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arXiv:2308.09123 · Physical review. D/Physical review. D.

Collective neutrino oscillations on a quantum computer with hybrid quantum-classical algorithm

Pooja Siwach, Kaytlin Harrison, A. B. Balantekin

Published Oct 27, 2023• 16 citations
arXivHTMLPDF

Abstract

We simulate the time evolution of collective neutrino oscillations in two-flavor settings on a quantum computer. We explore the generalization of Trotter-Suzuki approximation to time-dependent Hamiltonian dynamics. The trotterization steps are further optimized using the Cartan decomposition of two-qubit unitary gates $U\ensuremath{\in}SU(4)$ in the minimum number of controlled-NOT (CNOT) gates making the algorithm more resilient to the hardware noise. A more efficient hybrid quantum-classical algorithm is also explored to solve the problem on noisy intermediate-scale quantum devices.

DOI
10.1103/physrevd.108.083039

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We simulate the time evolution of collective neutrino oscillations in two-flavor settings on a quantum computer. We explore the generalization of Trotter-Suzuki approximation to time-dependent Hamiltonian dynamics. The trotterization steps are further optimized using the Cartan decomposition of two-qubit unitary gates U\ensuremath∈SU(4)U\ensuremath{\in}SU(4)U\ensuremath∈SU(4) in the minimum number of controlled-NOT (CNOT) gates making the algorithm more resilient to the hardware noise. A more efficient hybrid quantum-classical algorithm is also explored to solve the problem on noisy intermediate-scale quantum devices.
It is well known that the neutrino flavor in extreme astrophysical environments changes under the effect of three contributions: the vacuum oscillation, the interaction with the surrounding matter, and the collective oscillations due to interactions between different neutrinos. The latter adds a nonlinear contribution to the equations of motion, making the description of their dynamics complex. In this work we study various strategies to simulate the coherent collective oscillations of a system of NNN neutrinos in the two-flavor approximation using quantum computation. This was achieved by using a pair-neutrino decomposition designed to account for the fact that the flavor Hamiltonian, in the presence of the neutrino-neutrino term, presents an all-to-all interaction that makes the implementation of the evolution dependent on the qubit topology. We analyze the Trotter error caused by the decomposition demonstrating that the complexity of the implementation of time evolution scales polynomially with the number of neutrinos and that the noise from near-term quantum device simulation can be reduced by optimizing the quantum circuit decomposition and exploiting a full-qubit connectivity. We find that the gate complexity using second order Trotter-Suzuki formulas scales better with system size than with other decomposition methods such as quantum signal processing. We finally present the application and the results of our algorithm on a real quantum device based on trapped-ion qubits.
Collective neutrino flavor oscillations are of primary importance in understanding the dynamic evolution of core-collapse supernovae and subsequent terrestrial detection, but also among the most challenging aspects of numerical simulations. This situation is complicated by the quantum many-body nature of the problem due to neutrino-neutrino interactions which demands a quantum treatment. An additional complication is the presence of three flavors, which often is approximated by the electron flavor and a heavy lepton flavor. In this work, we provide both qubit and qutrit encodings for all three flavors, and develop optimized quantum circuits for the time evolution and analyze the Trotter error. We conclude our study with a hardware experiment of a system of two neutrinos with superconducting hardware: the IBM Torino device for qubits and AQT device for qutrits. We find that error mitigation greatly helps in obtaining a signal consistent with simulations. While hardware results are comparable at this stage, we expect the qutrit setup to be more convenient for large-scale simulations since it does not suffer from probability leakage into nonphsycial qubit space, unlike the qubit setup.
We simulate a self-interacting three-flavor neutrino system within a core-collapse supernova using a hybrid classical-quantum algorithm on a qutrit computer. Based on the Dirac-Frenkel evolution equations, we employ a variation of the quantum-assisted simulator to calculate the system's time evolution operator by performing qutrit Hadamard tests to find expectation values of unitary operators in the Hamiltonian. The time evolution simulation is then done classically. We find that the hybrid algorithm produces results comparable to an exact numerical integration out to times of t≈30 ω0−1t \approx 30 \,ω_0^{-1}t≈30ω0−1​ with time step δt=0.005 ω0−1δt = 0.005 \,ω_0^{-1}δt=0.005ω0−1​, where ω0ω_0ω0​ is the energy scale of the single neutrino vacuum oscillations. We discuss the lessons learned in simulating neutrino systems using this hybrid quantum-classical algorithm, along with the advantages it offers over quantum Trotterization.
