Quantum simulation has the potential to be an indispensable technique for the investigation of non-perturbative phenomena in strongly-interacting quantum field theories (QFTs). In the modern quantum era, with Noisy Intermediate Scale Quantum~(NISQ) simulators widely available and larger-scale quantum machines on the horizon, it is natural to ask: what non-perturbative QFT problems can be solved with the existing quantum hardware? We show that existing noisy quantum machines can be used to analyze the energy spectrum of a large family of strongly-interacting 1+1D QFTs. The latter exhibit a wide-range of non-perturbative effects like `quark confinement' and `false vacuum decay' which are typically associated with higher-dimensional QFTs of elementary particles. We perform quench experiments on IBM's ibmq_mumbai quantum simulator to compute the energy spectrum of 1+1D quantum Ising model with a longitudinal field. The latter model is particularly interesting due to the formation of mesonic bound states arising from a confining potential for the Ising domain-walls, reminiscent of t'Hooft's model of two-dimensional quantum chromodynamics. Our results demonstrate that digital quantum simulation in the NISQ era has the potential to be a viable alternative to numerical techniques such as density matrix renormalization group or the truncated conformal space methods for analyzing QFTs.
We suggest and demonstrate an all-optical quantum simulator for single-qubit noisy channels originating from the interaction with a fluctuating field. The simulator employs the polarization degree of freedom of a single photon, and exploits its spectral components to average over the realizations of the stochastic dynamics. As a proof of principle, we run simulations of dephasing channels driven either by Gaussian (Ornstein-Uhlenbeck) or non-Gaussian (random telegraph) stochastic processes.
Studying the zeroes of partition functions in the space of complex control parameters allows to understand formally how critical behavior of a many-body system can arise in the thermodynamic limit despite various no-go theorems for finite systems. In this work we propose protocols that can be realized in quantum simulators to measure the location of complex partition function zeroes of classical Ising models. The protocols are solely based on the implementation of simple two-qubit gates, local spin rotations, and projective measurements along two orthogonal quantization axes. Besides presentin…
We have developed a software library that simulates noisy quantum logic circuits. We represent quantum states by their density matrices in the Pauli basis, and incorporate possible errors in initialisation, logic gates, memory and measurement using simple models. Our quantum simulator is implemented as a new backend on IBM's open-source Qiskit platform. In this document, we provide its description, and illustrate it with some simple examples.
Solving intractable mathematical problems in simulators composed of atoms, ions, photons or electrons has recently emerged as a subject of intense interest. Here we extend this concept to phonons that are localised in spectrally pure resonances in an electromechanical system which enables their interactions to be exquisitely fashioned via electrical means. We harness this platform to emulate the Ising Hamiltonian whose spin 1/2 particles are replicated by the phase bistable vibrations from a parametric resonance where multiple resonances play the role of a spin bath. The coupling between the m…
Noisy mean field annealing (NMFA) is an algorithm that mimics a coherent Ising machine (CIM), which is an optical system for solving Ising problems. The NMFA has reproduced the solver performance of the CIM for systems of limited size even though it simplifies the interaction between spins with a mean-field approximation. However, recent experiments observing various thermodynamic quantities have revealed that the CIM can capture the phase transitions of the two-dimensional Ising models that the mean field cannot capture. This situation leads to a fundamental question as to how well the NMFA c…
Shift of quantum critical point of discrete time crystal on a noisy quantum simulator
The University of Tokyo（东京大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；IBM Quantum, IBM Research–Tokyo（IBM量子，IBM研究-东京）；Institute for AI and Beyond, The University of Tokyo（东京大学AI与未来研究所）；WPI Advanced Institute for Materials Research, Tohoku University（东北大学世界顶尖科学研究中心先进材料研究所）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）
The coupling of spins to long-wavelength bosonic modes is a prominent means to engineer long-range spin-spin interactions, and has been realized in a variety of platforms, such as atoms in optical cavities and trapped ions. To date, much of the experimental focus has been on the realization of long-range Ising models, but generalizations to other spin models are highly desirable. In this work, we explore a previously unappreciated connection between the realization of an XY model by off-resonant driving of single sideband of boson excitation (i.e.~a single-beam Mølmer-Sørensen scheme) and a bo…
Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground state energy of the Transverse Field Ising Model with long-range interactions with tunable range and we optimize the corresponding combinatorial classical problem by sampling …
