Quantum computers as universal quantum simulators: state-of-art and perspectives

Abstract

The past few years have witnessed the concrete and fast spreading of quantum technologies for practical computation and simulation. In particular, quantum computing platforms based on either trapped ions or superconducting qubits have become available for simulations and benchmarking, with up to few tens of qubits that can be reliably initialized, controlled, and measured. The present review aims at giving a comprehensive outlook on the state of art capabilities offered from these near-term noisy devices as universal quantum simulators, i.e. programmable quantum computers potentially able to calculate the time evolution of many physical models. First, we give a pedagogic overview on the basic theoretical background pertaining digital quantum simulations, with a focus on hardware-dependent mapping of spin-type Hamiltonians into the corresponding quantum circuit model as a key initial step towards simulating more complex models. Then, we review the main experimental achievements obtained in the last decade regarding the digital quantum simulation of such spin models, mostly employing the two leading quantum architectures. We compare their performances and outline future challenges, also in view of prospective hybrid technologies, towards the ultimate goal of reaching the long sought quantum advantage for the simulation of complex many body models in the physical sciences.

27 pages, 12 figures. Pre-submission manuscript, see Journal Reference for the final version

References in corpus (52)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Quantum Computing
• Charge insensitive qubit design derived from the Cooper pair box
• Probing many-body dynamics on a 51-atom quantum simulator
• Single-shot read-out of an individual electron spin in a quantum dot
• Coupling Superconducting Qubits via a Cavity Bus
• Trapped-Ion Quantum Computing: Progress and Challenges
• Microwave photonics with superconducting quantum circuits
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor
• Strongly Interacting Polaritons in Coupled Arrays of Cavities
• Universal Quantum Computation with Continuous-Variable Cluster States
• Quantum technologies with hybrid systems
• Quantum phase transitions of light
• High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit
• Superconducting qubit in waveguide cavity with coherence time approaching 0.1ms
• Photon blockade induced Mott transitions and XY spin models in coupled cavity arrays
• Experimental Comparison of Two Quantum Computing Architectures
• Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
• Benchmarking an 11-qubit quantum computer
• Spectral signatures of many-body localization with interacting photons
• Complete universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits
• Digital quantum simulation of fermionic models with a superconducting circuit
• Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect
• Numerical observation of Hawking radiation from acoustic black holes in atomic Bose-Einstein condensates
• Characterizing large-scale quantum computers via cycle benchmarking
• Strong magnetic coupling of an ultracold gas to a superconducting waveguide cavity
• Quantum computing with an electron spin ensemble
• The quantum optical Josephson interferometer
• Hybrid quantum device with nitrogen-vacancy centers in diamond coupled to carbon nanotubes
• Optical Abelian Lattice Gauge Theories
• Quantum circuits for strongly correlated quantum systems
• Protocols for optimal readout of qubits using a continuous quantum nondemolition measurement
• Quantum Information Processing with Nanomechanical Qubits
• Coherent manipulation of a molecular Ln-based nuclear qudit coupled to an electron qubit
• Digital Quantum Rabi and Dicke Models in Superconducting Circuits
• Quantum algorithm for simulating the dynamics of an open quantum system
• A scalable architecture for quantum computation with molecular nanomagnets
• Robust Ising Gates for Practical Quantum Computation
• An all-silicon single-photon source by unconventional photon blockade
• Discrete Abelian Gauge Theories for Quantum Simulations of QED
• Demonstration of two-atom entanglement with ultrafast optical pulses
• Quantum simulation of scattering in the quantum Ising model
• Observing the Nonequilibrium Dynamics of the Quantum Transverse-Field Ising Chain in Circuit QED
• Circuit QED and sudden phase switching in a superconducting qubit array
• Quantum Simulation of Dissipative Processes without Reservoir Engineering
• Universal and deterministic manipulation of the quantum state of harmonic oscillators: a route to unitary gates for Fock State qubits
• Dynamical localization simulated on a few qubits quantum computer
• Fermionic Models with Superconducting Circuits
• Simulating the Transverse Ising Model on a Quantum Computer: Error Correction with the Surface Code
• Ultrafast coherent excitation of a Ca${}^{+}$ ion

Cited by in corpus (69)

• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• Quantum-Coherent Nanoscience
• Crossing a topological phase transition with a quantum computer
• Learning to Measure: Adaptive Informationally Complete Generalized Measurements for Quantum Algorithms
• A perspective on scaling up quantum computation with molecular spins
• NISQ Computers: A Path to Quantum Supremacy
• Evidence of Kardar-Parisi-Zhang scaling on a digital quantum simulator
• Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits
• Progress toward favorable landscapes in quantum combinatorial optimization
• Blueprint of a Molecular Spin Quantum Processor
• Molecular spin qudits for quantum simulation of light-matter interactions
• Counteracting dephasing in Molecular Nanomagnets by optimized qudit encodings
• Topological two-dimensional Floquet lattice on a single superconducting qubit
• Digital quantum simulation of molecular dynamics and control
• Lattice Boltzmann-Carleman quantum algorithm and circuit for fluid flows at moderate Reynolds number
• Effective calculation of the Green's function in the time domain on near-term quantum processors
• Small, Highly Accurate Quantum Processor for Intermediate-Depth Quantum Simulations
• One-particle Green's functions from the quantum equation of motion algorithm
• Quantum neural networks force fields generation
• Quantifying the sensitivity to errors in analog quantum simulation
• Quantum algorithms for grid-based variational time evolution
• Experimental violations of Leggett-Garg's inequalities on a quantum computer
• Shallow unitary decompositions of quantum Fredkin and Toffoli gates for connectivity-aware equivalent circuit averaging
• Efficient Hamiltonian Simulation for Solving Option Price Dynamics
• Importance sampling for stochastic quantum simulations
• Quantum algorithms for scientific computing
• Digital Quantum Simulation of the Spin-Boson Model under Open System Dynamics
• Observation of topological prethermal strong zero modes
• Sublattice scars and beyond in two-dimensional $U(1)$ quantum link lattice gauge theories
• Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation
• A quantum algorithm for the direct estimation of the steady state of open quantum systems
• Quantum error mitigation for Fourier moment computation
• Digital quantum simulation of an extended Agassi model: Using machine learning to disentangle its phase-diagram
• Many-body entropies and entanglement from polynomially-many local measurements
• Quantum simulation of colour in perturbative quantum chromodynamics
• QOPTLib: a Quantum Computing Oriented Benchmark for Combinatorial Optimization Problems
• A Quantum Computing Implementation of Nuclear-Electronic Orbital (NEO) Theory: Towards an Exact pre-Born-Oppenheimer Formulation of Molecular Quantum Systems
• Adaptive projected variational quantum dynamics
• A Bayesian Approach for Characterizing and Mitigating Gate and Measurement Errors
• Entanglement Classification via Witness Operators generated by Support Vector Machine
• Calculating the many-body density of states on a digital quantum computer
• Simulating spectroscopy experiments with a superconducting quantum computer
• Hybrid Tree Tensor Networks for quantum simulation
• Real-time simulation of light-driven spin chains on quantum computers
• Scalable simulation of non-equilibrium quantum dynamics via classically optimised unitary circuits
• Dissipative generation of pure steady states and a gambler's ruin problem
• Workflow for practical quantum chemical calculations with quantum phase estimation algorithm: electronic ground and π-π* excited states of benzene and its derivatives†
• Deep Quantum Circuit Simulations of Low-Energy Nuclear States
• Quantum computing for genomics: conceptual challenges and practical perspectives
• Self-protected adiabatic quantum computation
• Observation of partial and infinite-temperature thermalization induced by repeated measurements on a quantum hardware
• All product eigenstates in Heisenberg models from a graphical construction
• Quantum Information Processing with Molecular Nanomagnets: an introduction
• Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum Systems
• Cost of Emulating a Small Quantum Annealing Problem in the Circuit-Model
• Harnessing Quantum Computing for Energy Materials: Opportunities and Challenges
• Quantum Simulation of Molecular Dynamics Processes -- A Benchmark Study Using Classical Simulator and Present-Day Quantum Hardware
• Integrating Quantum Algorithms Into Classical Frameworks: A Predictor-corrector Approach Using HHL
• Trotterless Simulation of Open Quantum Systems for NISQ Quantum Devices
• Toward extracting scattering phase shift from integrated correlation functions on quantum computers
• Adaptively partitioned analog quantum simulation on near-term quantum computers: The nonclassical free-induction decay of NV centers in diamond
• A circuit-differentiation framework for Green's functions on quantum computers
• Chemically Motivated Simulation Problems are Efficiently Solvable by a Quantum Computer
• Photonic Simulation of Localization Phenomena Using Boson Sampling
• Tunable Tradeoff between Quantum and Classical Computation via Nonunitary Zeno-like Dynamics
• Resource-efficient quantum algorithm for linear systems of equations
• Experimental decoherence in molecule interferometry
• Nonadiabatic Self-Healing of Trotter Errors in Digitized Counterdiabatic Dynamics