Effects of gate errors in digital quantum simulations of fermionic systems

Abstract

Digital quantum simulations offer exciting perspectives for the study of fermionic systems such as molecules or lattice models. However, with quantum error correction still being out of reach with present-day technology, a non-vanishing error rate is inevitable. We study the influence of gate errors on simulations of the Trotterized time evolution of the quantum system with focus on the fermionic Hubbard model. Specifically, we consider the effect of stochastic over-rotations in the applied gates. Depending on the particular algorithm implemented such gate errors may lead to a time evolution that corresponds to a disordered fermionic system, or they may correspond to unphysical errors, e.g., violate particle number conservation. We substantiate our analysis by numerical simulations of model systems. In addition we establish the relation between the gate fidelity and the strength of the over-rotations in a Trotterized quantum simulation. Based on this we provide estimates for the maximum number of Trotter steps which can be performed with sufficient accuracy for a given algorithm. This in turn implies, apart from obvious limitations on the maximum time of the simulation, also limits on the system size which can be handled.

arXiv comment12 pages, 12 figures

References in corpus (41)

• Charge insensitive qubit design derived from the Cooper pair box
• Surface codes: Towards practical large-scale quantum computation
• The theory of variational hybrid quantum-classical algorithms
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• Simulated Quantum Computation of Molecular Energies
• Error mitigation for short-depth quantum circuits
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Dynamical decoupling and noise spectroscopy with a superconducting flux qubit
• Effective quantum spin systems with ion traps
• Demonstration of a small programmable quantum computer with atomic qubits
• High-fidelity quantum logic gates using trapped-ion hyperfine qubits
• High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
• Quantum Error Correction for Beginners
• Towards Practical Quantum Variational Algorithms
• High-Fidelity Universal Gate Set for ${}^9$Be${}^{+}$ Ion Qubits
• Robust determination of molecular spectra on a quantum processor
• Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
• Experimental Quantum Computations on a Topologically Encoded Qubit
• Digital quantum simulation of fermionic models with a superconducting circuit
• From Few to Many: Observing the Formation of a Fermi Sea One Atom at a Time
• Can One Trust Quantum Simulators?
• Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
• Blueprint for a microwave trapped-ion quantum computer
• Experimental fault-tolerant universal quantum gates with solid-state spins under ambient conditions
• Quantum simulations of gauge theories with ultracold atoms: local gauge invariance from angular momentum conservation
• Exponentially more precise quantum simulation of fermions I: Quantum chemistry in second quantization
• Quantum simulator of an open quantum system using superconducting qubits: exciton transport in photosynthetic complexes
• Digital-Analog Quantum Simulations with Superconducting Circuits
• Fermion-Fermion Scattering in Quantum Field Theory with Superconducting Circuits
• Direct certification of a class of quantum simulations
• Analog Superconducting Quantum Simulator for Holstein Polarons
• Gate-error analysis in simulations of quantum computers with transmon qubits
• Quantum diffusion with disorder, noise and interaction
• Emulating the one-dimensional Fermi-Hubbard model by a double chain of qubits
• Quantum gates and architecture for the quantum simulation of the Fermi-Hubbard model
• Optimal Trotterization in universal quantum simulators under faulty control
• Charge diffusion in the one-dimensional Hubbard model
• Reconstructing the ideal results of a perturbed analog quantum simulator
• Estimating the error of an analog quantum simulator by additional measurements
• Refocusing two qubit gates with measurements for trapped ions
• Analyzing the spectral density of a perturbed analog quantum simulator using Keldysh formalism

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