Rydberg-atom quantum simulators are of keen interest because of their possibilities towards high-dimensional qubit architectures. Here we report three-dimensional conformation spectra of quantum-Ising Hamiltonian systems with programmed qubit connections. With a Rydberg-atom quantum simulator, various connected graphs, in which vertices and edges represent atoms and blockaded couplings, respectively, are constructed in two or three-dimensional space and their eigenenergies are probed during their topological transformations. Star, complete, cyclic, and diamond graphs, and their geometric inter…
Pilot-Wave Simulator: Exact Classical Sampling from Ideal and Noisy Quantum Circuits up to Hundreds of Qubits
Lomonosov Moscow State University（莫斯科国立大学）；University of Science and Technology of China（中国科学技术大学）；Peking University（北京大学）；Southern University of Science and Technology（南方科技大学）
Quantum computers are expected to help us to achieve accurate simulation of the dynamics of many-body quantum systems. However, the limitations of current NISQ devices prevents us from realising this goal today. Recently an algorithm for performing quantum simulations called quantum assisted simulator has been proposed that promises realization on current experimental devices. In this work, we extend the quantum assisted simulator to simulate the dynamics of a class of time-dependent Hamiltonians. We show that the quantum assisted simulator is easier to implement as well as can realize multi-q…
We consider the $d$-dimensional transverse-field Ising model with power-law interactions $J/r^{d+σ}$ in the presence of a noisy longitudinal field with zero average. We study the longitudinal-magnetization dynamics of an initial paramagnetic state after a sudden switch-on of both the interactions and the noisy field. While the system eventually relaxes to an infinite-temperature state with vanishing magnetization correlations, we find that two-time correlation functions show aging at intermediate times. Moreover, for times shorter than the inverse noise strength $κ$ and distances longer than $…
It is known that noisy topological quantum codes are related to random bond Ising models where the order-disorder phase transition in the classical model is mapped to the error threshold of the corresponding topological code. On the other hand, there is a dual mapping between classical spin models and quantum Calderbank-Shor-Stean (CSS) states where the partition function of a classical model defined on a hypergraph $H$ is written as an inner product of a product state and a CSS state on dual hypergraph $\tilde{H}$. It is then interesting to see what is the interpretation of the classical phas…
CERN Openlab（欧洲核子研究中心开放实验室）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Cambridge Quantum（剑桥量子公司）；University of Oviedo（奥维耶多大学）；University of Cambridge（剑桥大学）
In an earlier work, we introduced dual-Parameterized Quantum Circuit (PQC) Generative Adversarial Networks (GAN), an advanced prototype of a quantum GAN. We applied the model on a realistic High-Energy Physics (HEP) use case: the exact theoretical simulation of a calorimeter response with a reduced problem size. This paper explores the dual- PQC GAN for a more practical usage by testing its performance in the presence of different types of quantum noise, which are the major obstacles to overcome for successful deployment using near-term quantum devices. The results propose the possibility of r…
A quantum simulator is a restricted class of quantum computer that controls the interactions between quantum bits in a way that can be mapped to certain difficult quantum many-body problems. As more control is exerted over larger numbers of qubits, the simulator can tackle a wider range of problems, with the ultimate limit being a universal quantum computer that can solve general classes of hard problems. We use a quantum simulator composed of up to 53 qubits to study a non-equilibrium phase transition in the transverse field Ising model of magnetism, in a regime where conventional statistical…
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 …
Significant efforts are being directed towards developing a quantum annealer capable of solving combinatorial optimization problems. The challenges are Hamiltonian programming and large-scale implementations. Here we report quantum annealing demonstration of Ising Hamiltonians programmed with up to $N=22$ spins mapped on various Cayley tree graphs. Experiments are performed with a Rydberg-atom quantum simulator, in which rubidium single atoms are arranged in three dimensional space in such a way that their Rydberg atoms and blockaded strong couplings respectively represent the nodes and edges …
In this work, we present an efficient rank-compression approach for the classical simulation of Kraus decoherence channels in noisy quantum circuits. The approximation is achieved through iterative compression of the density matrix based on its leading eigenbasis during each simulation step without the need to store, manipulate, or diagonalize the full matrix. We implement this algorithm in an in-house simulator, and show that the low rank algorithm speeds up simulations by more than two orders of magnitude over an existing implementation of full rank simulator, and with negligible error in th…
The trapped ion quantum simulator has demonstrated qualitative properties of different physical models for up to tens of ions. In particular, a linear ion chain naturally hosts long-range Ising interactions under the laser driving, which has been used for various phenomena such as quantum phase transition, localization, thermalization and information propagation. For near-term practical usage, a central task is to find more quantitative applications of the noisy quantum simulators that are robust to small errors in the parameters. Here we report the quantum simulation of a long-range transvers…
