Bahman Ghandchi & Dirk Oliver Theis (Ketita): Technical Report
Parameterized quantum circuits (PQC, aka, variational quantum circuits) are among the proposals for a computational advantage over classical computation of near-term (not fault tolerant) digital quantum computers. PQCs have to be "trained" — i.e., the expectation value function has to be maximized over the space of parameters. This paper deals with the number of samples (or "runs" of the quantum computer) which are required to train the PQC, and approaches it from an information theoretic viewpoint. The main take-away is a disparity in the large amount of information contained in a single exact evaluation of the expectation value, vs the exponentially small amount contained in the random sample obtained from a single run of the quantum circuit. |
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Dirk Oliver Theis (Ketita), Javier Gil Vidal: Frontiers in Physics
The topic area of this paper parameterized quantum circuits (quantum neural networks) which are trained to estimate a given function, specifically the type of circuits proposed by Mitarai et al. (Phys. Rev. A, 2018). The input is encoded into amplitudes of states of qubits. The no-cloning principle of quantum mechanics suggests that there is an advantage in redundantly encoding the input value several times. We follow this suggestion and prove lower bounds on the number of redundant copies for two types of input encoding. We draw conclusions for the architecture design of QNNs. |
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Dirk Oliver Theis (Ketita), Javier Gil Vidal: Technical report
Mitarai, Negoro, Kitagawa, and Fujii proposed a type of parameterized quantum circuits, for which they gave a way to estimate derivatives wrt the parameters using only changes in the values of the parameters, not in the circuit itself, i.e., no ancillas or controlled operations. Recently, Schuld et al. have extended the results, but they need to revert to ancillas and controlled operations for some cases. In this note, we extend the types of MiNKiF circuits for which derivatives can be computed without ancillas or controlled operations — at the cost of a larger number of evaluation points. We also propose a "training" (i.e., optimizing the parameters) which takes advantage of our approach. |
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Tore Vincent Carstens & Dirk Oliver Theis (Ketita): Technical report
We consider active (i.e., requring 2n parallel control operations) QRAM-like effect Σₓ |x⟩⟨x|⊗Uₓ with the sum ranging over all values of n bits, and Uₓ unitaries preparing results depending on an additional set of (disjoint) qubits. We observe that it can be realized, as a quantum circuit of depth O(n+√m) (where m is the size of the result register) plus the maximum over all x of the circuit depths of controlled-Uₓ operations. |