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Register a new userMonitoring Quantum Simulators via Quantum Non-Demolition Couplings to Atomic Clock Qubits
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We discuss monitoring the time evolution of an analog quantum simulator via a quantum non-demolition (QND) coupling to an auxiliary `clock qubit. The QND variable of interest is the `energy of the quantum many-body system, represented by the Hamiltonian of the quantum simulator. We describe a physical implementation of the underlying QND Hamiltonian for Rydberg atoms trapped in tweezer arrays using laser dressing schemes for a broad class of spin models. As an application, we discuss a quantum protocol for measuring the spectral form factor of quantum many-body systems, where the aim is to identify signatures of ergodic vs. non-ergodic dynamics, which we illustrate for disordered 1D Heisenberg and Floquet spin models on Rydberg platforms. Our results also provide the physical ingredients for running quantum phase estimation protocols for measurement of energies, and preparation of energy eigenstates for a specified spectral resolution on an analog quantum simulator.
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The realization of quantum adiabatic dynamics is at the core of implementations of adiabatic quantum computers. One major issue is to efficiently compromise between the long time scales required by the adiabatic protocol and the detrimental effects of the environment, which set an upper bound to the time scale of the operation. In this work we propose a protocol which achieves fast adiabatic dynamics by coupling the system to an external environment by the means of a quantum-non-demolition (QND) Hamiltonian. We analyse the infidelity of adiabatic transfer for a Landau-Zener problem in the presence of QND measurement, where the qubit couples to a meter which in turn quickly dissipates. We analyse the protocols fidelity as a function of the strength of the QND coupling and of the relaxation time of the meter. In the limit where the decay rate of the ancilla is the largest frequency scale of the dynamics, the QND coupling induces an effective dephasing in the adiabatic basis. Optimal conditions for adiabaticity are found when the coupling with the meter induces dissipative dynamics which suppresses unwanted diabatic transitions.
We introduce the concept of embedding quantum simulators, a paradigm allowing the efficient quantum computation of a class of bipartite and multipartite entanglement monotones. It consists in the suitable encoding of a simulated quantum dynamics in the enlarged Hilbert space of an embedding quantum simulator. In this manner, entanglement monotones are conveniently mapped onto physical observables, overcoming the necessity of full tomography and reducing drastically the experimental requirements. Furthermore, this method is directly applicable to pure states and, assisted by classical algorithms, to the mixed-state case. Finally, we expect that the proposed embedding framework paves the way for a general theory of enhanced one-to-one quantum simulators.
The control of many-body quantum dynamics in complex systems is a key challenge in the quest to reliably produce and manipulate large-scale quantum entangled states. Recently, quench experiments in Rydberg atom arrays (Bluvstein et. al., arXiv:2012.12276) demonstrated that coherent revivals associated with quantum many-body scars can be stabilized by periodic driving, generating stable subharmonic responses over a wide parameter regime. We analyze a simple, related model where these phenomena originate from spatiotemporal ordering in an effective Floquet unitary, corresponding to discrete time-crystalline (DTC) behavior in a prethermal regime. Unlike conventional DTC, the subharmonic response exists only for Neel-like initial states, associated with quantum scars. We predict robustness to perturbations and identify emergent timescales that could be observed in future experiments. Our results suggest a route to controlling entanglement in interacting quantum systems by combining periodic driving with many-body scars.
We propose a quantum algorithm in an embedding ion-trap quantum simulator for the efficient computation of N-qubit entanglement monotones without the necessity of full tomography. Moreover, we discuss possible realistic scenarios and study the associated decoherence mechanisms.
Finding the global minimum in a rugged potential landscape is a computationally hard task, often equivalent to relevant optimization problems. Simulated annealing is a computational technique which explores the configuration space by mimicking thermal noise. By slow cooling, it freezes the system in a low-energy configuration, but the algorithm often gets stuck in local minima. In quantum annealing, the thermal noise is replaced by controllable quantum fluctuations, and the technique can be implemented in modern quantum simulators. However, quantum-adiabatic schemes become prohibitively slow in the presence of quasidegeneracies. Here we propose a strategy which combines ideas from simulated annealing and quantum annealing. In such hybrid algorithm, the outcome of a quantum simulator is processed on a classical device. While the quantum simulator explores the configuration space by repeatedly applying quantum fluctuations and performing projective measurements, the classical computer evaluates each configuration and enforces a lowering of the energy. We have simulated this algorithm for small instances of the random energy model, showing that it potentially outperforms both simulated thermal annealing and adiabatic quantum annealing. It becomes most efficient for problems involving many quasi-degenerate ground states.
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