Analog Quantum Simulator of a Quantum Field Theory with Fermion-Spin Systems in Silicon
Ali Rad, Alexander Schuckert, Eleanor Crane, Gautam Nambiar, Fan Fei, Jonathan Wyrick, Richard M. Silver, Mohammad Hafezi, Zohreh Davoudi, Michael J. Gullans
Simulating fermions coupled to spin degrees of freedom, relevant for a range of quantum field theories, represents a promising application for quantum simulators. Mapping fermions to qubits is challenging in $2+1$ and higher spacetime dimensions, and mapping bosons demands substantial quantum-computational overhead. These features complicate the realization of mixed fermion-boson quantum systems in digital quantum computers. We propose a native fermion-(large-)spin analog quantum simulator by utilizing dopant arrays in silicon. Specifically, we show how to use a dynamical lattice of coupled nuclear spins and conduction-band electrons to realize a quantum field theory: an extended Jackiw-Rebbi model involving coupled fermions and quantum rotors. We demonstrate the feasibility of observing dynamical mass generation and a confinement-deconfinement quantum phase transition in 1+1 dimensions on this platform, even in the presence of strong long-range Coulomb interactions. Furthermore, we employ finite-temperature Hartree-Fock-Bogoliubov simulations to investigate the dynamics of mass generation in two-dimensional square and honeycomb arrays, showing that this phenomenon can be simulated with realistic experimental parameters. Our findings reveal two distinct phases, and demonstrate robustness against the addition of Coulomb interactions. Finally, we discuss experimental signatures of the phases through transport and local charge sensing in dopant arrays. This study lays the foundation for quantum simulations of quantum field theories exhibiting fermions coupled to spin degrees of freedom using donors in silicon.
An important step in quantum simulation is to measure the many-body correlations of the simulated model. For a practical quantum simulator composed of finite number of qubits and cavities, in contrast to ideal many-body systems in the thermodynamic limit, a measurement device can generate strong backaction on the simulator, which could prevent the accurate readout of the correlation functions. Here we calculate the readout of a detector coupled to an analog quantum simulator. We show that reliable characterization of the many-body correlations in the simulator can be achieved when the coupling…
Unitary Sampling Expectation-Value Reconstruction (USER) is used to determine expectation values that are not directly accessible on an analog quantum simulator.
Analog quantum simulators can be used to study quantum correlation in novel many-body systems by emulating the Hamiltonian of these systems. One essential question in quantum simulation is to probe the properties of an emulated many-body system. Here we present a circuit QED scheme for probing such properties by measuring the spectrum of a superconducting resonator coupled to a quantum simulator. We first study a general framework of this approach, and show that the spectrum of the resonator is directly related to the correlation function of the coupling operator between the resonator and the …
Analog quantum simulation is expected to be a significant application of near-term quantum devices. Verification of these devices without comparison to known simulation results will be an important task as the system size grows beyond the regime that can be simulated classically. We introduce a set of experimentally-motivated verification protocols for analog quantum simulators, discussing their sensitivity to a variety of error sources and their scalability to larger system sizes. We demonstrate these protocols experimentally using a two-qubit trapped-ion analog quantum simulator and numerica…
We propose an analog quantum simulator for the Holstein molecular-crystal model based on a superconducting circuit QED system in the dispersive regime. By varying the driving field on the superconducting resonators, one can readily access both the adiabatic and anti-adiabatic regimes of this model. Strong e-ph coupling required for small-polaron formation can also be reached. We show that small-polaron state of arbitrary quasimomentum can be generated by applying a microwave pulse to the resonators. We also show that significant squeezing in the resonator modes can be achieved in the polaron-c…
With quantum computers being out of reach for now, quantum simulators are the alternative devices for efficient and more exact simulation of problems that are challenging on conventional computers. Quantum simulators are classified into analog and digital, with the possibility of constructing "hybrid" simulators by combining both techniques. In this paper, we focus on analog quantum simulators of open quantum systems and address the limit that they can beat classical computers. In particular, as an example, we discuss simulation of the chlorosome light-harvesting antenna from green sulfur bact…
