We present a robust protocol to reshape interactions in a spin ensemble based on global control pulse sequences applied to multiple subensembles in parallel. This setting arises naturally from ensembles of solid-state defects or multi-species atomic arrays. We show that it is provably computationally hard to find pulse sequences that simultaneously engineer interactions both within and between subensembles. Despite its formal hardness, we identify a set of necessary or sufficient conditions under which one can synthesize a target Hamiltonian from the native one. Moreover, we introduce efficient numerical strategies for designing pulse sequences that engineer target Hamiltonians robust against common control imperfections. As a specific application, we discuss the robust generation of two-mode spin squeezing in dual-species atomic ensembles, which is a challenging task without subensemble control. Our results provide a practical toolbox to design novel quantum simulation and sensing experiments with minimal control overhead.
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7+2+13 pages, 3+0+2 figures; v2: additional proof of NP-hardness, minor edits
We present a robust protocol to reshape interactions in a spin ensemble based on global control pulse sequences applied to multiple subensembles in parallel. This setting arises naturally from ensembles of solid-state defects or multi-species atomic arrays. We show that it is provably computationally hard to find pulse sequences that simultaneously engineer interactions both within and between subensembles. Despite its formal hardness, we identify a set of necessary or sufficient conditions under which one can synthesize a target Hamiltonian from the native one. Moreover, we introduce efficient numerical strategies for designing pulse sequences that engineer target Hamiltonians robust against common control imperfections. As a specific application, we discuss the robust generation of two-mode spin squeezing in dual-species atomic ensembles, which is a challenging task without subensemble control. Our results provide a practical toolbox to design novel quantum simulation and sensing experiments with minimal control overhead.
Implementing the time evolution under a desired target Hamiltonian is critical for various applications in quantum science. Due to the exponential increase of parameters in the system size and due to experimental imperfections, this task can be challenging in quantum many-body settings. We introduce an efficient and robust scheme to engineer arbitrary local many-body Hamiltonians. To this end, our scheme applies single-qubit π or π/2 pulses to an always-on system Hamiltonian, which we assume to be native to a given platform. These sequences are constructed by efficiently solving a linear program (LP) which minimizes the total evolution time. In this way, we can engineer target Hamiltonians that are only limited by the locality of the interactions in the system Hamiltonian. Based on average Hamiltonian theory and by using robust composite pulses, we make our schemes robust against errors, including finite-pulse-time errors and various control errors. To demonstrate the performance of our scheme, we provide numerical simulations. In particular, we solve the Hamiltonian-engineering problem on a laptop for arbitrary two-local Hamiltonians on a two-dimensional square lattice with 196 qubits in only 60 s. Moreover, we simulate the engineering of general Heisenberg Hamiltonians from Ising Hamiltonians with imperfect single-qubit pulses for smaller system sizes, and achieve a fidelity larger than 99.9%, which is orders of magnitude better than nonrobust implementations.
Implementing the time evolution under a desired target Hamiltonian is critical for various applications in quantum science. Due to the exponential increase of parameters in the system size and due to experimental imperfections, this task can be challenging in quantum many-body settings. We introduce an efficient and robust scheme to engineer arbitrary local many-body Hamiltonians. To this end, our scheme applies single-qubit π or π / 2 pulses to an always-on system Hamiltonian, which we assume to be native to a given platform. These sequences are constructed by efficiently solving a linear program (LP) which minimizes the total evolution time. In this way, we can engineer target Hamiltonians that are only limited by the locality of the interactions in the system Hamiltonian. Based on average Hamiltonian theory and by using robust composite pulses, we make our schemes robust against errors, including finite-pulse-time errors and various control errors. To demonstrate the performance of our scheme, we provide numerical simulations. In particular, we solve the Hamiltonian-engineering problem on a laptop for arbitrary two-local Hamiltonians on a two-dimensional square lattice with 196 qubits in only 60 s. Moreover, we simulate the engineering of general Heisenberg Hamiltonians from Ising Hamiltonians with imperfect single-qubit pulses for smaller system sizes, and achieve a fidelity larger than 99.9%, which is orders of magnitude better than nonrobust implementations.