The Suzuki-Trotter decomposition, which digitalizes quantum time evolution, provides a promising framework for simulating quantum dynamics on quantum hardware and exploring quantum advantage over classical computation. However, conventional Trotter circuits require a large number of non-local gates, lowering their faithfulness to the ideal dynamics when implemented on current noisy quantum hardware. While most previous studies have focused on circuit optimization, we instead propose a new Trotter decomposition that is intrinsically circuit-efficient for simulating quantum dynamics on near-term devices. Our method substantially reduces both the residual error by Trotter decomposition and the number of CNOT operations compared to conventional Trotter decompositions by exploiting the symmetry of the target model to construct an effective Hamiltonian with fewer two-qubit gates. We demonstrate the noise robustness of the proposed approach through numerical simulations of a nine-site Heisenberg model under realistic noise, and further validate its experimental practicality on the IBM superconducting device, achieving a state fidelity exceeding 0.980.980.98 when combined with quantum error mitigation in the three-site case. The proposed circuit design is also compatible with existing circuit optimization techniques. Our results establish a practical route toward noise-resilient quantum simulation in many-body dynamics.
Neutrinos are fascinating, elusive particles that play crucial roles in astrophysical environments such as dense stars, and the early universe, where they dominate energy transport and entropy. As neutral fermions in the Standard Model, neutrinos interact only weakly and exist in three flavors: electron, muon, and tau neutrinos. The discovery of neutrino flavor oscillation—a quantum phenomenon- reveals that neutrinos possess tiny mass, likely less than 0.2 eV. In dense environments, collective neutrino oscillations involving self-interactions emerge, complicating the numerics. However, these oscillations can be naturally simulated using quantum computers, by taking only two flavors as an isospin doublet leading to a spin model. In this review, we discuss the hybrid quantum-classical Lanczos (QLanczos) algorithm, which is used to find the eigenvalues of the collective neutrino Hamiltonian. This method uses the quantum imaginary-time evolution (QITE) to simulate the non-unitary imaginary-time evolution (ITE) of a quantum system using only unitary operations. Unlike variational algorithms that rely on a fixed ansatz, ITE always converges to the ground state. We also explore, as an altenative ITE, the probability ITE (PITE), in which an ancillary qubit is added to apply the ITE operator within an extended unitary. Once the ancilla is measured, the acted state collapses to the desired state. we also address the case with no mid-circuit measurements by employing quantum signal processing techniques.
The Suzuki–Trotter decomposition, which digitalizes quantum time evolution, provides a promising framework for simulating quantum dynamics on quantum hardware and exploring quantum advantage over classical computation. However, conventional Trotter circuits require a large number of non-local gates, lowering their faithfulness to the ideal dynamics when implemented on current noisy quantum hardware. While most previous studies have focused on circuit optimization, we instead propose a new Trotter decomposition that is intrinsically circuit-efficient for simulating quantum dynamics on near-term devices. Our method substantially reduces both the residual error by Trotter decomposition and the number of CNOT operations compared to conventional Trotter decompositions by exploiting the symmetry of the target model to construct an effective Hamiltonian with fewer two-qubit gates. We demonstrate the noise robustness of the proposed approach through numerical simulations of a nine-site Heisenberg model under realistic noise and further validate its experimental practicality on the IBM superconducting device, achieving a state fidelity exceeding 0.98 when combined with quantum error mitigation in the three-site case. The proposed circuit design is also compatible with existing circuit optimization techniques. Our results establish a practical route toward noise-resilient quantum simulation in many-body dynamics.