Simulation Of Spin Systems Research Articles

Analogue Quantum Simulation with Fixed-Frequency Transmon Qubits

We experimentally assess the suitability of transmon qubits with fixed frequencies and fixed interactions for the realization of analogue quantum simulations of spin systems. We test a set of necessary criteria for this goal on a commercial quantum processor using full quantum process tomography and more efficient Hamiltonian tomography. Significant single qubit errors at low amplitudes are identified as a limiting factor preventing the realization of analogue simulations on currently available devices. We additionally find spurious dynamics in the absence of drive pulses, which we identify with coherent coupling between the qubit and a low dimensional environment. With moderate improvements, analogue simulation of a rich family of time-dependent many-body spin Hamiltonians may be possible.

Programmable Heisenberg interactions between Floquet qubits

The trade-off between robustness and tunability is a central challenge in the pursuit of quantum simulation and fault-tolerant quantum computation. In particular, quantum architectures are often designed to achieve high coherence at the expense of tunability. Many current qubit designs have fixed energy levels and consequently limited types of controllable interactions. Here by adiabatically transforming fixed-frequency superconducting circuits into modifiable Floquet qubits, we demonstrate an XXZ Heisenberg interaction with fully adjustable anisotropy. This interaction model can act as the primitive for an expressive set of quantum operations, but is also the basis for quantum simulations of spin systems. To illustrate the robustness and versatility of our Floquet protocol, we tailor the Heisenberg Hamiltonian and implement two-qubit iSWAP, CZ and SWAP gates with good estimated fidelities. In addition, we implement a Heisenberg interaction between higher energy levels and employ it to construct a three-qubit CCZ gate, also with a competitive fidelity. Our protocol applies to multiple fixed-frequency high-coherence platforms, providing a collection of interactions for high-performance quantum information processing. It also establishes the potential of the Floquet framework as a tool for exploring quantum electrodynamics and optimal control.

Programmable Quantum Simulations of Bosonic Systems with Trapped Ions.

Trapped atomic ion crystals are a leading platform for quantum simulations of spin systems, with programmable and long-range spin-spin interactions mediated by excitations of phonons in the crystal. We describe a complementary approach for quantum simulations of bosonic systems using phonons in trapped-ion crystals, here mediated by excitations of the trapped-ion spins. The scheme enables a high degree of programability across a dense graph of bosonic couplings, utilizing long-lived collective phonon modes in a trapped-ion chain. As such, it is well suited for tackling hard problems such as boson sampling and simulations of long-range bosonic and spin-boson Hamiltonians.

Trotter Errors from Dynamical Structural Instabilities of Floquet Maps in Quantum Simulation

Even small Trotter step sizes can lead to significant errors in the quantum simulation of spin systems, revealing a crucial interplay between physical properties of the simulated Hamiltonian and the Trotterized evolution.

Fast approximate simulation of finite long-range spin systems

Tau leaping is a popular method for performing fast approximate simulation of certain continuous time Markov chain models typically found in chemistry and biochemistry. This method is known to perform well when the transition rates satisfy some form of scaling behaviour. In a similar spirit to tau leaping, we propose a new method for approximate simulation of spin systems which approximates the evolution of spin at each site between sampling epochs as an independent two-state Markov chain. When combined with fast summation methods, our method offers considerable improvement in speed over the standard Doob–Gillespie algorithm. We provide a detailed analysis of the error incurred for both the number of sites incorrectly labelled and for linear functions of the state.

Programmable quantum simulations of spin systems with trapped ions

Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting quantum spin models. Effective spins are represented by appropriate internal energy levels within each ion, and the spins can be measured with near-perfect efficiency using state-dependent fluorescence techniques. By applying optical fields that exert optical dipole forces on the ions, their Coulomb interaction can be modulated to produce long-range and tunable spin-spin interactions that can be reconfigured by shaping the spectrum and pattern of the laser fields, in a prototypical example of a quantum simulator. Here we review the theoretical mapping of atomic ions to interacting spin systems, the preparation of complex equilibrium states, the study of dynamical processes in these many-body interacting quantum systems, and the use of this platform for optimization and other tasks. The use of such quantum simulators for studying spin models may inform our understanding of exotic quantum materials and shed light on the behavior of interacting quantum systems that cannot be modeled with conventional computers.

Full-Scale Ab Initio Simulation of Magic-Angle-Spinning Dynamic Nuclear Polarization.

