Preparing Renormalization Group Fixed Points on NISQ Hardware
arXiv:2109.09787
Abstract
Noisy intermediate-scale quantum (NISQ) hardware is typically limited to low-depth quantum circuits to limit the number of opportunities for introduction of error by unreliable quantum gates. A less-explored alternative approach is to repeatedly apply a quantum channel with a desired quantum state as a stable fixed point. Increased circuit depth can in this case be beneficial rather than harmful due to dissipative self-correction. The quantum channels constructed from MERA circuits can be interpreted in terms of the renormalization group(RG), and their fixed points are RG fixed points, i.e. scale-invariant systems such as conformal field theories. Here, building upon the theoretical proposal of Kim and Swingle, we numerically and experimentally study the robust preparation of the ground state of the critical Ising model using circuits adapted from the work of Evenbly and White. The experimental implementation exhibits self-correction through renormalization seen in the convergence and stability of local observables, and makes essential use of the ability to measure and reset individual qubits afforded by the "quantum CCD" architecture of the Honeywell ion-trap. We also numerically test error mitigation by zero-noise extrapolation schemes specially adapted for renormalization circuits, which are able to outperform typical extrapolation schemes using lower gate overhead.
arXiv comment21 pages, 11 figures
References in corpus (18)
- Quantum Computing in the NISQ era and beyond
- Error mitigation for short-depth quantum circuits
- Bulk Locality and Quantum Error Correction in AdS/CFT
- Preparation of Entangled States by Quantum Markov Processes
- Quantum Computing Using Dissipation to Remain in a Decoherence-Free Subspace
- Algorithms for entanglement renormalization
- A dissipative quantum Church-Turing theorem
- Efficient variational simulation of non-trivial quantum states
- Quantum MERA Channels
- Entanglement renormalization and wavelets
- Efficiency of open quantum walk implementation of dissipative quantum computing algorithms
- Dissipative Universal Lindbladian Simulation
- Rigorous free fermion entanglement renormalization from wavelet theory
- De Sitter Space as a Tensor Network: Cosmic No-Hair, Complementarity, and Complexity
- Robust entanglement renormalization on a noisy quantum computer
- Modular Quantum Information Processing by Dissipation
- Recycling qubits in near-term quantum computers
- Noise reduction using past causal cones in variational quantum algorithms