Neutrino oscillations in a quantum processor

Quantum computing technologies promise to revolutionize calculations in many areas of physics, chemistry, and data science. Their power is expected to be especially pronounced for problems where direct analogs of a quantum system under study can be encoded coherently within a quantum computer. A first step toward harnessing this power is to express the building blocks of known physical systems within the language of quantum gates and circuits. In this paper we present a quantum calculation of an archetypal quantum system: neutrino oscillations. We define gate arrangements that implement the neutral lepton mixing operation and neutrino time evolution in two-, three-, and four-flavor systems. We then calculate oscillation probabilities by coherently preparing quantum states within the processor, time evolving them unitarily, and performing measurements in the flavor basis, with close analogy to the physical processes realized in neutrino oscillation experiments. Evaluations on publicly available quantum processors obtain excellent agreement with classical calculations. We provide recipes for modeling oscillation in the standard three-flavor paradigm as well as beyond-standard-model scenarios, including systems with sterile neutrinos, nonstandard interactions, Lorentz symmetry violation, and anomalous decoherence.

Figure 1

(a) Preparation of neutrino flavor and mass basis states in the $2\times 2$ quantum computation, (b) PMNS gate, and (c) time-evolution gates. (d) PMNS gate and (c) time-evolution gate in the $3\times 3$ quantum computation.

Figure 2

Quantum circuits embodying two-flavor neutrino oscillation for (a) ${\nu }_e$ disappearance, (b) ${\nu }_{\mu }\to {\nu }_e$, and (c) ${\nu }_{\mu }\to {\nu }_{\tau }$.

Figure 3

Two-flavor electron-neutrino survival probability as a function of the neutrino energy. The green line shows the theoretical calculation using a classical computer. The black circle markers indicate a quantum computer simulation and the black square markers are the output of the IBM Q quantum computer.

Figure 4

Calculations of three-flavor neutrino oscillations evaluated using a quantum computer (squares), quantum computer simulator (circles), and theory (lines). The quantum computer results have been corrected for gate read errors based on the matrix $M$ described in the text. The two plots (a) and (b) show three-flavor oscillation probabilities calculated in two characteristic $L/E$ ranges.

Figure 5

Quantum circuits for two BSM oscillation scenarios: (a) sterile neutrino oscillations and (b) anomalous decoherence in the mass basis.

Figure 6

Three-flavor neutrino oscillation experiment as run on the IBM quantum computer.