Parallel and Sequential Optical Computing

Thomas J. Naughton, Damien Woods

Ray LaPierre

Quantum computers can use a superposition to run many states simultaneously through an algorithm, rather than sequentially as in a classical computer. This principle is called quantum parallelism. This chapter refines our notion of quantum parallelism and introduces computational complexity to quantify the power of quantum computers.

Noam Scully, Sisi Zhou

Unitary process tomography is the act of learning how an unknown unitary gate acts on a quantum system. It is an essential procedure for realizing a functioning quantum computer. As quantum technologies develop, it is important to understand the computational resources needed to conduct unitary process tomography using a variety of types of circuits. In particular, when measuring error in diamond distance, it is known how to achieve optimal query complexity using a sequential circuit architecture, but it had not been known whether a parallel circuit architecture could achieve the same optimal query complexity. In this work, we prove that unitary process tomography with near-optimal query complexity is indeed possible using a parallel circuit by introducing an explicit, novel parallel procedure. This closes the gap between sequential and parallel circuits up to a logarithmic factor, showing that parallel and sequential strategies are nearly equally capable for this task.

Ray LaPierre

Quantum computers can use a superposition to run many states simultaneously through an algorithm, rather than sequentially as in a classical computer. This principle is called quantum parallelism. This chapter refines our notion of quantum parallelism and introduces computational complexity to quantify the power of quantum computers.

Entong He, Zihao Li, Yuxiang Yang

In the study of quantum process tomography, it has remained open how to learn a unitary channel in diamond distance with strictly parallel queries as efficiently as with sequential queries. Sequential queries allow one to exploit adaptivity to refine the estimate and adjust the learning strategy accordingly, whereas such adjustments are impossible for parallel queries. From the perspective of higher-order quantum operations, any parallel learning strategy can be simulated by a sequential one, whereas the converse does not hold in general, suggesting that sequential learning strategies are potentially more powerful. Contrary to this intuition, we present a new protocol for learning an unknown $d$-dimensional unitary channel to within $\varepsilon$ in diamond distance using $\mathcal{O}(d^2/\varepsilon)$ parallel queries, matching the lower bound presented in [Haah, Kothari, O'Donnell, and Tang, FOCS '23]. Our protocol thus closes the gap between parallel and sequential strategies for unitary channel tomography. As applications, it achieves optimal query complexity for boundary-regime quantum channel tomography and improves the query efficiency of the best-known protocol for tomography of fermionic linear optics.

Thomas J. Naughton, Damien Woods