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arXiv:1108.0182 · New Journal of Physics

Quantum simulation of neutrino oscillations with trapped ions

C Noh, B. M. Rodríguez-Lara, Dimitris G. Angelakis

Published Mar 16, 2012• 22 citations
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Abstract

We propose a scheme for simulating the dynamics of neutrino oscillations using trapped ions. For neutrinos in 1 + 1 dimensions, our scheme is experimentally implementable with existing trapped-ion technology. We show that the three-generation neutrino oscillations can be realized with three ions for 1 + 3 and 1 + 1 dimensions where the latter case only requires experimentally proven two-ion interactions. For this case, we discuss two setups utilizing different types of spin–spin interactions. Our method can be readily applied to two-generation neutrino oscillations requiring fewer ions and lasers. We give a brief outline of a possible experimental scenario.

DOI
10.1088/1367-2630/14/3/033028

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We propose a scheme for simulating the dynamics of neutrino oscillations using trapped ions. For neutrinos in 1 + 1 dimensions, our scheme is experimentally implementable with existing trapped-ion technology. We show that the three-generation neutrino oscillations can be realized with three ions for 1 + 3 and 1 + 1 dimensions where the latter case only requires experimentally proven two-ion interactions. For this case, we discuss two setups utilizing different types of spin–spin interactions. Our method can be readily applied to two-generation neutrino oscillations requiring fewer ions and lasers. We give a brief outline of a possible experimental scenario.
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.
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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.
Superconducting qubits offer a versatile platform for quantum simulation. In this architecture, quantum information can be encoded in the bosonic modes of a microwave cavity, offering an alternative to conventional qubit-based encoding schemes. These cavity bosonic modes can be manipulated using a single ancillary qubit. In this work, we investigate the quantum simulation of two- and three-flavor neutrino oscillations using Fock-basis encoding of a cavity mode. We design pulse sequences for implementing the required unitary operations through selective number-dependent arbitrary phase (SNAP) and displacement gates. Pulse-level control is employed to realize high-fidelity gate operations on the encoded cavity mode. The resulting neutrino oscillation probabilities obtained from quantum simulation exhibit close agreement with the corresponding theoretical predictions, demonstrating the feasibility of cavity-based bosonic encoding schemes for quantum simulation.
We show that trapped ions are ideally suited for the simulation of quantum spin systems and for the observation of a rich variety of quantum phase transitions. By changing the laser intensities and polarizations, the dynamics of the internal states of the ions can be controlled in such a way that an Ising or Heisenberg-like interaction is induced between effective spins. Our scheme allows us to build an analog quantum simulator of spin systems with trapped ions and to observe and analyze quantum phase transitions with unprecedented opportunities for the measurement and manipulation of spins. The requirements for our proposal are met by current technology: it does not rely on the use of quantum gates, and striking many-body effects can be observed even when the fidelity of the simulation is smaller than the one required for quantum computation. Our proposal with trapped ions would solve many of the problems that are faced in the implementation of quantum simulations with neutral atoms in optical lattices.
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.