Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1011.3061 · Physical Review Letters

Optimal Control for Unitary Preparation of Many-Body States: Application to Luttinger Liquids

Armin Rahmani, Claudio Chamon

Published Jul 1, 2011• 41 citations
arXivHTMLPDF

Abstract

Many-body ground states can be prepared via unitary evolution in cold atomic systems. Given the initial state and a fixed time for the evolution, how close can we get to a desired ground state if we can tune the Hamiltonian in time? Here we study this optimal control problem focusing on Luttinger liquids with tunable interactions. We show that the optimal protocol can be obtained by simulated annealing. We find that the optimal interaction strength of the Luttinger liquid can have a nonmonotonic time dependence. Moreover, the system exhibits a marked transition when the ratio τ/L of the preparation time to the system size exceeds a critical value. In this regime, the optimal protocols can prepare the states with almost perfect accuracy. The optimal protocols are robust against dynamical noise.

DOI
10.1103/physrevlett.107.016402

Related papers

State preparation in a Jaynes-Cummings lattice with quantum optimal control

Prabin Parajuli, Anuvetha Govindarajan, Lin Tian

High-fidelity preparation of quantum states in an interacting many-body system is often hindered by the lack of knowledge of such states and by limited decoherence times. Here, we study a quantum optimal control (QOC) approach for fast generation of quantum ground states in a finite-sized Jaynes-Cummings lattice with unit filling. Our result shows that the QOC approach can generate quantum many-body states with high fidelity when the evolution time is above a threshold time, and it can significantly outperform the adiabatic approach. We study the dependence of the threshold time on the parameter constraints and the connection of the threshold time with the quantum speed limit. We also show that the QOC approach can be robust against control errors. Our result can lead to advances in the application of the QOC to many-body state preparation.

arXiv:2306.11968•Scientific Reports•Nov 14, 2023•5 citations

Cooling through optimal control of quantum evolution

Armin Rahmani, Takuya Kitagawa, Eugene Demler +1 more

Nonadiabatic unitary evolution with tailored time-dependent Hamiltonians can prepare systems of cold-atomic gases with various desired properties such as low excess energies. For a system of two one-dimensional quasicondensates coupled with a time-varying tunneling amplitude, we show that the optimal protocol, for maximizing any figure of merit in a given time, is bang-bang, i.e., the coupling alternates between only two values through a sequence of sudden quenches. Minimizing the energy of one of the quasicondensates with such a nonadiabatic protocol, and then decoupling it at the end of the process, can result in effective cooling beyond the current state of the art. Our cooling method can be potentially applied to arbitrary systems through an integration of the experiment with simulated annealing computations.

arXiv:1210.5244•Physical Review A•Apr 8, 2013•36 citations

Ultrafast critical ground state preparation via bang–bang protocols

Luca Innocenti, Gabriele De Chiara, Mauro Paternostro +1 more

Abstract The fast and faithful preparation of the ground state of quantum systems is a challenging but crucial task for several applications in the realm of quantum-based technologies. Decoherence limits the maximum time-window allowed to an experiment to faithfully achieve such desired states. This is of particular significance in systems featuring a quantum phase transition, where the vanishing energy gap challenges an adiabatic ground state preparation. We show that a bang–bang protocol, consisting of a time evolution under two different values of an externally tunable parameter, allows for a high-fidelity ground state preparation in evolution times no longer than those required by the application of standard optimal control techniques, such as the chopped-random basis quantum optimization. In addition, owing to their reduced number of variables, such bang–bang protocols are very well suited to optimization tasks, reducing the high computational cost of other optimal control protocols. We benchmark the performance of such approach through two paradigmatic models, namely the Landau–Zener and the Lipkin–Meshkov–Glick model. Remarkably, we find that the critical ground state of the latter model, i.e. its ground state at the critical point, can be prepared with a high fidelity in a total evolution time that scales slower than the inverse of the vanishing energy gap.

arXiv:2007.07381•New Journal of Physics•Aug 24, 2020•12 citations

Time-Efficient Quantum Many-Body State Synthesis and its Optimization via Warm Start Strategies

Prashasti Tiwari, Dylan Lewis, Sougato Bose

Quantum mechanical ground states of many-body systems can be important resources for various investigations: for quantum sensing, for benchmarking quantum hardware with classically solvable states, as the initial states for nonequilibrium quantum dynamics following quenches, the simulation of quantum processes that start by coupling systems in ground states, eg, could be a process in quantum chemistry, while their approximations are required as inputs to quantum phase estimation algorithm. However, preparing ground states can be challenging; for example, it may require adiabatic switching of Hamiltonian terms slower than an inverse gap, which can be time consuming and bring in decoherence. Here we investigate the possibility of preparing a many-body entangled ground state of a certain Hamiltonian, which can be called a quantum ``problem'' Hamiltonian, using the time evolution of an initial fiducial state by another time independent ``solver'' Hamiltonian with couplings up to unit strength for a very short fixed (unit) time: a ``time efficient'' ansatz. The parameters of the solver Hamiltonian are optimised classically minimising energy as the cost function. We present a study of up to $n=14$ qubit many-body states prepared using this methodology. Importantly, we find that a strategy of combining a warm start (an already prepared ground state of a $n-1$ qubit Hamiltonian) and incrementally adding extra couplings of a qubit is the best scaling strategy to prepare the ground state of a $n$-qubit Hamiltonian.

