Simulation of complex dynamics of mean-field p-spin models using measurement-based quantum feedback control

 

---

M. H. Muñoz-Arias¹, I. H. Deutsch¹, P. S. Jessen², and P. M. Poggi¹

1. Center for Quantum Information and Control, CQuIC, Department of Physics and Astronomy,
University of New Mexico, Albuquerque, New Mexico 87131, USA
2. Center for Quantum Information and Control, CQuIC, College of Optical Sciences and
Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
 

We study the application of a new method for simulating nonlinear dynamics of many-body spin systems using quantum measurement and feedback [Munoz-Arias et al., Phys. Rev. Lett. 124, 110503 (2020)] to a broad class of many-body models known as p-spin Hamiltonians, which describe Ising-like models on a completely connected graph with p-body interactions. The method simulates the desired mean field dynamics in the thermodynamic limit by combining nonprojective measurements of a component of the collective spin with a global rotation conditioned on the measurement outcome. We apply this protocol to simulate the dynamics of the p-spin Hamiltonians and demonstrate how different aspects of criticality in the mean-field regime are readily accessible with our protocol. We study applications including properties of dynamical phase transitions and the emergence of spontaneous symmetry breaking in the adiabatic dynamics of the collective spin for different values of the parameter p. We also demonstrate how this method can be employed to study the quantum-to-classical transition in the dynamics continuously as a function of system size.
 

Back | Full Text

A small, highly accurate quantum processor for intermediate-depth quantum simulations

 

---

N. K. Lysne¹, K. W. Kuper¹, P. M. Poggi², I. H. Deutsch², and P. S. Jessen¹

1. Center for Quantum Information and Control, Wyant College of Optical Sciences,
University of Arizona, Tucson, Arizona 85721, USA
2. Center for Quantum Information and Control, Department of Physics and Astronomy,
University of New Mexico, Albuquerque, New Mexico 87131, USA
 

Analog quantum simulation is widely considered a step on the path to fault tolerant quantum computation. With current noisy hardware, the accuracy of an analog simulator will degrade after just a few time steps, especially when simulating complex systems likely to exhibit quantum chaos. Here we describe a quantum simulator based on the combined electron-nuclear spins of individual Cs atoms, and its use to run high fidelity simulations of three different model Hamiltonians for >100 time steps. While not scalable to exponentially large Hilbert spaces, it provides the accuracy and programmability required to explore the interplay between dynamics, imperfections, and accuracy in quantum simulation.
 

Back | Full Text

Simulating nonlinear dynamics of collective spins via quantum measurement and feedback

 

---

M. H. Muñoz¹, P. M. Poggi¹, P. S. Jessen², and I. H. Deutsch¹

1. Center for Quantum Information and Control, University of New Mexico,
Albuquerque, New Mexico 87131, USA
2. Center for Quantum Information and Control, University of Arizona,
Tucson, Arizona 85721, USA
 

We study a method to simulate quantum many-body dynamics of spin ensembles using measurement- based feedback. By performing a weak collective measurement on a large ensemble of two-level quantum systems and applying global rotations conditioned on the measurement outcome, one can simulate the dynamics of a mean-field quantum kicked top, a standard paradigm of quantum chaos. We analytically show that there exists a regime in which individual quantum trajectories adequately recover the classical limit, and show the transition between noisy quantum dynamics to full deterministic chaos described by classical Lyapunov exponents. We also analyze the effects of decoherence, and show that the proposed scheme represents a robust method to explore the emergence of chaos from complex quantum dynamics in a realistic experimental platform based on an atom-light interface.
 

Back | Full Text

Experimental Study of Optimal Measurements for Quantum State Tomography

 

---

H. Sosa-Martinez¹, N. K. Lysne¹,C. H. Baldwin², A. Kalev², I. H. Deutsch², P. S. Jessen¹

1. Center for Quantum Information and Control, University of Arizona, Tucson, Arizona 85721, USA
2. Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131, USA
 

Quantum tomography is a critically important tool to evaluate quantum hardware, making it essential to develop optimized measurement strategies that are both accurate and efficient. We compare a variety of strategies using nearly pure test states. Those that are informationally complete for all states are found to be accurate and reliable even in the presence of errors in the measurements themselves, while those designed to be complete only for pure states are far more efficient but highly sensitive to such errors. Our results highlight the unavoidable trade-offs inherent in quantum tomography.
 

