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arXiv:2506.11964

Universal cooling of quantum systems via randomized measurements

Josias Langbehn, G. Mouloudakis, King, Emma, Raphaël Menu, I. V. Gornyi, Giovanna Morigi, Yuval Gefen, Christiane P. Koch

Published Jun 13, 2025• 0 citations
arXivHTMLPDF

Abstract

Designing cooling protocols is believed to require knowledge of the system spectrum. In contrast, cooling in nature occurs whenever the system is coupled to a cold bath. How does nature know how to cool? A natural cold bath can be mimicked with a reservoir of "meter" qubits that are initialized in their ground state. We show that a quantum system can be cooled without knowledge of system details when system-meter interactions and meter splittings are chosen randomly. For sufficiently small interaction strengths and long interaction times, the protocol ensures that resonant energy-exchange processes, leading to cooling, dominate over heating. Effectively, the dynamics is then captured by the rotating-wave approximation, which we identify as the basic mechanism for robust and scalable cooling of complex quantum systems through generic, structure-independent protocols. This offers a versatile universal framework for controlling quantum matter far from equilibrium, in particular, for quantum computing and simulation.

DOI
10.48550/arxiv.2506.11964

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Designing cooling protocols is believed to require knowledge of the system spectrum. In contrast, cooling in nature occurs whenever the system is coupled to a cold bath. How does nature know how to cool? A natural cold bath can be mimicked with a reservoir of "meter" qubits that are initialized in their ground state. We show that a quantum system can be cooled without knowledge of system details when system-meter interactions and meter splittings are chosen randomly. For sufficiently small interaction strengths and long interaction times, the protocol ensures that resonant energy-exchange processes, leading to cooling, dominate over heating. Effectively, the dynamics is then captured by the rotating-wave approximation, which we identify as the basic mechanism for robust and scalable cooling of complex quantum systems through generic, structure-independent protocols. This offers a versatile universal framework for controlling quantum matter far from equilibrium, in particular, for quantum computing and simulation.
We introduce a method for digital preparation of ground states of simulated Hamiltonians, inspired by cooling in nature and adapted to leverage the capabilities of digital quantum hardware. The cold bath is simulated by a single ancillary qubit, which is reset periodically and coupled to the system nonperturbatively. Studying this cooling method on a 1-qubit system toy model, we optimize two cooling protocols based on weak-coupling and strong-coupling approaches. Extending the insight from the 1-qubit system model, we develop two scalable protocols for larger systems. The LogSweep protocol extends the weak-coupling approach by sweeping energies to resonantly match any targeted transition. We test LogSweep on the 1D transverse-field Ising model, demonstrating approximate ground-state preparation with an error that can be made polynomially small in the computation time for all three phases of the system. The BangBang protocol extends the strong-coupling approach, and exploits a heuristics for local Hamiltonians to maximize the probability of deexciting system transitions in the shortest possible time. Although this protocol does not promise long-time convergence, it allows for a rapid cooling to an approximation of the ground state, making this protocol appealing for near-term demonstrations.
Invasiveness of quantum measurements is a genuinely quantum mechanical feature that is not necessarily detrimental: Here we show how quantum measurements can be used to fuel a cooling engine. We illustrate quantum measurement cooling (QMC) by means of a prototypical two-stroke two-qubit engine which interacts with a measurement apparatus and two heat reservoirs at different temperatures. We show that feedback control is not necessary for operation while entanglement must be present in the measurement projectors. We quantify the probability that QMC occurs when the measurement basis is chosen randomly, and find that it can be very large as compared to the probability of extracting energy (heat engine operation), while remaining always smaller than the most useless operation, namely, dumping heat in both baths. These results show that QMC can be very robust to experimental noise. A possible low-temperature solid-state implementation that integrates circuit QED technology with circuit quantum thermodynamics technology is presented.
