We propose an analog quantum simulator that uses ion traps to realize the many-body electron-electron Coulomb interaction of an electron gas. This proposal maps a system that is difficult to solve and control to an experimentally-feasible setup that can be realized with current technologies. Using a dilatation transform, we show that ion traps can efficiently simulate electronic Coulomb interactions. No complexity overhead is added if only the energy spectrum is desired, and only a simple unitary transform is needed on the initial state otherwise. The runtime of the simulation is found to be much shorter than the timescale of the corresponding electronic system, minimizing susceptibility of the proposed quantum simulator to external noise and decoherence. This proposal works in any number of dimensions, and could be used to simulate different topological phases of electrons in graphene-like structures, by using ions trapped in honeycomb lattices.
While quantum simulators promise to explore quantum many-body physics beyond classical computation, their capabilities are limited by the available native interactions in the hardware. On many platforms, accessible Hamiltonians are largely restricted to one- and two-body interactions, limiting access to multi-body Hamiltonians and to systems governed by simultaneous, non-commuting interaction terms that are central to condensed matter, quantum chemistry, and high-energy physics. We introduce and experimentally demonstrate a hybrid digital-analog protocol that overcomes these limitations by embedding analog evolution between shallow entangling-gate layers. This method produces effective Hamiltonians with simultaneous non-commuting three- and four-body interactions that are generated non-perturbatively and without Trotter error -- capabilities not practically attainable on near-term hardware using purely digital or purely analog schemes. We implement our scheme on a trapped-ion quantum processor and use it to realize a topological spin chain exhibiting prethermal strong zero modes persisting at high temperature, as well as models featuring three- and four-body interactions. Our hardware-agnostic and scalable method opens new routes to realizing complex many-body physics across quantum platforms.
Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.
Duality transformations are very important in both classical and quantum physics. They allow one to relate two seemingly different formulations of the same physical realm through clever mathematical manipulations, and offer numerous advantages for the study of many-body physics. In this work, we suggest a method which introduces them to the world of quantum simulation too: a feasible scheme for implementing duality transformations as physical operations, mapping between dual quantum states showing the same observable physics, rather than just a mathematical trick. Demonstrating with Abelian lattice models, we show how duality transformations could be implemented in the laboratory as sequences of single- and two-body operations---unitaries and measurements.
Physics
Quantum simulation can map challenging problems in complex materials onto better defined ones in simpler, easier-to-manipulate systems. Physical implementations range from trapped ions to superconducting qubits, each having distinct strengths and weaknesses. Nguyen et al. propose a quantum simulator that seems to combine many of the best features of the existing simulators in one system, while being within current experimental reach. The simulator is based on circular Rydberg atoms—with a highly excited electron orbiting the nucleus along a roughly circular path—where the atoms can be trapped by laser light, can be read out one by one, and have very long lifetimes. The interactions between such atoms would make it possible to simulate some of the most challenging problems in many-body physics.
Phys. Rev. X 8 , 011032 (2018).
We present a quantum circuit that implements the random dilation superchannel, transforming parallel queries of an unknown quantum channel into the same number of parallel queries of a randomly chosen dilation isometry of the input channel. This is a natural generalization of the random purification channel, that transforms copies of an unknown mixed state to copies of a randomly chosen purification state. The circuit complexity of our construction is
O(poly(n,logdI,logdO)), where
n is the number of queries and
dI and
dO are the input and output dimensions of the input channel, respectively. This random dilation superchannel is extended to the sequential queries approximately, by transforming the parallel random dilation isometry into sequential random dilation unitaries with
O(poly(dI)) overhead in the number of queries. We also show that our results can be further extended to the case of quantum superchannels. On the other hand, we show a no-go theorem on the exact random dilation of sequential queries with
o(poly(min{dI,dO})) query overhead, showcasing a fundamental difference between the parallel and sequential cases. As an application, we show an efficient storage-and-retrieval of an unknown quantum channel, which improves the program cost exponentially in the retrieval error
ε. For the case where the Kraus rank
r is the least possible (i.e.,
r=dI/dO), we show quantum circuits that transform
n parallel queries of an unknown quantum channel
Λ to
Θ(nα) parallel queries of
Λ for any
α<2 approximately, and implement its Petz recovery map for the maximally mixed reference state probabilistically and exactly.