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arXiv:2111.05401 · Physical review. D/Physical review. D.

Scalable qubit representations of neutrino mixing matrices

M. J. Molewski, B. J. P. Jones

Published Mar 29, 2022• 15 citations
arXivHTMLPDF

Abstract

Oscillating neutrino beams exhibit quantum coherence over distances of thousands of kilometers. Their unambiguously quantum nature suggests an appealing test system for direct quantum simulation. Such techniques may enable presently analytically intractable calculations involving multineutrino entanglements, such as collective neutrino oscillations in supernovas, but only once oscillation phenomenology is properly reexpressed in the language of quantum circuits. Here we resolve outstanding conceptual issues regarding encoding of arbitrarily mixed neutrino flavor states in the Hilbert space of an n-qubit quantum computer. We introduce algorithms to encode mixing and oscillation of any number of flavor-mixed neutrinos, both with and without $CP$-violation, with an efficient number of prescriptive input parameters in terms of subrotations of the Pontecorvo-Maki-Nakagawa-Sakata matrix in standard form. Examples encoded for an IBM-Q quantum computer are shown to converge to analytic predictions both with and without $CP$-violation.

DOI
10.1103/physrevd.105.056024

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Oscillating neutrino beams exhibit quantum coherence over distances of thousands of kilometers. Their unambiguously quantum nature suggests an appealing test system for direct quantum simulation. Such techniques may enable presently analytically intractable calculations involving multineutrino entanglements, such as collective neutrino oscillations in supernovas, but only once oscillation phenomenology is properly reexpressed in the language of quantum circuits. Here we resolve outstanding conceptual issues regarding encoding of arbitrarily mixed neutrino flavor states in the Hilbert space of an n-qubit quantum computer. We introduce algorithms to encode mixing and oscillation of any number of flavor-mixed neutrinos, both with and without CPCPCP-violation, with an efficient number of prescriptive input parameters in terms of subrotations of the Pontecorvo-Maki-Nakagawa-Sakata matrix in standard form. Examples encoded for an IBM-Q quantum computer are shown to converge to analytic predictions both with and without CPCPCP-violation.
Neutrino oscillations can be efficiently simulated on a quantum computer using the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) theory in close analogy to the physical processes realized in experiments. We simulate three-flavor neutrino oscillations on a two-qubit NMR quantum information processor. The three-flavor neutrino states were encoded into the two-qubit system, leaving one redundant basis state (representing an unphysical sterile neutrino). We simulated the neutrino oscillations in different scenarios, including propagation in vacuum and through surrounding matter, and both with and without a CP violating phase δδδ at a Deep Underground Neutrino Experiment (DUNE) baseline distance of L = 1285 km. The oscillation probabilities were obtained after unitarily time evolving the initial flavor state and and comparisons were performed between different scenarios. Further, we design and implement an optimized quantum circuit encoding all four parameters (three mixing angles-θ12,θ23,θ13θ_{12},θ_{23},θ_{13}θ12​,θ23​,θ13​ and one complex phase δδδ) to implement the PMNS unitary matrix, which relates the flavor and mass eigenstates. The interaction with matter is considered as a perturbation to the vacuum Hamiltonian, and the same quantum circuit is employed with an approximation of two mixing angles (θ12θ_{12}θ12​ and θ13θ_{13}θ13​ ) and mass eigenvalues. Our experimental results match well with numerical simulations and highlight the potential of quantum computers for exploring the physics of neutrino oscillations.
Neutrino oscillations are genuine quantum phenomena in which coherent oscillations are maintained over a long distance. As a result, in principle, the phenomena can be studied efficiently using quantum simulations. In today's noisy quantum hardware, encoding neutrinos in a multiqubit system requires a redundant basis and tricky entangling gates. We encode a three-flavor neutrino in a superconducting qutrit and study its oscillations using Pontecorvo-Maki-Nakagawa-Sakata theory with time evolution expressed in terms of single qutrit gates. The qutrit is engineered from the multilevel structure of IBM transmon devices. High-fidelity gate control and readout are fine-tuned using programming microwave pulses using a high-level language. Our quantum simulations on real hardware match the analytical calculations well in three oscillation cases: vacuum, interaction with matter, and CPCPCP violation.
Abstract Neutrino oscillations can be efficiently simulated on a quantum computer using the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) theory in close analogy to the physical processes realized in experiments. We simulate three-flavor neutrino oscillations on a two-qubit NMR quantum information processor. The three-flavor neutrino states were encoded into the two-qubit system, leaving one redundant basis state (representing an unphysical sterile neutrino). The neutrino oscillations were experimentally simulated in different scenarios, including propagation in vacuum and through surrounding matter, and both with and without a CP violating phase δ at a Deep Underground Neutrino Experiment (DUNE) baseline distance of L = 1285 km. The oscillation probabilities were obtained after unitarily time evolving the initial flavor state and comparisons were performed between different scenarios. The interaction with matter is considered as a perturbation to the vacuum Hamiltonian, and the same quantum circuit is employed with an approximation of two mixing angles (θ 12 and θ 13) and mass eigenvalues. Our experimental results match well with numerical simulations and highlight the potential of quantum computers for exploring the physics of neutrino oscillations.
As a result of a nontrivial mixing matrix, neutrinos cannot be simultaneously in a flavor and mass eigenstate. We formulate and discuss information entropic relations that quantify the associated quantum uncertainty. We also formulate a protocol to determine the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix from quantum manipulations and measurements on an entangled lepton-neutrino pair. The entangled state features neutrino oscillations in a conditional probability involving measurements on the lepton and the neutrino. They can be switched off by choosing a specific observable on the lepton side which is determined by the PMNS matrix. The parameters of the latter, including the CPCPCP-violating phase $\ensuremath{\delta}$, can be obtained by guessing them and improving the guess by minimizing the remaining oscillations.
We explore the utility of qutrits and qubits for simulating the flavor dynamics of dense neutrino systems. The evolution of such systems impacts some important astrophysical processes, such as core-collapse supernovae and the nucleosynthesis of heavy nuclei. Many-body simulations require classical resources beyond current computing capabilities for physically relevant system sizes. Quantum computers are therefore a promising candidate to efficiently simulate the many-body dynamics of collective neutrino oscillations. Previous quantum simulation efforts have primarily focused on properties of the two-flavor approximation due to their direct mapping to qubits. Here, we present new quantum circuits for simulating three-flavor neutrino systems on qutrit- and qubit-based platforms, and demonstrate their feasibility by simulating systems of two, four, and eight neutrinos on IBM and Quantinuum quantum computers.