Hamiltonian simulation algorithms for near-term quantum hardware

The quantum circuit model is the de-facto way of designing quantum algorithms. Yet any level of abstraction away from the underlying hardware incurs overhead. In this work, we develop quantum algorithms for Hamiltonian simulation "one level below” the circuit model, exploiting the underlying control over qubit interactions available in most quantum hardware and deriving analytic circuit identities for synthesising multi-qubit evolutions from two-qubit interactions. We then analyse the impact of these techniques under the standard error model where errors occur per gate, and an error model with a constant error rate per unit time. To quantify the benefits of this approach, we apply it to time-dynamics simulation of the 2D spin Fermi-Hubbard model. Combined with new error bounds for Trotter product formulas tailored to the non-asymptotic regime and an analysis of error propagation, we find that e.g. for a 5 × 5 Fermi-Hubbard lattice we reduce the circuit depth from 1, 243, 586 using the best previous fermion encoding and error bounds in the literature, to 3, 209 in the per-gate error model, or the circuit-depth-equivalent to 259 in the per-time error model. This brings Hamiltonian simulation, previously beyond reach of current hardware for non-trivial examples, significantly closer to being feasible in the NISQ era

Translationally Invariant Universal Quantum Hamiltonians in 1D

. Recent work has characterized rigorously what it means for one quantum system to simulate another and demonstrated the existence of universal Hamiltonians—simple spin lattice Hamiltonians that can replicate the entire physics of any other quantum many-body system. Previous universality results have required proofs involving complicated ‘chains’ of perturbative ‘gadgets.’ In this paper, we derive a significantly simpler and more powerful method of proving universality of Hamiltonians, directly leveraging the ability to encode quantum computation into ground states. This provides new insight into the origins of universal models and suggests a deep connection between universality and complexity. We apply this new approach to show that there are universal models even in translationally invariant spin chains in 1D. This gives as a corollary a new Hamiltonian complexity result that the local Hamiltonian problem for translationally invariant spin chains in one dimension with an exponentially small promise gap is PSPACE-complete. Finally, we use these new universal models to construct the first known toy model of 2D–1D holographic duality between local Hamiltonians

Compact fermion to qubit mappings

Mappings between fermions and qubits are valuable constructions in physics. To date only a handful exist. In addition to revealing dualities between fermionic and spin systems, such mappings are indispensable in any quantum simulation of fermionic physics on quantum computers. The number of qubits required per fermionic mode, and the locality of mapped fermionic operators strongly impact the cost of such simulations. We present a fermion to qubit mapping that outperforms all previous local mappings in both the qubit to mode ratio and the locality of mapped operators. In addition to these practically useful features, the mapping bears an elegant relationship to the toric code, which we discuss. Finally, we consider the error mitigating properties of the mapping—which encodes fermionic states into the code space of a stabilizer code. Although there is an implicit tradeoff between low weight representations of local fermionic operators, and high distance code spaces, we argue that fermionic encodings with low-weight representations of local fermionic operators can still exhibit error mitigating properties which can serve a similar role to that played by high code distances. In particular, when undetectable errors correspond to “natural” fermionic noise. We illustrate this point explicitly both for this encoding and the Verstraete-Cirac encoding

Microrheology, stress fluctuations and active behavior of living cells

We report the first measurements of the intrinsic strain fluctuations of living cells using a recently-developed tracer correlation technique along with a theoretical framework for interpreting such data in heterogeneous media with non-thermal driving. The fluctuations' spatial and temporal correlations indicate that the cytoskeleton can be treated as a course-grained continuum with power-law rheology, driven by a spatially random stress tensor field. Combined with recent cell rheology results, our data imply that intracellular stress fluctuations have a nearly $1/\omega^2$ power spectrum, as expected for a continuum with a slowly evolving internal prestress.Comment: 4 pages, 2 figures, to appear in Phys. Rev. Let

Fragmentation is crucial for the steady-state dynamics of actin filaments

Despite the recognition that actin filaments are important for numerous cellular processes, and decades of investigation, the dynamics of in vitro actin filaments are still not completely understood. Here, we follow the time evolution of the length distribution of labeled actin reporter filaments in an unlabeled F-actin solution via fluorescence microscopy. Whereas treadmilling and diffusive length fluctuations cannot account for the observed dynamics, our results suggest that at low salt conditions, spontaneous fragmentation is crucial

Alpine Space Prospective Study. Sustainable territorial development in the Alpine Space: Towards long term transnational cooperation