Strongly interacting fermions underpin some of the most challenging problems in condensed matter physics, such as high-temperature superconductivity. The low-energy states of these systems encode their essential microscopic properties, yet remain largely inaccessible to classical methods. Quantum simulation offers a promising path forward, and among state-preparation strategies, engineered dissipation has emerged as a particularly compelling approach. Existing cooling protocols, however, typically rely on knowledge of the quasiparticle spectrum or mappings to free-fermion limits. In this letter, we introduce a randomized, symmetry-preserving cooling algorithm that requires no spectral information, using only local coupling operators to ancilla degrees of freedom with randomly sampled energy splittings to drive generic fermionic systems toward their low-energy manifold. We benchmark the protocol on canonical correlated fermionic models relevant to high-temperature superconductors, spanning metallic, density-wave, paired, superconducting, and phase-separated phases. Across all models, we observe universal cooling behavior: monotonic energy relaxation, concentration of spectral weight at low energies, and stabilization of correlated ground-state order. Our results establish randomized dissipative cooling as a general strategy for preparing strongly correlated fermionic states on programmable quantum devices.
In this work, we study the dynamics of a two-level system (qubit) embedded in a finite-temperature structured bath under periodical nondemolition measurements. The system under measurements will reach a quasisteady state, whose effective temperature can be maintained lower than that of the surrounding environment. We study the influence of the environmental modes from different regimes of frequency on the qubit. The spectrum of the bath consisting of a large number of bosonic harmonic oscillators can be approximately divided into three parts according to their effects of cooling or heating. Due to the spectral analysis over the structured bath based on a time-convolutionless master equation beyond the rotating-wave approximation, we propose a necessary cooling condition for the bath in the context of quantum nonselective and nondemolition measurements. It consists of two parts: (i) the logarithmic derivative of the spectrum around the system transition frequency should be large enough, at least larger than one-half of the inverse temperature of the bath; (ii) the spectrum should have a sharp high-frequency cutoff that cannot be far detuning from the system transition frequency. From this condition, we find that environments with two popular types of spectra, i.e., the modified Lorentzian models and the super-Ohmic models, are available for cooling the open quantum system.
Cooling an arbitrary mixed state to a pure ground state requires transferring its entropy to an environment. Can a single coherent bath contact accomplish this without repeated bath resets? We develop a new cooling mechanism that transfers the input information into bath degrees of freedom that subsequently decouple, while the system and the remaining bath follow a ground-state path. The bath is discarded only at the end, and the system Hamiltonian remains on and unmodified throughout. We rigorously realize this mechanism for a class of weakly interacting, gapped fermionic systems with local interactions. Starting from any mixed state, our protocol prepares the interacting ground state in total physical time polylogarithmic in the system size and inverse global trace-norm error. It uses two initially empty bath modes per system mode and a single pulse shared across all onsite system--bath couplings. The same pulse prepares each admissible system's own ground state without knowledge of its microscopic parameters. The guarantees follow directly from a non-Markovian system--bath dynamics without an effective Lindbladian description.
Heat-Bath Algorithmic Cooling is a set of techniques for producing highly pure quantum systems by utilizing a surrounding heat-bath and unitary interactions. These techniques originally used the thermal environment only to fully thermalize ancillas at the environment temperature. Here we extend HBAC protocols by optimizing over the thermalization strategy. We find, for any d -dimensional system in an arbitrary initial state, provably optimal cooling protocols with surprisingly simple structure and exponential convergence to the ground state. Compared to the standard ones, these schemes can use fewer or no ancillas and exploit memory effects to enhance cooling. We verify that the optimal protocols are robusts to various deviations from the ideal scenario. For a single target qubit, the optimal protocol can be well approximated with a Jaynes-Cummings interaction between the system and a single thermal bosonic mode for a wide range of environmental temperatures. This admits an experimental implementation close to the setup of a micromaser, with a performance competitive with leading proposals in the literature. The proposed protocol provides an experimental setup that illustrates how non-Markovianity can be harnessed to improve cooling. On the technical side we 1. introduce a new class of states called maximally active states and discuss their thermodynamic significance in terms of optimal unitary control, 2. introduce a new set of thermodynamic processes, called β-permutations , whose access is sufficient to simulate a generic thermalization process, 3. show how to use abstract toolbox developed within the resource theory approach to thermodynamics to perform challenging optimizations, while combining it with open quantum system dynamics tools to approximate optimal solutions within physically realistic setups.