Back | Full Text

Dispersive response of atoms trapped near the surface of an optical nanofiber with applications to quantum nondemolition measurement and spin squeezing

 

---

X. Qi¹, B. Q. Baragiola^1,2, P. S. Jessen³, I. H. Deutsch¹

1. Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131, USA
2. Centre for Engineered Quantum Systems, Macquarie University, Sydney, NSW, 2109, Australia
3. Center for Quantum Information and Control, University of Arizona, Tucson, Arizona 85721, USA
 

We study the strong coupling between photons and atoms that can be achieved in an optical nanofiber geometry when the interaction is dispersive. While the Purcell enhancement factor for spontaneous emission into the guided mode does not reach the strong-coupling regime for individual atoms, one can obtain high cooperativity for ensembles of a few thousand atoms due to the tight confinement of the guided modes and constructive interference over the entire chain of trapped atoms. We calculate the dyadic Greens function, which determines the scattering of light by atoms in the presence of the fiber, and thus the phase shift and polarization rotation induced on the guided light by the trapped atoms. The Greens function is related to a full Heisenberg-Langevin treatment of the dispersive response of the quantized field to tensor polarizable atoms.We apply our formalism to quantum nondemolition (QND) measurement of the atoms via polarimetry.We study shot-noise-limited detection of atom number for atoms in a completely mixed spin state and the squeezing of projection noise for atoms in clock states. Compared with squeezing of atomic ensembles in free space, we capitalize on unique features that arise in the nanofiber geometry including anisotropy of both the intensity and polarization of the guided modes. We use a first-principles stochastic master equation to model the squeezing as a function of time in the presence of decoherence due to optical pumping. We find a peak metrological squeezing of -5 dB is achievable with current technology for -2500 atoms trapped 180 nm from the surface of a nanofiber with radius a = 225 nm.
 

Back | Full Text

Accurate and robust unitary transformation of a high-dimensional quantum system

 

---

B. E. Anderson¹, H. Sosa-Martinez¹, C. A. Riofrio², I. H. Deutsch², P.S. Jessen¹

1. Center for Quantum Information and Control, College of Optical Sciences and Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
2. Center for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
 

Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge becomes how to implement these with high fidelity in the presence of experimental imperfections and decoherence. For two-level systems (qubits) most aspects of unitary control are well understood, but for systems with Hilbert space dimension d>2 (qudits), many questions remain regarding the optimal design of control Hamiltonians and the feasibility of robust implementation. Here we show that arbitrary, randomly chosen unitary transformations can be efficiently designed and implemented in a large dimensional Hilbert space (d=16) associated with the electronic ground state of atomic 133Cs, achieving fidelities above 0.98 as measured by randomized benchmarking. Generalizing the concepts of inhomogeneous control and dynamical decoupling to d>2 systems, we further demonstrate that these qudit unitary maps can be made robust to both static and dynamic perturbations. Potential applications include improved fault-tolerance in universal quantum computation, nonclassical state preparation for high-precision metrology, implementation of quantum simulations, and the study of fundamental physics related to open quantum systems and quantum chaos.
 

Back | Full Text

Three-dimensional light-matter interface for collective spin squeezing in atomic ensembles

 

---

B. Q. Baragiola¹, L. M. Norris¹, E. Montaño², P. G. Mickelson², P. S. Jessen², I. H. Deutsch¹

1. Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131, USA
2. Center for Quantum Information and Control, University of Arizona, Tucson, Arizona 85721, USA
 