We study an analog quantum simulator coupled to a reservoir with a known spectral density. The reservoir perturbs the quantum simulation by causing decoherence. The simulator is used to measure an operator average, which cannot be calculated using any classical means. Since we cannot predict the result, it is difficult to estimate the effect of the environment. Especially, it is difficult to resolve whether the perturbation is small or if the actual result of the simulation is in fact very different from the ideal system we intend to study. Here, we show that in specific systems a measurement …
The influence of interface roughness scattering (IRS) on the performances of silicon nanowire field-effect transistors (NWFETs) is numerically investigated using a full 3D quantum transport simulator based on the atomistic sp3d5s* tight-binding model. The interface between the silicon and the silicon dioxide layers is generated in a real-space atomistic representation using an experimentally derived autocovariance function (ACVF). The oxide layer is modeled in the virtual crystal approximation (VCA) using fictitious SiO2 atoms. <110>-oriented nanowires with different diameters and randomly gen…
Despite the pristine abilities of analog quantum simulators to study quantum dynamics, possibilities to detect currents are sparse. Here, we propose a flexible non-invasive technique to measure currents in quantum many-body systems by weakly coupling the system to an ancilla, followed by a measurement of the ancilla population. We numerically benchmark the scheme at the example of interacting bosons in a Harper-Hofstadter optical-lattice ladder, and discuss potential experimental error sources. The highly flexible protocol can be used with both hard-core and soft-core bosons as well as fermion…
Cold atom optical lattices allow for the study of quantum localization and mobility edges in a disorder-free environment. We predict the existence of an Anderson-like insulator with sharp mobility edges in a one-dimensional nearly-periodic optical lattice. We show that the mobility edge manifests itself as the early onset of pinning in center of mass dipole oscillations in the presence of a magnetic trap which should be observable in optical lattices.
Simulation of interacting electron systems is one of the great challenges of modern quantum chemistry and solid state physics. Controllable quantum systems offer the opportunity to create artificial structures which mimic the system of interest. An interesting quantity to extract from these quantum simulations is the spectral function. We map a noisy quantum simulator onto a fermionic system and investigate the influence of decoherence on the simulation of the spectral density using a diagrammatic approach on Keldysh contour. We show that features stronger than the single-qubit decoherence rat…
Well-controlled quantum systems can potentially be used as quantum simulators. However, a quantum simulator is inevitably perturbed by coupling to additional degrees of freedom. This constitutes a major roadblock to useful quantum simulations. So far there are only limited means to understand the effect of perturbation on the results of quantum simulation. Here, we present a method which, in certain circumstances, allows for the reconstruction of the ideal result from measurements on a perturbed quantum simulator. We consider extracting the value of the correlator $\langle\hat{O}^i(t) \hat{O}^…
Programming long-range interactions in analog quantum simulators
Institute of Fundamental Physics IFF-CSIC（基础物理研究所）；Departamento de Física, Facultad de Ciencias Ambientales y Bioquímica, Universidad de Castilla-La Mancha（卡斯蒂利亚-拉曼恰大学环境科学与生物化学学院物理系）
We study how chaos, introduced by a weak perturbation, affects the reliability of the output of analog quantum simulation. As a toy model, we consider the Lipkin-Meshkov-Glick (LMG) model. Inspired by the semiclassical behavior of the order parameter in the thermodynamic limit, we propose a protocol to measure the quantum phase transition in the ground state and the dynamical quantum phase transition associated with quench dynamics. We show that the presence of a small time-dependent perturbation can render the dynamics of the system chaotic. We then show that the estimates of the critical poi…
We propose a scheme for investigating the nonequilibrium aspects of small-polaron physics using an array of superconducting qubits and microwave resonators. This system, which can be realized with transmon or gatemon qubits, serves as an analog simulator for a lattice model describing a nonlocal coupling of a quantum particle (excitation) to dispersionless phonons. We study its dynamics following an excitation-phonon (qubit-resonator) interaction quench using a numerically exact approach based on a Chebyshev-moment expansion of the time-evolution operator of the system. We thereby glean hereto…
