Source-linked AI summary
Simulating quantum many-body dynamics on a current digital quantum computer
Adam Smith, M. S. Kim, Frank Pollmann, Johannes Knolle
TL;DR
The paper addresses whether current universal quantum computers can simulate condensed-matter quantum dynamics beyond classical reach. It studies global quenches and correlators on IBM quantum hardware, finding that quantitative accuracy remains inadequate while several qualitative phenomena are observable.
Problem
Universal quantum computers are being considered for quantum dynamics beyond classical computation, motivating benchmarks of their present capabilities and limitations.
Method
The paper simulates far-from-equilibrium global quenches on IBM quantum computers and measures magnetization, correlators, and related dynamical quantities.
Results
Current machines show low quantitative accuracy for quantum dynamics but reproduce qualitative signatures of localization, interactions, ballistic correlation spreading, and entanglement generation.
Takeaways & Limitations
Digital quantum simulation requires an order of magnitude improvement in fidelity and coherence before realistically outperforming classical computers for these dynamical problems.
Takeaways & Limitations
Daily recalibration and large device errors make simulation data depend on the computation day and selected qubits.
Abstract
from arXiv · showhide
Universal quantum computers are potentially an ideal setting for simulating many-body quantum dynamics that is out of reach for classical digital computers. We use state-of-the-art IBM quantum computers to study paradigmatic examples of condensed matter physics -- we simulate the effects of disorder and interactions on quantum particle transport, as well as correlation and entanglement spreading. Our benchmark results show that the quality of the current machines is below what is necessary for quantitatively accurate continuous time dynamics of observables and reachable system sizes are small comparable to exact diagonalization. Despite this, we are successfully able to demonstrate clear qualitative behaviour associated with localization physics and many-body interaction effects.
INTRODUCTION
Universal quantum computers are emerging as flexible platforms for simulating quantum dynamics that are difficult for classical computers. This paper situates IBM quantum hardware within broader quantum-simulation efforts and benchmarks its capabilities for condensed-matter dynamics.
- Hardware platforms: Quantum devices span trapped ions, cavity QED, photonic circuits, silicon quantum dots, superconducting circuits, and proposed non-abelian anyon platforms.Superconducting circuits had reached devices containing up to 72 qubits in the context described here.
- Quantum simulation: Quantum simulation uses another quantum system to study many-body dynamics that are notoriously hard for classical computers.Purpose-built simulators have accessed physics beyond classical numerical methods, including Hubbard models and many-body localization.
- Universal quantum computers: Universal quantum computers offer one flexible device for simulations that would otherwise require several experiments using disparate methods.They may also enable studies of lattice gauge theories with dynamical gauge fields, whose required multi-body couplings are difficult to realize experimentally.
- IBM Q: IBM Q provided public access to small quantum computers and a Python API, supporting experiments on molecules, entangled states, and quantum algorithms.The network included public 5- and 16-qubit machines, alongside partner-accessible 20-qubit machines.
- Paper scope: The paper benchmarks far-from-equilibrium global quenches on an IBM 20-qubit quantum computer using physical correlators to assess simulation capabilities and limitations.The chosen models are presented as central to condensed-matter physics and as exhibiting diverse phenomenology.
RESULTS
IBM quantum computers reproduce several qualitative signatures of many-body dynamics, including localization, interaction effects, ballistic correlation spreading, and entanglement growth, but quantitative accuracy degrades rapidly with time and circuit size.
- For Jt > 1, measured local magnetization approaches zero, while agreement between exact diagonalization and numerical Trotterization indicates machine errors dominate Trotter-approximation errors.
- Quenches from domain-wall states show short-time agreement with exact diagonalization and Trotter evolution, including a linear light-cone structure that worsens at longer times and larger system sizes.Accuracy drops when additional Trotter steps increase the circuit gate count.
- Increasing disorder reduces domain-wall spreading, qualitatively reproducing Anderson localization at short times despite low numerical accuracy.The data becomes biased toward the scrambled value as Trotter steps increase.