Theoretical models aimed at describing magic-angle-spinning (MAS) dynamic nuclear polarization (DNP) NMR have great potential in facilitating the in silico design of DNP polarizing agents and formulations. These models must typically face a trade-off between the accuracy of a strict quantum mechanical description and the need for using realistically large spin systems, for instance, using phenomenological models. Here, we show that the use of aggressive state-space restrictions and an optimization strategy allows full-scale ab initio MAS-DNP simulations of spin systems containing thousands of nuclei. Our simulations are shown to reproduce experimental DNP enhancements quantitatively, including their MAS rate dependence, for both frozen solutions and solid materials. They also reveal the importance of a previously unrecognized structural feature found in some polarizing agents that helps minimize the sensitivity losses imposed by the spin diffusion barrier.

Protective measurement of a qubit by a qubit probe

We study the protective measurement of a qubit by a second qubit acting as a probe. Consideration of this model is motivated by the possibility of its experimental implementation in multiqubit systems such as trapped ions. In our scheme, information about the expectation value of an arbitrary observable of the system qubit is encoded in the rotation of the state of the probe qubit. We describe the structure of the Hamiltonian that gives rise to this measurement and analyze the resulting dynamics under a variety of realistic conditions, such as noninfinitesimal measurement strengths, repeated measurements, non-negligible intrinsic dynamics of the probe, and interactions of the system and probe qubits with an environment. We propose an experimental realization of our model in an ion trap. The experiment may be performed with existing technology and makes use of established experimental methods for the engineering and control of Hamiltonians for quantum gates and quantum simulations of spin systems.

Two antibacterial and PPARα/γ-agonistic unsaturated keto fatty acids from a coral-associated actinomycete of the genus Micrococcus.

A pair of geometrically isomeric unsaturated keto fatty acids, (6E,8Z)- and (6E,8E)-5-oxo-6,8-tetradecadienoic acids (1 and 2), were isolated from the culture broth of an actinomycete of the genus Micrococcus, which was associated with a stony coral, Catalaphyllia sp. Their chemical structures were elucidated by spectroscopic analysis including NMR and MS, with special assistance of spin system simulation studies for the assignment of an E geometry at C8 in 2. As metabolites of microbes, compounds 1 and 2 are unprecedented in terms of bearing a 2,4-dienone system. Both 1 and 2 showed antibacterial activity against the plant pathogen Rhizobium radiobacter and the fish pathogen Tenacibaculum maritimum, with a contrasting preference that 1 is more effective to the former strain while 2 is so to the latter. In addition, compounds 1 and 2 displayed agonistic activity against peroxisome proliferator-activated receptors (PPARs) with an isoform specificity towards PPARα and PPARγ.

Toward the first quantum simulation with quantum speedup

With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical computers, but that requires the fewest resources for a quantum computer. We consider quantum simulation of spin systems, which could be applied to understand condensed matter phenomena. We synthesize explicit circuits for three leading quantum simulation algorithms, using diverse techniques to tighten error bounds and optimize circuit implementations. Quantum signal processing appears to be preferred among algorithms with rigorous performance guarantees, whereas higher-order product formulas prevail if empirical error estimates suffice. Our circuits are orders of magnitude smaller than those for the simplest classically infeasible instances of factoring and quantum chemistry, bringing practical quantum computation closer to reality.

Nanoscale magnetic localization in exchange strength modulated ferromagnets

Although ferromagnetism is in general a long-range collective phenomenon, it is possible to induce local spatial variations of magnetic properties in ferromagnetic materials. For example, systematic variation of the exchange coupling strength can be used to create systems that behave as if they are comprised of virtually independent segments that exhibit "local" Curie temperatures. Such localization of thermodynamic behavior leads to boundaries between strongly and weakly magnetized regions that can be controllably moved within the material with temperature. The utility of this interesting functionality is largely dependent on the inherent spatial resolution of magnetic properties - specifically the distance over which the exchange strength and corresponding properties behave locally. To test the degree to which this type of localization can be realized in materials, we have fabricated epitaxial films of Co[1-x]Ru[x] alloy featuring a nanometer scale triangular wave-like concentration depth profile. Continuous nanoscale modulation of the local Curie temperature was observed using polarized neutron reflectometry. These results are consistent with mean-field simulations of spin systems that encompass the possibility of delocalized exchange coupling, and show that composition grading can be used to localize magnetic properties in films down to the nanometer level. Since this is demonstrated here for an itinerant metal, we assert that for virtually any modulated magnetic material system, collective effects can be suppressed to length scales smaller than about 3 nm, so that magnetic behavior overall can be well described in terms of local material properties.

