Collective Neutrino Oscillations on a Quantum Computer

Abstract

We calculate the energy levels of a system of neutrinos undergoing collective oscillations as functions of an effective coupling strength and radial distance from the neutrino source using the quantum Lanczos (QLanczos) algorithm implemented on IBM Q quantum computer hardware. Our calculations are based on the many-body neutrino interaction Hamiltonian introduced in Ref. [1]. We show that the system Hamiltonian can be separated into smaller blocks, which can be represented using fewer qubits than those needed to represent the entire system as one unit, thus reducing the noise in the implementation on quantum hardware. We also calculate transition probabilities of collective neutrino oscillations using a Trotterization method which is simplified before subsequent implementation on hardware. These calculations demonstrate that energy eigenvalues of a collective neutrino system and collective neutrino oscillations can both be computed on quantum hardware with certain simplification to within good agreement with exact results. a *

Standard model physics and the digital quantum revolution: thoughts about the interface

“…Using the efficient simulation strategies presented in the previous section, quantum computers are expected to be able to simulate efficiently the real-time dynamics of systems with local interactions. As perhaps the most straightforward application of these ideas, direct simulations of Hamiltonian dynamics starting from a reference state have recently appeared e.g., the probability of pair production and chiral dynamics in the Schwinger model [40,448,449], the three-body contact density in a simple model for the triton [46], the time-dependent Coulomb excitation of the deuteron colliding with an heavy-ion [450], the spin dynamics of a pair of nucleons interacting through a tensor interaction [333] and the entanglement and flavor evolution in collective neutrino oscillations [451,452].…”

Hierarchical qubit maps and hierarchically implemented quantum error correction

“…Currently in the noisy intermediate-scale quantum (NISQ) era [1], digital quantum devices available for scientific applications have modest numbers of physical qubits, limited but improving fidelity, noisy gate operations, and short coherence times. Device noise in current simulations is mitigated to some degree by selecting a configuration with the highest-fidelity qubits and desired entangling gates within a given quantum processing unit; extrapolating entangling gate errors with global controlled-NOT replacement [2][3][4][5][6][7][8][9][10][11][12][13][14][15] and local stochastic insertions [16,17]; postselection of physical subspaces [16,18]; addressing measurement errors through inversion of simple noise models [19], classical conditional probabilities [20], and majority voting [12]; and time-dependent in vivo calibration work flows and in-medium gate correction [8]. Excitingly, first steps toward experimental demonstration of quantum error correction (QEC) have emerged, e.g., recent demonstrations of exponential convergence of the repetition code [21][22][23][24], error detection in the surface code [25][26][27][28][29][30] on the 53-qubit Sycamore superconducting processor [23,31], fault-tolerant operations in the nine-qubit Bacon-Shor code on 13 trapped 171 Yb + ions [24], and real-time error correction in the [7,1,…”

Hierarchical Qubit Maps and Hierarchical Quantum Error Correction

“…Currently in the NISQ-era [1], digital quantum devices available for scientific applications have modest numbers of physical qubits, limited but improving fidelity, noisy gate operations, and short coherence times. Device noise in current simulations is mitigated to some degree by: selecting a configuration with the highest fidelity qubits and desired entangling gates within a given quantum processing unit; extrapolating entangling gate errors with global CNOT replacement [2][3][4][5][6][7][8][9][10][11][12][13][14][15] and local stochastic insertions [16,17]; post-selection of physical subspaces [16,18]; addressing measurement errors through inversion of simple noise models [19], classical conditional probabilities [20] and majority voting [12]; and time-dependent in-vivo calibration workflows and "in-medium" gate correction [8]. Excitingly, first steps toward experimental demonstration of quantum error correction (QEC) have emerged, e.g., recent demonstrations of exponential convergence of the repetition code [21][22][23][24], error detection in the surface code [25][26][27][28][29][30] on the 53-qubit Sycamore superconducting processor [23,31], fault-tolerant operations in the 9-qubit Bacon-Shor code on 13 trapped 171 Y b + ions [24], and real-time error correction in the [ [7,1,…”