We present practical methods to measure entanglement for quantum simulators that can be realized with trapped ions, cold atoms, and superconducting qubits. Focussing on long- and short-range Ising-type Hamiltonians, we introduce schemes that are applicable under realistic experimental conditions including mixedness due to, e.g., noise or temperature. In particular, we identify a single observable whose expectation value serves as a lower bound to entanglement and which may be obtained by a simple quantum circuit. As such circuits are not (yet) available for every platform, we investigate the p…
We investigate the relative volume of parent Hamiltonians having a target ground state up to some fixed error $ε$, a quantity which sets a benchmark on the performance of quantum simulators. For vanishing error, this relative volume is of measure zero, whereas for a generic $ε$ we show that it increases with the dimension of the Hilbert space. We also address the volume of parent Hamiltonians when they are restricted to be local. For translationally invariant Hamiltonians, we provide an upper bound to their relative volume. Finally, we estimate numerically the relative volume of parent Hamilto…
Recent work has shown that quantum simulation is a valuable tool for learning empirical models for quantum systems. We build upon these results by showing that a small quantum simulators can be used to characterize and learn control models for larger devices for wide classes of physically realistic Hamiltonians. This leads to a new application for small quantum computers: characterizing and controlling larger quantum computers. Our protocol achieves this by using Bayesian inference in concert with Lieb-Robinson bounds and interactive quantum learning methods to achieve compressed simulations f…
Quantum many body system in equilibrium can be effectively characterized using the framework of quantum statistical mechanics. However, nonequilibrium behaviour of quantum many body systems remains elusive, out of the range of such a well established framework. Experiments in quantum simulators are now opening up a route towards the generation of quantum states beyond this equilibrium paradigm. As an example in closed quantum many body systems, dynamical quantum phase transitions behave as phase transitions in time with physical quantities becoming nonanalytic at critical times, extending impo…
To bridge the gap between limited hardware access and the huge demand for experiments for Noisy Intermediate-Scale Quantum (NISQ) computing system study, a simulator which can capture the modeling of both the quantum processor and its classical control system to realize early-stage evaluation and design space exploration, is naturally invoked but still missing. This paper presents SANQ, a Simulation framework for Architecting NISQ computing system. SANQ consists of two components, 1) an optimized noisy quantum computing (QC) simulator with flexible error modeling accelerated by eliminating red…
Quantum simulators, machines that can replicate the dynamics of quantum systems, are being built as useful devices and are seen as a stepping stone to universal quantum computers. A key difference between the two is that computers have the ability to perform the logic gates that make up algorithms. We propose a method for learning how to construct these gates efficiently by using the simulator to perform optimal control on itself. This bypasses two major problems of purely classical approaches to the control problem: the need to have an accurate model of the system, and a classical computer mo…
The accurate computational determination of chemical, materials, biological, and atmospheric properties has critical impact on a wide range of health and environmental problems, but is deeply limited by the computational scaling of quantum-mechanical methods. The complexity of quantum-chemical studies arises from the steep algebraic scaling of electron correlation methods, and the exponential scaling in studying nuclear dynamics and molecular flexibility. To date, efforts to apply quantum hardware to such quantum chemistry problems have focused primarily on electron correlation. Here, we provi…
Currently available noisy intermediate-scale quantum (NISQ) devices are limited by the number of qubits that can be used for quantum chemistry calculations on molecules. We show herein that the number of qubits required for simulations on a quantum computer can be reduced by limiting the number of orbitals in the active space. Thus, we have utilized ansätze that approximate exact classical matrix eigenvalue decomposition methods (Full Configuration Interaction). Such methods are appropriate for computations with the Variational Quantum Eigensolver algorithm to perform computational investigati…
QDarts: A Quantum Dot Array Transition Simulator for finding charge transitions in the presence of finite tunnel couplings, non-constant charging energies and sensor dots
We present a route towards the quantum simulation of exotic quantum magnetism in ion traps by exploiting dual relations between different spin models. Our strategy allows one to start from Hamiltonians that can be realized with current technology, while properties of an exotic dual model are inferred from measurements of non-local, string-order-like, operators. The latter can be achieved from fluorescence, or from certain spectroscopic measurements, both of which can be combined with finite-size scaling by controlling the number of ions in the dual quantum simulator. We apply this concept to p…