Towards Quantum Simulation with Circular Rydberg Atoms

The main objective of quantum simulation is an in-depth understanding of many-body physics. It is important for fundamental issues (quantum phase transitions, transport, . . . ) and for the development of innovative materials. Analytic approaches to many-body systems are limited and the huge size of their Hilbert space makes numerical simulations on classical computers intractable. A quantum simulator avoids these limitations by transcribing the system of interest into another, with the same dynamics but with interaction parameters under control and with experimental access to all relevant observables. Quantum simulation of spin systems is being explored with trapped ions, neutral atoms and superconducting devices. We propose here a new paradigm for quantum simulation of spin-1/2 arrays providing unprecedented flexibility and allowing one to explore domains beyond the reach of other platforms. It is based on laser-trapped circular Rydberg atoms. Their long intrinsic lifetimes combined with the inhibition of their microwave spontaneous emission and their low sensitivity to collisions and photoionization make trapping lifetimes in the minute range realistic with state-of-the-art techniques. Ultra-cold defect-free circular atom chains can be prepared by a variant of the evaporative cooling method. This method also leads to the individual detection of arbitrary spin observables. The proposed simulator realizes an XXZ spin-1/2 Hamiltonian with nearest-neighbor couplings ranging from a few to tens of kHz. All the model parameters can be tuned at will, making a large range of simulations accessible. The system evolution can be followed over times in the range of seconds, long enough to be relevant for ground-state adiabatic preparation and for the study of thermalization, disorder or Floquet time crystals. This platform presents unrivaled features for quantum simulation.

Quantum dynamics of nuclear spins and spin relaxation in organic semiconductors

We investigate the role of the nuclear spin quantum dynamics in hyperfine-induced spin relaxation of hopping carriers in organic semiconductors. The fast hopping regime with a small carrier spin precession during a waiting time between hops is typical for organic semiconductors possessing long spin coherence times. We consider this regime and focus on a carrier random walk diffusion in one dimension, where the effect of the nuclear spin dynamics is expected to be the strongest. Exact numerical simulations of spin systems with up to 25 nuclear spins are performed using the Suzuki-Trotter decomposition of evolution operator. Larger nuclear spin systems are modeled utilizing the spin-coherent state $P$-representation approach developed earlier. We find that the nuclear spin dynamics strongly influences the carrier spin relaxation at long times. If the random walk is restricted to a small area, it leads to the quenching of carrier spin polarization at a non-zero value at long times. If the random walk is unrestricted, the carrier spin polarization acquires a long-time tail, decaying as $ 1/\sqrt{t}$. Based on the numerical results, we devise a simple formula describing the effect quantitatively.

Creating arbitrary 2D arrays of single atoms for the simulation of spin systems with Rydberg states

We present an experimental setup for creating arbitrary two-dimensional arrays of optical microtraps to trap single atoms for experiments with Rydberg atoms. We use a spatial light modulator to manipulate the spatial phase of a far red-detuned optical dipole trap beam, which allows us to create arbitrary arrays of optical microtraps, by focusing the beam with an in-vacuum high numerical-aperture aspheric lens. We load atoms in the microtraps from a dilute cloud of cold atoms, having at most one atom in each trap due to fast light-assisted collisions. Real-time analysis of the atomic fluorescence with a sensitive CCD camera allows us to determine the filling of each trap individually with a >10 Hz rate. We can create strong interactions between the atoms by exciting them to Rydberg states, with an efficiency of single atom resolved Rydberg detection of >95%.

Multi-Kepler GPU vs. multi-Intel MIC for spin systems simulations

We present and compare the performances of two many-core architectures: the Nvidia Kepler and the Intel MIC both in a single system and in cluster configuration for the simulation of spin systems. As a benchmark we consider the time required to update a single spin of the 3D Heisenberg spin glass model by using the Over-relaxation algorithm. We present data also for a traditional high-end multi-core architecture: the Intel Sandy Bridge. The results show that although on the two Intel architectures it is possible to use basically the same code, the performances of a Intel MIC change dramatically depending on (apparently) minor details. Another issue is that to obtain a reasonable scalability with the Intel Phi coprocessor (Phi is the coprocessor that implements the MIC architecture) in a cluster configuration it is necessary to use the so-called offload mode which reduces the performances of the single system. As to the GPU, the Kepler architecture offers a clear advantage with respect to the previous Fermi architecture maintaining exactly the same source code. Scalability of the multi-GPU implementation remains very good by using the CPU as a communication co-processor of the GPU. All source codes are provided for inspection and for double-checking the results.