An analog computer makes use of continuously changeable quantities of a system, such as its electrical, mechanical, or hydraulic properties, to solve a given problem. While these devices are usually computationally more powerful than their digital counterparts, they suffer from analog noise which does not allow for error control. We will focus on analog computers based on active electrical networks comprised of resistors, capacitors, and operational amplifiers which are capable of simulating any linear ordinary differential equation. However, the class of nonlinear dynamics they can solve is l…
We present a self-consistent one-dimensional (1D) quantum transport simulator based on the Contact Block Reduction (CBR) method, aiming for very fast and robust transport simulation of 1D quantum devices. Applying the general CBR approach to 1D open systems results in a set of very simple equations that are derived and given in detail for the first time. The charge self-consistency of the coupled CBR-Poisson equations is achieved by using the predictor-corrector iteration scheme with the optional Anderson acceleration. In addition, we introduce a new way to convert an equilibrium electrostatic…
Universal Dynamics with Globally Controlled Analog Quantum Simulators
Department of Physics, Harvard University（哈佛大学物理系）；School of Engineering and Applied Sciences, Harvard University（哈佛大学工程与应用科学学院）；Robotics Institute, Carnegie Mellon University（卡内基梅隆大学机器人研究所）；Harmoniqs, Inc.（Harmoniqs公司）；Department of Mathematics, Harvard University（哈佛大学数学系）
In recent years quantum simulation has made great strides culminating in experiments that operate in a regime that existing supercomputers cannot easily simulate. Although this raises the possibility that special purpose analog quantum simulators may be able to perform computational tasks that existing computers cannot, it also introduces a major challenge: certifying that the quantum simulator is in fact simulating the correct quantum dynamics. We provide an algorithm that, under relatively weak assumptions, can be used to efficiently infer the Hamiltonian of a large but untrusted quantum sim…
Spinor Bose-Einstein condensate as an analog simulator of molecular bending vibrations
Universitat Autònoma de Barcelona（巴塞罗那自治大学）；ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学技术研究院）；Universitat de València-CSIC（瓦伦西亚大学-CSIC）
Analog Circuit-QED Simulator of Quantum Spin Dynamics Through the Extended Bose-Hubbard Model
Russian Quantum Center（俄罗斯量子中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；SKKU Advanced Institute of Nanotechnology (SAINT), Sungkyunkwan University（成均馆大学 SKKU 纳米技术高级研究所 (SAINT)）；Institute of Fundamental Physics IFF-CSIC（西班牙国家研究委员会基础物理研究所 (IFF-CSIC)）；National University of Science and Technology “MISIS”（国立科技大学 MISIS）；Lebedev Physical Institute, Russian Academy of Sciences（俄罗斯科学院列别捷夫物理研究所）；Department of Chemistry, Yonsei University（延世大学化学系）；Department of Quantum Information, Yonsei University（延世大学量子信息系）
In analogy to the Coulomb and the Pauli spin blockade, based on the electrostatic repulsion and the Pauli exclusion principle respectively, the concept of valley blockade in Silicon nanostructures is explored. The valley parity operator is defined. Valley blockade is determined by the parity conservation of valley composition eigenvectors in quantum transport. A Silicon quantum changeover switch based on a triple of donor quantum dots capable to separate electrons having opposite valley parity by virtue of the valley parity conservation is proposed. The quantum changeover switch represents a n…
The development of quantum information platforms such as quantum computers and quantum simulators that will rival classical Turing computations are typically viewed as a threat to secure data transmissions and therefore to crypto-systems and financial markets in general. We propose to use such platforms as a proof-of-work protocol for blockchain technology, which underlies cryptocurrencies providing a way to document the transactions in a permanent decentralised public record and to be further securely and transparently monitored. We reconsider the basis of blockchain encryption and suggest to…
Quantum field theories are the cornerstones of modern physics, providing relativistic and quantum mechanical descriptions of physical systems at the most fundamental level. Simulating real-time dynamics within these theories remains elusive in classical computing. This provides a unique opportunity for quantum simulators, which hold the promise of revolutionizing our simulation capabilities. Trapped-ion systems are successful quantum-simulator platforms for quantum many-body physics and can operate in digital, or gate-based, and analog modes. Inspired by the progress in proposing and realizing…
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 i…
We propose a scalable analog quantum simulator for quantum electrodynamics (QED) in two spatial dimensions. The setup for the U(1) lattice gauge field theory employs inter-species spin-changing collisions in an ultra-cold atomic mixture trapped in an optical lattice. Building on the previous one-dimensional implementation scheme of Ref. [1] we engineer spatial plaquette terms for magnetic fields, thus solving a major obstacle towards experimental realizations of realistic gauge theories in higher dimensions. We apply our approach to pure gauge theory and discuss how the phenomenon of confineme…