Dynamical decoupling and Hamiltonian engineering are well-established techniques that have been used to control qubit systems. However, designing the corresponding methods for qudit systems has been challenging due to the lack of a Bloch sphere representation, more complex interactions, and additional control constraints. By identifying several general structures associated with such problems, we develop a formalism for the robust dynamical decoupling and Hamiltonian engineering of strongly interacting qudit systems. Our formalism significantly simplifies qudit pulse-sequence design while naturally incorporating robustness conditions necessary for experimental practicality. We experimentally demonstrate these techniques in a strongly interacting, disordered ensemble of spin-1 nitrogen-vacancy centers, achieving more than an order-of-magnitude improvement in coherence time over existing pulse sequences. We further describe how our techniques enable the engineering of exotic many-body phenomena such as quantum many-body scars, and open up new opportunities for quantum metrology with enhanced sensitivities. These results enable wide-reaching new applications for dynamical decoupling and Hamiltonian engineering in many-body physics and quantum metrology. Published by the American Physical Society 2024
While quantum devices rely on interactions between constituent subsystems and with their environment to operate, native interactions alone often fail to deliver targeted performance. Coherent pulsed control provides the ability to tailor effective interactions, known as Hamiltonian engineering. We propose a Hamiltonian engineering method that maximizes desired interactions while mitigating deleterious ones by conducting a pulse sequence search using constrained optimization. The optimization formulation incorporates pulse sequence length and cardinality penalties consistent with linear or integer programming. We apply the general technique to magnetometry with solid state spin ensembles in which inhomogeneous interactions between sensing spins limit coherence. Defining figures of merit for broadband Ramsey magnetometry, we present novel pulse sequences which outperform known techniques for homonuclear spin decoupling in both spin-1/2 and spin-1 systems. When applied to nitrogen vacancy (NV) centers in diamond, this scheme partially preserves the Zeeman interaction while zeroing dipolar coupling between negatively charged NV − centers. Such a scheme is of interest for NV − magnetometers which have reached the NV − –NV − coupling limit. We discuss experimental implementation in NV ensembles, as well as applicability of the current approach to more general spin bath decoupling and superconducting qubit control.
Implementing the time evolution under a desired target Hamiltonian is critical for various applications in quantum science. Due to the exponential increase in the number of parameters with system size and experimental imperfections, this task can be challenging in quantum many-body settings. We introduce an efficient and robust scheme to engineer arbitrary local many-body Hamiltonians. To this end, our scheme applies single-qubit π or π/2 pulses to an always-on system Hamiltonian, which we assume to be native to a given platform. These sequences are constructed by efficiently solving a linear program (LP) which minimizes the total evolution time. In this way, we can engineer target Hamiltonians that are only limited by the locality of the interactions in the system Hamiltonian. Based on average Hamiltonian theory and using robust composite pulses, we make our schemes robust against errors, including finite pulse time errors and various control errors. To demonstrate the performance of our scheme, we provide numerical simulations. In particular, we solve the Hamiltonian engineering problem on a laptop for arbitrary two-local Hamiltonians on a 2D square lattice with 196 qubits in only 60 seconds. Moreover, we simulate the engineering of general Heisenberg Hamiltonians from Ising Hamiltonians using imperfect single-qubit pulses for smaller system sizes and achieve a fidelity exceeding 99.9%, which is orders of magnitude better than non-robust implementations.
We propose and analyze a method to engineer effective interactions in an ensemble of d-level systems (qudits) driven by global control fields. In particular, we present (i) a necessary and sufficient condition under which a given interaction can be decoupled, (ii) the existence of a universal sequence that decouples any (cancelable) interaction, and (iii) an efficient algorithm to engineer a target Hamiltonian from an initial Hamiltonian (if possible). We illustrate the potential of this method with two examples. Specifically, we present a 6-pulse sequence that decouples effective spin-1 dipolar interactions and demonstrate that a spin-1 Ising chain can be engineered to study transitions among three distinct symmetry protected topological phases. Our work enables new approaches for the realization of both many-body quantum memories and programmable analog quantum simulators using existing experimental platforms.