Abstract Dissipative engineering is a powerful tool for quantum state preparation, and has drawn significant attention in quantum algorithms and quantum many-body physics in recent years. In this work, we introduce a novel approach using the Lindblad dynamics to efficiently prepare the ground state for general ab initio electronic structure problems on quantum computers, without variational parameters. These problems often involve Hamiltonians that lack geometric locality or sparsity structures, which we address by proposing two generic types of jump operators for the Lindblad dynamics. Type-I jump operators break the particle number symmetry and should be simulated in the Fock space. Type-II jump operators preserves the particle number symmetry and can be simulated more efficiently in the full configuration interaction space. For both types of jump operators, we prove that in a simplified Hartree-Fock framework, the spectral gap of our Lindbladian is lower bounded by a universal constant. For physical observables such as energy and reduced density matrices, the convergence rate of our Lindblad dynamics with Type-I jump operators remains universal, while the convergence rate with Type-II jump operators only depends on coarse grained information such as the number of orbitals and the number of electrons. To validate our approach, we employ a Monte Carlo trajectory-based algorithm for simulating the Lindblad dynamics for full ab initio Hamiltonians, demonstrating its effectiveness on molecular systems amenable to exact wavefunction treatment.
Abstract Dissipative engineering is a powerful tool for quantum state preparation, and has drawn significant attention in quantum algorithms and quantum many-body physics in recent years. In this work, we introduce a novel approach using the Lindblad dynamics to efficiently prepare the ground state for general ab initio electronic structure problems on quantum computers, without variational parameters. These problems often involve Hamiltonians that lack geometric locality or sparsity structures, which we address by proposing two generic types of jump operators for the Lindblad dynamics. Type-I jump operators break the particle number symmetry and should be simulated in the Fock space. Type-II jump operators preserves the particle number symmetry and can be simulated more efficiently in the full configuration interaction space. For both types of jump operators, we prove that in a simplified Hartree-Fock framework, the spectral gap of our Lindbladian is lower bounded by a universal constant. For physical observables such as energy and reduced density matrices, the convergence rate of our Lindblad dynamics with Type-I jump operators remains universal, while the convergence rate with Type-II jump operators only depends on coarse grained information such as the number of orbitals and the number of electrons. To validate our approach, we employ a Monte Carlo trajectory-based algorithm for simulating the Lindblad dynamics for full ab initio Hamiltonians, demonstrating its effectiveness on molecular systems amenable to exact wavefunction treatment.
Electronic excited states are central to a vast array of physical and chemical phenomena, yet accurate and efficient methods for preparing them on quantum devices remain challenging and comparatively underexplored. We introduce a general dissipative algorithm for selectively preparing ab initio electronic excited states. The key idea is to recast excited-state preparation as an effective ground-state problem by suitably modifying the underlying Lindblad dynamics so that the target excited state becomes the unique steady state of a designed quantum channel. We develop three complementary strategies, tailored to different types of prior information about the excited state, such as symmetry and approximate energy. We demonstrate the effectiveness and versatility of these schemes through numerical simulations of atomic and molecular spectra, including valence excitations in prototypical planar conjugated molecules and transition-metal complexes. Taken together, these results provide a new pathway for advancing quantum simulation methods for realistic strongly correlated electronic systems.
We study a qDRIFT-type randomized method to simulate Lindblad dynamics by decomposing its generator into an ensemble of Lindbladians, L = ∑ a ∈ A L a , where each L a comprises a simple Hamiltonian and a single jump operator. Assuming an efficient quantum simulation is available for the Lindblad evolution e t L a , we implement e t L a for a randomly sampled L a at each time step according to a probability distribution μ over the ensemble { L a } a ∈ A . This randomized strategy reduces the quantum cost of simulating Lindblad dynamics, particularly in quantum many-body systems with a large or even infinite number of jump operators.Our contributions are two-fold. First, we provide a detailed convergence analysis of the proposed randomized method, covering both average and typical algorithmic realizations. This analysis extends the known results for the random product formula from closed systems to open systems, ensuring rigorous performance guarantees. Second, based on the random product approximation, we derive a new quantum Gibbs sampler algorithm that utilizes jump operators sampled from a Clifford-random circuit. This generator (i) can be efficiently implemented using our randomized algorithm, and (ii) exhibits a spectral gap lower bound that depends on the spectrum of the Hamiltonian. Our results present a new instance of a class of Hamiltonians for which the thermal states can be efficiently prepared using a quantum Gibbs sampling algorithm.
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.
Inspired by classical Markov Chain Monte Carlo (MCMC) methods, dissipative quantum algorithms are an emerging class of methods for preparing quantum states on a quantum computer. They operate by simulating a dissipative process governed by a mathematical operator known as the Lindbladian. The performance of these algorithms can be limited by the sequential implementation of the Lindbladian's constituent jump operators, which leads to high circuit depth. To address this issue, this work analyzes a parallelization scheme to implement jump operators simultaneously. We leverage the structure of geometric locality to show that individual jump operators remain spatially localized. This exponentially reduces the circuit depth per time step, resulting in an overall polynomial improvement. Numerical experiments demonstrate a 53x reduction in query depth for a 1D benchmark system of 100 qubits. The reduced circuit depth makes dissipative algorithms more practical for near-term quantum computing.
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.
We introduce a mapping between the ground state of interacting fermionic Hamiltonians and the non-equilibrium steady state of a purely dissipative open quantum system. Within the framework of third quantization, we map the Fermi-Hubbard Hamiltonian onto Lindblad jump operators acting on Majorana fermions. Remarkably, both hopping and interaction terms map onto jump operators that preserve the Gaussianity of Majorana fermions along individual quantum trajectories. As a result, the dynamics can be unravelled and each trajectory can be simulated efficiently using only two-point correlation functions, with a computational cost that scales polynomially with system size. We further show that finite particle number requires negative dissipative rates, leading to an intrinsically non-Markovian dynamics. The corresponding trajectory unravelling involves both positive and negative stochastic weights and exhibits a sign problem and large fluctuations, so that convergence requires an exponentially large number of trajectories. The overall computational cost remains exponential in system size despite the efficient Gaussian representation of individual trajectories, but is crucially dependent on the computational complexity of the non-Markovian unravelling, motivating further studies on the efficiency of such unravellings.