- Interactions hinder short-time spreading through an energy cost, producing behavior distinct from disorder even when the observed short-time trends are similar.The longer-time behavior differs: interactions generically lead toward ergodic and thermalizing dynamics, unlike localization.
- In a linear potential, increasing interaction strength increases Nhalf because interaction-energy reduction can offset the potential-energy increase.This trend is qualitatively reproduced experimentally but is less pronounced than in the disorder and nearest-neighbor-interaction cases.
- Connected spin correlations spread ballistically, and IBM data qualitatively captures both the light-cone structure and the point where correlations reach the system boundary.The experiment shows a slightly faster apparent light cone, consistent with effective renormalization of Hamiltonian parameters from machine errors.
- IBM measurements reproduce qualitative entanglement dynamics: QFI follows von Neumann entropy, grows linearly after a Néel quench, and FQ/N > 1 witnesses entanglement.For a domain-wall quench, qualitative behavior is retained but absolute values deviate more strongly.
- Practical accuracy measures are needed alongside reported gate errors to track device development and diagnose error sources.The Mermin inequality is used as one such measure, with violations consistently observed across four days.
DISCUSSION
The IBM devices demonstrate qualitative signatures of localization, interactions, and correlation spreading, but their quantitative accuracy remains below what is needed to outperform classical methods for dynamical simulations. The discussion therefore emphasizes improving device quality, while identifying error correction and additional physical settings as important directions.
- Current performance: Current IBM machines show low quantitative accuracy relative to exact numerics at the limited system sizes and timescales reached.This exposes limitations in present error rates and/or device isolation.
- Qualitative dynamics: The simulations nevertheless capture localization, many-body interaction effects, ballistic quantum-correlation spreading, expectation values, and two-point correlators.They also show compensation between energy costs from on-site potentials and neighboring-site interactions.
- Needed improvements: At least an order-of-magnitude improvement in gate fidelities and/or T1/T2 times is needed, rather than simply adding more qubits.Gate counts and execution time grow linearly with system size and the number of Trotter steps.
- Error correction: Surface codes are identified as a promising error-correction approach because they can work with moderately low fidelities.The broader challenge remains improving device quality, isolation, and control.
- Outlook: Digital quantum simulation remains in its infancy and requires roughly an order-of-magnitude improvement in fidelity and coherence to outperform classical computers on these dynamical problems.The results provide a benchmark for future improvements and a snapshot of early quantum-simulation capabilities.
METHODS
The simulations prepare product-state quenches, approximate time evolution with Trotterized circuits, measure observables from repeated computational-basis samples, and mitigate errors using conservation-law constraints. The study balances Trotter accuracy and circuit cost while selecting qubits and assessing reproducibility across recalibrated devices.
- State preparation and evolution: The protocol prepares domain-wall or Néel product states and evolves them using discrete Trotter steps on IBM quantum computers.The initial states are tensor-product states in the z-basis, and each Trotter step applies a discrete approximation to time evolution.
- State preparation and evolution: The time step ∆t is fixed to control approximation accuracy, while varying the final step supplies additional data points because only up to 5 Trotter steps can be implemented.Smaller ∆t improves Trotter accuracy but requires more steps, which increases circuit cost and exposure to machine errors.
- State preparation and evolution: Trotterized evolution decomposes each discrete operator into one- and two-qubit unitaries, then into CNOT gates and single-qubit rotations.The basic and symmetric decompositions provide different accuracy-cost trade-offs; the symmetric error scales as O(m(∆t)3), versus O(m(∆t)2) for the basic decomposition.
- Measurement and error mitigation: Conservation-law filtering discards measurement outcomes outside the physical Hilbert space, reducing the leading bit-flip contribution from ∆ to ∆2 when errors are sufficiently small.The mitigation becomes ineffective when multiple bit-flip errors are significant or when the retained-state fraction approaches the physical-subspace fraction.
- Device selection and reproducibility: The analysis uses 6–10 qubits selected for low average CNOT errors, then compares simulations across days because daily recalibration changes device performance and the best qubit subset.Despite substantial day-to-day fluctuations, the reported qualitative behavior remains reproducible, including linear light-cone spreading of correlations.