We study the three-dimensional nature of the quantum interface between an ensemble of cold, trapped atomic spins and a paraxial laser beam, coupled through a dispersive interaction. To achieve strong entanglement between the collective atomic spin and the photons, one must match the spatial mode of the collective radiation of the ensemble with the mode of the laser beam while minimizing the effects of decoherence due to optical pumping. For ensembles coupling to a probe field that varies over the extent of the cloud, the set of atoms that indistinguishably radiates into a desired mode of the field defines an inhomogeneous spin wave. Strong coupling of a spin wave to the probe mode is not characterized by a single parameter, the optical density, but by a collection of different effective atom numbers that characterize the coherence and decoherence of the system. To model the dynamics of the system, we develop a full stochastic master equation, including coherent collective scattering into paraxial modes, decoherence by local inhomogeneous diffuse scattering, and backaction due to continuous measurement of the light entangled with the spin waves. This formalism is used to study the squeezing of a spin wave via continuous quantum nondemolition measurement. We find that the greatest squeezing occurs in parameter regimes where spatial inhomogeneities are significant, far from the limit in which the interface is well approximated by a one-dimensional, homogeneous model.
 

Back | Full Text

Quantum Control in the Cs 6S_1/2 Ground Manifold Using Radio-Frequency and Microwave Magnetic Fields

 

---

A. Smith¹, B. E. Anderson¹, H. Sosa-Martinez¹, C. A. Riofrio², I. H. Deutsch², P.S. Jessen¹

1. Center for Quantum Information and Control, College of Optical Sciences and Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
2. Center for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
 

We implement arbitrary maps between pure states in the 16-dimensional Hilbert space associated with the ground electronic manifold of ¹³³Cs. This is accomplished by driving atoms with phase modulated radio-frequency and microwave fields, using modulation waveforms found via numerical optimization and designed to work robustly in the presence of imperfections. We evaluate the performance of a sample of randomly chosen state maps by randomized benchmarking, obtaining an average fidelity > 99%. Our protocol advances state-of-the-art quantum control and has immediate applications in quantum metrology and tomography.
 

Back | Full Text

Robust site-resolvable quantum gates in an optical lattice via inhomogeneous control

 

---

J. H. Lee¹, E. Montano¹, I. H. Deutsch², P. S. Jessen¹

1. Center for Quantum Information and Control, College of Optical Sciences and Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
2. Center for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
 

The power of optical lattices for quantum simulation and computation is greatly enhanced when atoms at individual lattice sites can be accessed for measurement and control. Experiments routinely use high-resolution microscopy to obtain site-resolved images in real time, and site-resolved spin flips have been implemented using microwaves resonant with frequency-shifted target atoms in focused light fields. Here we show that methods adapted from inhomogeneous control can greatly increase the performance of such resonance addressing, allowing the targeting of arbitrary single-qubit quantum gates on selected sites with minimal cross-talk to neighbouring sites and significant robustness against uncertainty in the atom position. We further demonstrate the simultaneous implementation of different gates at adjacent sites with a single global microwave pulse. Coherence is verified through two-pulse experiments, and the average gate fidelity is measured to be 95±3%. Our approach may be useful in other contexts such as ion traps and nitrogen-vacancy centres in diamond.
 

Back | Full Text

Enhanced Squeezing of a Collective Spin via Control of Its Qudit Subsystems

 

---

Leigh M. Norris^1,2, Collin M. Trail³, Poul S. Jessen^1,4, Ivan H. Deutsch^1,2

1. Center for Quantum Information and Control (CQuIC)
2. Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131-0001, USA
3. Institute for Quantum Information Science, University of Calgary, Calgary, Alberta, Canada T2N 1N4
4. College of Optical Sciences and Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
 

Unitary control of qudits can improve the collective spin squeezing of an atomic ensemble. Preparing the atoms in a state with large quantum fluctuations in magnetization strengthens the entangling Faraday interaction. The resulting increase in interatomic entanglement can be converted into metrologically useful spin squeezing. Further control can squeeze the internal atomic spin without compromising entanglement, providing an overall multiplicative factor in the collective squeezing. We model the effects of optical pumping and study the tradeoffs between enhanced entanglement and decoherence. For realistic parameters we see improvements of ~10 dB.
 

Back | Full Text