Quantum Circuit Architecture

We present a method for optimizing quantum circuits architecture, based on the notion of a quantum comb, which describes a circuit board where one can insert variable subcircuits. Unexplored quantum processing tasks, such as cloning and storing or retrieving of gates, can be optimized, along with setups for tomography and discrimination or estimation of quantum circuits.

Figure 1

A quantum circuit board.

Figure 2

Connection of two quantum circuits $\mathcal{A}$ and $\mathcal{B}$. Wires are labeled according to Rule 1. The Choi operator of the resulting circuit $\mathcal{C}$ is given by the link product of Rule 3.

Figure 3

Every circuit-board can be reshaped in form of a “comb,” with an ordered sequence of slots, each between two successive teeth. The pins represent quantum systems, entering or exiting from the board (the horizontal arrow represents the quantum information flow).

Figure 4

Each quantum comb is equivalent to a causal network, with all inputs on the left and all outputs on the right. The Choi operator of a comb is the Choi operator of the corresponding causal network.

Figure 5

A quantum comb realizes different transformations of quantum circuits, namely, it can send (a) a series of channels into a channel, (b) a series of channels into a comb, or (c) an input comb into an output comb.

Figure 6

Quantum-algorithm learning. One wants to run an undisclosed unitary $U$ on a quantum state $\psi$ which is available after the lapse of time in which the uses of $U$ are available.

Figure 7

Quantum tester: comb for measuring quantum combs, e.g., memory channels and sequences of unitaries.