Digital Quantum Simulation of Spin Systems in Superconducting Circuits

We propose the implementation of a digital quantum simulator for prototypical spin models in a circuit quantum electrodynamics architecture. We consider the feasibility of the quantum simulation of Heisenberg and frustrated Ising models in transmon qubits coupled to coplanar waveguide microwave resonators. Furthermore, we analyze the time evolution of these models and compare the ideal spin dynamics with a realistic version of the proposed quantum simulator. Finally, we discuss the key steps for developing the toolbox of digital quantum simulators in superconducting circuits.

Janus II: A new generation application-driven computer for spin-system simulations

This paper describes the architecture, the development and the implementation of Janus II, a new generation application-driven number cruncher optimized for Monte Carlo simulations of spin systems (mainly spin glasses). This domain of computational physics is a recognized grand challenge of high-performance computing: the resources necessary to study in detail theoretical models that can make contact with experimental data are by far beyond those available using commodity computer systems. On the other hand, several specific features of the associated algorithms suggest that unconventional computer architectures–that can be implemented with available electronics technologies–may lead to order of magnitude increases in performance, reducing to acceptable values on human scales the time needed to carry out simulation campaigns that would take centuries on commercially available machines. Janus II is one such machine, recently developed and commissioned, that builds upon and improves on the successful JANUS machine, which has been used for physics since 2008 and is still in operation today. This paper describes in detail the motivations behind the project, the computational requirements, the architecture and the implementation of this new machine and compares its expected performances with those of currently available commercial systems.

Multi-GPU codes for spin systems simulations

We present and compare different approaches for using multiple Graphics Processing Units in the simulation of spin systems. As a benchmark we consider the time required to update a single spin of the 3D Heisenberg spin glass model, by using both the Over-relaxation and the Heat Bath algorithms. The results show that a suitable combination of techniques allows to hide almost completely the communication overhead by using the CPU as a communication co-processor of the GPU. Large scale simulations on clusters of GPUs can be efficiently carried out by following the same approach also for other applications where a clear cut exists between bulk and boundaries data.

A two-dimensional lattice ion trap for quantum simulation

Quantum simulations of spin systems could enable the solution of problems that otherwise require infeasible classical resources. Such a simulation may be implemented using a well-controlled system of effective spins, such as a two-dimensional lattice of locally interacting ions. We propose here a layered planar rf trap design that can be used to create arbitrary two-dimensional lattices of ions. The design also leads naturally to ease of microfabrication. As a first experimental demonstration, we confine S88r+ ions in a millimeter-scale lattice trap and verify numerical models of the trap by measuring the motional frequencies. We also confine 440 nm diameter charged microspheres and observe ion-ion repulsion between ions in neighboring lattice sites. Our design, when scaled to smaller ion-ion distances, is appropriate for quantum simulation schemes, e.g., that of Porras and Cirac [Phys. Rev. Lett. 92, 207901 (2004)]. We note, however, that in practical realizations of the trap, an increase in the secular frequency with decreasing ion spacing may make a coupling rate that is large relative to the decoherence rate in such a trap difficult to achieve.

Rapid magnetic resonance quantification on the brain: Optimization for clinical usage

A method is presented for rapid simultaneous quantification of the longitudinal T(1) relaxation, the transverse T(2) relaxation, the proton density (PD), and the amplitude of the local radio frequency B(1) field. All four parameters are measured in one single scan by means of a multislice, multiecho, and multidelay acquisition. It is based on a previously reported method, which was substantially improved for routine clinical usage. The improvements comprise of the use of a multislice spin-echo technique, a background phase correction, and a spin system simulation to compensate for the slice-selective RF pulse profile effects. The aim of the optimization was to achieve the optimal result for the quantification of magnetic resonance parameters within a clinically acceptable time. One benchmark was high-resolution coverage of the brain within 5 min. In this scan time the measured intersubject standard deviation (SD) in a group of volunteers was 2% to 8%, depending on the tissue (voxel size = 0.8 x 0.8 x 5 mm). As an example, the method was applied to a patient with multiple sclerosis in whom the diseased tissue could clearly be distinguished from healthy reference values. Additionally it was shown that, using the approach of synthetic MRI, both accurate conventional contrast images as well as quantification maps can be generated based on the same scan.