Protocol for Implementing Quantum Nonparametric Learning with Trapped Ions

Abstract

Nonparametric learning is able to make reliable predictions by extracting information from similarities between a new set of input data and all samples. Here we point out a quantum paradigm of nonparametric learning which offers an exponential speedup over the sample size. By encoding data into quantum feature space, similarity between the data is defined as an inner product of quantum states. A quantum training state is introduced to superpose all data of samples, encoding relevant information for learning its bipartite entanglement spectrum. We demonstrate that a trained state for prediction can be obtained by entanglement spectrum transformation, using quantum matrix toolbox. We further workout a feasible scheme to implement the quantum nonparametric learning with trapped ions, and demonstrate the power of quantum superposition for machine leaning with a state-of-the-art technology.

Shuttle-Exploiting Attacks and Their Defenses in Trapped-Ion Quantum Computers

“…Assuming a victim size of 12, the trap states after initial mapping will be {T0 (EC = 2): [0, 1, 2, ..., 13, 14], T1 (EC = 2): [15,16,17] + [12Q victim]}. Here, EC = excess capacity.…”

“…Therefore, according to the shuttle direction policy in Listing 1, the first ion in the gate MS q[14], q [15] i.e., ion 14 will move from T0 to T1. Thus, the updated trap states are {T0 (EC = 3): [0, 1, 2, ..., 13], T1 (EC = 1): [14,15,16,17] + ([12Q victim]}. (Note, the victim size information is required to compute the excess capacity of the shared trap T1 and to find the shuttle direction accurately.)…”

“…As T0 has more EC (= 3) than T1 (EC = 1), ion 14 will again move but this time from T1 to T0. Finally, the updated trap states after this gate will be {T0 (EC = 2): [0, 1, 2, ..., 13, 14], T1 (EC = 2): [15,16,17] + [12Q victim]}. A partial shuttle controller block of block length 80 is illustrated in Figure 6a.…”

“…Suppose, the actual victim size during run is 5. Then, the actual trap states and excess capacities will be as follows at the beginning: T0 (EC = 2): [0, 1, ..., 14], T1 (EC = 7): [15,16,17] + [5Q victim]. Gate # sc1 will need a shuttle as ion 14 is in T0 and ion 15 is in T1.…”

“…Gate # sc1 will need a shuttle as ion 14 is in T0 and ion 15 is in T1. Updated trap states will be T0 (EC = 3): [0, 1, ..., 13], T1 (EC = 6): [14,15,16,17] + [5Q victim] (Note T1 EC > T0 EC, different than the assumption). Gate # sc2 will also require a shuttle as the ions are in different traps.…”