Linear Paul traps have been used recently to simulate the transverse field Ising model with long-range spin-spin couplings. We study the intrinsic effects of phonon creation (from the initial phonon ground state) on the spin-state probability and spin entanglement for such quantum spin simulators. While it has often been assumed that phonon effects are benign because they play no role in the pure Ising model, they can play a significant role when a transverse field is added to the model. We use a many-body factorization of the quantum time-evolution operator of the system, adiabatic perturbati…
Trapped ions are pre-eminent candidates for building quantum information processors and quantum simulators. They have been used to demonstrate quantum gates and algorithms, quantum error correction, and basic quantum simulations. However, to realise the full potential of such systems and make scalable trapped-ion quantum computing a reality, there exist a number of practical problems which must be solved. These include tackling the observed high ion-heating rates and creating scalable trap structures which can be simply and reliably produced. Here, we report on cryogenically operated silicon i…
The recent rapid experimental advancement in the engineering of quantum many-body systems opens the avenue to controlled studies of fundamental physics problems via digital or analog quantum simulations. Here, we systematically analyze the capability of analog ion traps to explore relativistic meson spectra on current devices. We focus on the E_8 quantum field theory regime, which arises due to longitudinal perturbations at the critical point of the transverse-field Ising model. As we show through exact numerics, for sufficiently strong long-range suppression in experimentally accessible spin …
Peking University（北京大学）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；China Center of Advanced Science and Technology（中国高等科学技术中心）；School of Computer Science, Peking University（北京大学计算机学院）
Classical simulators play a major role in the development and benchmark of quantum algorithms and practically any software framework for quantum computation provides the option of running the algorithms on simulators. However, the development of quantum simulators was substantially separated from the rest of the software frameworks which, instead, focus on usability and compilation. Here, we demonstrate the advantage of co-developing and integrating simulators and compilers by proposing a specialized compiler pass to reduce the simulation time for arbitrary circuits. While the concept is broad…
Topological order is now being established as a central criterion for characterizing and classifying ground states of condensed matter systems and complements categorizations based on symmetries. Fractional quantum Hall systems and quantum spin liquids are receiving substantial interest because of their intriguing quantum correlations, their exotic excitations and prospects for protecting stored quantum information against errors. Here we show that the Hamiltonian of the central model of this class of systems, the Toric Code, can be directly implemented as an analog quantum simulator in lattic…
Controlled quantum mechanical devices provide a means of simulating more complex quantum systems exponentially faster than classical computers. Such "quantum simulators" rely heavily upon being able to prepare the ground state of Hamiltonians, whose properties can be used to calculate correlation functions or even the solution to certain classical computations. While adiabatic preparation remains the primary means of producing such ground states, here we provide a different avenue of preparation: cooling to the ground state via simulated dissipation. This is in direct analogy to contemporary e…
A custom-built and precisely controlled quantum system may offer access to a fundamental understanding of another, less accessible system of interest. A universal quantum computer is currently out of reach, but an analog quantum simulator that makes the relevant observables, interactions, and states of a quantum model accessible could permit experimental insight into complex quantum dynamics that are intractable on conventional computers. Several platforms have been suggested and proof-of-principle experiments have been conducted. Here we characterise two-dimensional arrays of three ions trapp…
In this review, we present the ongoing developments in bridging the gap between holography and experiments. To this end, we discuss information scrambling and models of quantum teleportation via Gao-Jafferis-Wall wormhole teleportation. We review the essential basics and summarize some of the recent works that have so far been obtained in quantum simulators towards a goal of realizing analogous models of holography in a lab.