quant-pharXiv:2511.12923•Nov 18, 2025•0 citations

Optimal protocols for quantum quenches of finite duration in the Luttinger model

Ádám Bácsi, Masudul Haque, Balázs Dóra

Reaching a target quantum state from an initial state within a finite temporal window is a challenging problem due to nonadiabaticity. We study the optimal protocol for switching on interactions to reach the ground state of a weakly interacting Luttinger liquid within a finite time $\ensuremath{\tau}$, starting from the noninteracting ground state. The protocol is optimized by minimizing the excess energy at the end of the quench, or by maximizing the overlap with the interacting ground state. We find that the optimal protocol is symmetric with respect to $\ensuremath{\tau}/2$, and can be expressed as a functional of the occupation numbers of the bosonic modes in the final state. For short quench durations, the optimal protocol exhibits fast oscillation and excites high-energy modes. In the limit of large $\ensuremath{\tau}$, minimizing energy requires a smooth protocol while maximizing overlap requires a linear quench protocol. In this limit, the minimal energy and maximal overlap are both universal functions of the system size and the duration of the protocol.

arXiv:1902.09320•Physical review. B./Physical review. B•Jun 6, 2019•4 citations

Rigorous error bounds for dissipative thermal state preparation from weak system-bath coupling

Christopher Ong, S. A. Parameswaran, Benedikt Placke +1 more

Thermal state preparation is a central challenge in the simulation of quantum many-body systems. Yet, provably efficient algorithms for this task were only introduced recently [Chen et al. Nature 646, 561 (2025)]. These algorithms are based on dissipative Lindbladian evolution which exactly fixes the thermal state. Controlled and efficient digital simulation of this evolution, although possible in principle, remains out of reach for present-day quantum hardware. Subsequent work has therefore focused on analog approximations of the proposed Lindbladians via `collision models' with relatively modest requirements -- a resettable bath of ancilla qubits whose couplings to the system can be tuned in time-dependent fashion -- while still admitting rigorous fixed-point error bounds. Existing rigorous approaches, however, do not exploit the fact that these constructions generically implement not only the desired Lindblad dynamics, but also an additional unitary evolution generated by the system Hamiltonian which may aid convergence to the thermal state [Lloyd and Abanin arXiv:2506.21318 (2025)]. Here, we show that this unitary contribution does indeed tighten the fixed-point error bound and demonstrate that it is rigorously controlled by the system-bath coupling strength $J$, scaling as $J^2$. This demonstrates that the effect of the spurious `Lamb shift' term generated by the system-bath interaction can be controlled by tuning $J$. We clarify the role, previously observed, of a randomized implementation in suppressing possible resonances of the drive with the many-body spectrum, and bound the additional variance that this randomization imposes on observables. Finally, we numerically study aspects of the protocol which are relevant for its practical realization, such as the mixing time.

