Accurately computing electronic properties of a quantum ring

Abstract

A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform. However, achieving the accuracy needed to outperform classical methods has been an outstanding challenge. Here, using eighteen superconducting qubits, we provide an experimental blueprint for an accurate condensed-matter simulator and demonstrate how to probe fundamental electronic properties. We benchmark the underlying method by reconstructing the single-particle band-structure of a one-dimensional wire. We demonstrate nearly complete mitigation of decoherence and readout errors and arrive at an accuracy in measuring energy eigenvalues of this wire with an error of ~0.01 rad, whereas typical energy scales are of order 1 rad. Insight into this unprecedented algorithm fidelity is gained by highlighting robust properties of a Fourier transform, including the ability to resolve eigenenergies with a statistical uncertainty of 1e-4 rad. Furthermore, we synthesize magnetic flux and disordered local potentials, two key tenets of a condensed-matter system. When sweeping the magnetic flux, we observe avoided level crossings in the spectrum, a detailed fingerprint of the spatial distribution of local disorder. Combining these methods, we reconstruct electronic properties of the eigenstates where we observe persistent currents and a strong suppression of conductance with added disorder. Our work describes an accurate method for quantum simulation and paves the way to study novel quantum materials with superconducting qubits.

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• Formation of robust bound states of interacting microwave photons
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• Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer
• Effective calculation of the Green's function in the time domain on near-term quantum processors
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• Local variational quantum compilation of a large-scale Hamiltonian dynamics
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• Quantum hardware calculations of periodic systems with partition-measurement symmetry verification: simplified models of hydrogen chain and iron crystals
• Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers
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• Small-world complex network generation on a digital quantum processor
• Networked Quantum Services
• Learning Noise via Dynamical Decoupling of Entangled Qubits
• Quantum computation of molecular structure using data from challenging-to-classically-simulate nuclear magnetic resonance experiments
• Macroscopic effects of localised measurements in jammed states of quantum spin chains
• Multi-Level Variational Spectroscopy using a Programmable Quantum Simulator
• Overhead-constrained circuit knitting for variational quantum dynamics
• Benchmarking universal quantum gates via channel spectrum
• Deterministic one-way logic gates on a cloud quantum computer
• Experimental Quantum Learning of a Spectral Decomposition
• Characterizing Coherent Errors using Matrix-Element Amplification
• Variational generation of spin squeezing on one-dimensional quantum devices with nearest-neighbor interactions
• Programmable quantum simulations on a trapped-ions quantum simulator with a global drive
• Error-mitigated deep-circuit quantum simulation of open systems: steady state and relaxation rate problems
• Qubit assignment using time reversal
• Context Aware Fidelity Estimation
• Coherence-preserving cooling of nuclear spin qubits in a weak magnetic field
• Computing n-time correlation functions without ancilla qubits
• Optimal Low-Depth Quantum Signal-Processing Phase Estimation
• Non-Hermitian topological quantum states in a reservoir-engineered transmon chain
• Optimizing for periodicity: a model-independent approach to flux crosstalk calibration for superconducting circuits
• Experimental observation of exact quantum critical states
• Time-adaptive phase estimation
• Variational simulation of higher-spin systems on qubit-based quantum simulators
• Quantum problem of the potential of a ring charged on the symmetry axis
• Correcting and extending Trotterized quantum many-body dynamics
• Mitigating Errors in Analog Quantum Simulation by Hamiltonian Reshaping or Hamiltonian Rescaling
• Synthetic fractional flux quanta in a ring of superconducting qubits
• Synthetic $\pi$-flux system in 2D superconducting qubit array with tunable coupling
• Synchronized Aharonov-Bohm Motifs via Engineered Dissipation
• Symmetry breaking and restoration on a fermionic quantum ring