This "Prospective Study" argues that a long term transnational cooperation will be able to pursue the sustainable territorial development in the Alpine Space only at the condition of a substantial improvement of the current experience. This regards an increased awareness of the complexity of issues and challenges currently at stake in the Alpine area but especially, in this light, the capacity of involving all relevant institutional and socioeconomic stakeholders in the building of shared transnational strategie

Bronze Age globalisation and Eurasian impacts on later Jōmon social change

From northern China, millet agriculture spread to Korea and the Maritime Russian Far East by 3500–2700 BC. While the expansion of agricultural societies across the Sea of Japan did not occur until around 900 BC, the intervening period saw major transformations in the Japanese archipelago. The cultural florescence of Middle Jōmon central Honshu underwent a collapse and reorganisation into more decentralised settlements. Mobility increased as Late Jōmon influences spread from eastern into western Japan, and populations expanded to offshore islands such as Okinawa and the Kurils. In Kyushu and other parts of western Japan, the eastern Jōmon expansion was associated with the cultivation of adzuki and soybeans but, contrary to earlier assessments, there is no evidence for the introduction of cereal crops at this time. Here, we analyse archaeological and historical linguistic evidence of connections between the Eurasian mainland and the Japanese Islands c. 3500 to 900 BC. A re-evaluation of archaeological material discussed since the 1920s concludes that the transformations in Jōmon society during this period were at least in part a response to contacts with Eurasian Bronze Age cultures. Evidence for linguistic contact between Koreanic and the Ainuic languages which are presumed to have been spoken by Jōmon populations is also consistent with new Bronze Age mobilities. Although prehistoric Japan was one of the most isolated regions of Eurasia, we conclude that the historical evolution of societies in the Japanese archipelago after the third millennium BC was linked with processes of Bronze Age globalisation.紀元前 3500–2700 年頃、アワ・キビ農耕が中国東北部から朝鮮半島と極東ロシアに広がった. 農耕社会が実際に日本海を渡るのは、時代をはるかに下る紀元前900年頃まで待たねばならない. しかし、この時期、日本列島の縄文社会にも大きな変化がみられる. 中部地方の縄文中期文化の輝きは失われ、大型集落は放棄され、分散型居住パターンへと社会の再編成が行われた. 縄文後期の文化要素が東から西日本へ広がり、琉球列島や千島列島等の離島への移動が多くなり、社会の流動性が増した. 九州等、列島西部では、東方からの縄文文化がダイズ・アズキ栽培と共に広がった. 一方、この時期には穀物栽培の証拠は認められていない. 本論では、考古学と言語学の分析により起源前 3500~900 年頃の間のユーラシア大陸と日本列島の交流について検討する. そのうえで、 1920 年代以来議論された考古資料の再評価の結果、縄文後晩期の社会変化は少なくても部分的には大陸の青銅器時代文化との接触に起因すると論じる. 縄文人が話したと推定されるアイヌ語族(Ainuic)と朝鮮語族 (Koreanic) との言語的交流も青銅器時代の新しい流動性と一致する. 先史時代の日本列島はユーラシアで最も孤立した地域の一つだったにも関わらず、紀元前3千年紀後の列島の歴史的展開は青銅器時代のグローバリゼーションのプロセスと関連していたと結論する.- Introduction - Social Change in the Middle to Final Jōmon: Overview - Middle–Final Jōmon Interactions Between Continental East Asia and Japan -- Cultivated Plants and Domesticated Animals -- Agricultural Tools -- Bronze and Bronze Skeuomorphs -- The Itoku Site -- Stone Axes -- Linguistic Interaction - Discussion - Conclusion

Alpine Space Prospective Study. Sustainable territorial development in the Alpine Space: Towards long term transnational cooperation

This "Prospective Study" argues that a long term transnational cooperation will be able to pursue the sustainable territorial development in the Alpine Space only at the condition of a substantial improvement of the current experience. This regards an increased awareness of the complexity of issues and challenges currently at stake in the Alpine area but especially, in this light, the capacity of involving all relevant institutional and socioeconomic stakeholders in the building of shared transnational strategies

One-Bead Microrheology with Rotating Particles

We lay the theoretical basis for one-bead microrheology with rotating particles, i.e, a method where colloids are used to probe the mechanical properties of viscoelastic media. Based on a two-fluid model, we calculate the compliance and discuss it for two cases. We first assume that the elastic and fluid component exhibit both stick boundary conditions at the particle surface. Then, the compliance fulfills a generalized Stokes law with a complex shear modulus whose validity is only limited by inertial effects, in contrast to translational motion. Secondly, we find that the validity of the Stokes regime is reduced when the elastic network is not coupled to the particleComment: 7 pages, 5 figures, submitted to Europhys. Let