that the linear simulation time barrier in dissipative state preparation can be overcome and clarify the bath and filter-design constraints that govern further complexity improvements.