quant-pharXiv:2605.03011•Physical Review A•May 6, 2026•0 citations
Many-body ground states can be prepared via unitary evolution in cold atomic systems. Given the initial state and a fixed time for the evolution, how close can we get to a desired ground state if we can tune the Hamiltonian in time? Here we study this optimal control problem focusing on Luttinger liquids with tunable interactions. We show that the optimal protocol can be obtained by simulated annealing. We find that the optimal interaction strength of the Luttinger liquid can have a nonmonotonic time dependence. Moreover, the system exhibits a marked transition when the ratio τ/L of the preparation time to the system size exceeds a critical value. In this regime, the optimal protocols can prepare the states with almost perfect accuracy. The optimal protocols are robust against dynamical noise.
High-fidelity preparation of quantum states in an interacting many-body system is often hindered by the lack of knowledge of such states and by limited decoherence times. Here, we study a quantum optimal control (QOC) approach for fast generation of quantum ground states in a finite-sized Jaynes-Cummings lattice with unit filling. Our result shows that the QOC approach can generate quantum many-body states with high fidelity when the evolution time is above a threshold time, and it can significantly outperform the adiabatic approach. We study the dependence of the threshold time on the parameter constraints and the connection of the threshold time with the quantum speed limit. We also show that the QOC approach can be robust against control errors. Our result can lead to advances in the application of the QOC to many-body state preparation.
Nonadiabatic unitary evolution with tailored time-dependent Hamiltonians can prepare systems of cold-atomic gases with various desired properties such as low excess energies. For a system of two one-dimensional quasicondensates coupled with a time-varying tunneling amplitude, we show that the optimal protocol, for maximizing any figure of merit in a given time, is bang-bang, i.e., the coupling alternates between only two values through a sequence of sudden quenches. Minimizing the energy of one of the quasicondensates with such a nonadiabatic protocol, and then decoupling it at the end of the process, can result in effective cooling beyond the current state of the art. Our cooling method can be potentially applied to arbitrary systems through an integration of the experiment with simulated annealing computations.
Abstract The fast and faithful preparation of the ground state of quantum systems is a challenging but crucial task for several applications in the realm of quantum-based technologies. Decoherence limits the maximum time-window allowed to an experiment to faithfully achieve such desired states. This is of particular significance in systems featuring a quantum phase transition, where the vanishing energy gap challenges an adiabatic ground state preparation. We show that a bang–bang protocol, consisting of a time evolution under two different values of an externally tunable parameter, allows for a high-fidelity ground state preparation in evolution times no longer than those required by the application of standard optimal control techniques, such as the chopped-random basis quantum optimization. In addition, owing to their reduced number of variables, such bang–bang protocols are very well suited to optimization tasks, reducing the high computational cost of other optimal control protocols. We benchmark the performance of such approach through two paradigmatic models, namely the Landau–Zener and the Lipkin–Meshkov–Glick model. Remarkably, we find that the critical ground state of the latter model, i.e. its ground state at the critical point, can be prepared with a high fidelity in a total evolution time that scales slower than the inverse of the vanishing energy gap.
Quantum mechanical ground states of many-body systems can be important resources for various investigations: for quantum sensing, for benchmarking quantum hardware with classically solvable states, as the initial states for nonequilibrium quantum dynamics following quenches, the simulation of quantum processes that start by coupling systems in ground states, eg, could be a process in quantum chemistry, while their approximations are required as inputs to quantum phase estimation algorithm. However, preparing ground states can be challenging; for example, it may require adiabatic switching of Hamiltonian terms slower than an inverse gap, which can be time consuming and bring in decoherence. Here we investigate the possibility of preparing a many-body entangled ground state of a certain Hamiltonian, which can be called a quantum ``problem'' Hamiltonian, using the time evolution of an initial fiducial state by another time independent ``solver'' Hamiltonian with couplings up to unit strength for a very short fixed (unit) time: a ``time efficient'' ansatz. The parameters of the solver Hamiltonian are optimised classically minimising energy as the cost function. We present a study of up to n=14n=14n=14 qubit many-body states prepared using this methodology. Importantly, we find that a strategy of combining a warm start (an already prepared ground state of a n−1n-1n−1 qubit Hamiltonian) and incrementally adding extra couplings of a qubit is the best scaling strategy to prepare the ground state of a nnn-qubit Hamiltonian.
Reaching a target quantum state from an initial state within a finite temporal window is a challenging problem due to nonadiabaticity. We study the optimal protocol for switching on interactions to reach the ground state of a weakly interacting Luttinger liquid within a finite time $\ensuremath{\tau}$, starting from the noninteracting ground state. The protocol is optimized by minimizing the excess energy at the end of the quench, or by maximizing the overlap with the interacting ground state. We find that the optimal protocol is symmetric with respect to $\ensuremath{\tau}/2$, and can be expressed as a functional of the occupation numbers of the bosonic modes in the final state. For short quench durations, the optimal protocol exhibits fast oscillation and excites high-energy modes. In the limit of large $\ensuremath{\tau}$, minimizing energy requires a smooth protocol while maximizing overlap requires a linear quench protocol. In this limit, the minimal energy and maximal overlap are both universal functions of the system size and the duration of the protocol.
Thermal state preparation is a central challenge in the simulation of quantum many-body systems. Yet, provably efficient algorithms for this task were only introduced recently [Chen et al. Nature 646, 561 (2025)]. These algorithms are based on dissipative Lindbladian evolution which exactly fixes the thermal state. Controlled and efficient digital simulation of this evolution, although possible in principle, remains out of reach for present-day quantum hardware. Subsequent work has therefore focused on analog approximations of the proposed Lindbladians via `collision models' with relatively modest requirements -- a resettable bath of ancilla qubits whose couplings to the system can be tuned in time-dependent fashion -- while still admitting rigorous fixed-point error bounds. Existing rigorous approaches, however, do not exploit the fact that these constructions generically implement not only the desired Lindblad dynamics, but also an additional unitary evolution generated by the system Hamiltonian which may aid convergence to the thermal state [Lloyd and Abanin arXiv:2506.21318 (2025)]. Here, we show that this unitary contribution does indeed tighten the fixed-point error bound and demonstrate that it is rigorously controlled by the system-bath coupling strength JJJ, scaling as J2J^2J2. This demonstrates that the effect of the spurious `Lamb shift' term generated by the system-bath interaction can be controlled by tuning JJJ. We clarify the role, previously observed, of a randomized implementation in suppressing possible resonances of the drive with the many-body spectrum, and bound the additional variance that this randomization imposes on observables. Finally, we numerically study aspects of the protocol which are relevant for its practical realization, such as the mixing time.