In the classical RAM, we have the following useful property. If we have an algorithm that uses M memory cells throughout its execution, and in addition is sparse, in the sense that, at any point in time, only m out of M cells will be non-zero, then we may “compress” it into another algorithm which uses only m log M memory and runs in almost the same time. We may do so by simulating the memory using either a hash table, or a self-balancing tree. We show an analogous result for quantum algorithms equipped with quantum random-access gates. If we have a quantum algorithm that runs in time T and uses M qubits, such that the state of the memory, at any time step, is supported on computational-basis vectors of Hamming weight at most m, then it can be simulated by another algorithm which uses only O(m log M) memory, and runs in time Õ(T ). We show how this theorem can be used, in a black-box way, to simplify the presentation in several papers. Broadly speaking, when there exists a need for a space-efficient history-independent quantum data structure, it is often possible to construct a space-inefficient, yet sparse, quantum data structure, and then appeal to our main theorem. This results in simpler and shorter arguments.

We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a random oracle:

Generating entanglement between more parties is one of the central tasks and challenges in the backdrop of building quantum technologies. I will discuss two recently proposed protocols to create genuine multipartite entangled states in networks -- measurement-based and deterministic schemes. In the former case, we employ weak entangling measurement on two parties as the basic unit of operation to produce entanglement between more parties starting from an entangled state with a lesser number of parties and auxiliary single-qubit systems which we call “multipartite entanglement inflation”. The latter deterministic procedure involves optimization over a set of two-qubit arbitrary unitary operators and the entanglement of the initial resource state which we refer to as entanglement circulation.

Non-Hermitian rotation-time reversal (RT)-symmetric spin models possess two distinct phases, the unbroken phase in which the entire spectrum is real and the broken phase which contains complex eigenspectral, thereby indicating a transition point, referred to as an exceptional point. We report that the dynamical quantities, namely short and long time average of Lo Schmidt echo which is the overlap between the initial and the final states, and the corresponding rate function, can faithfully predict the exceptional point known in the equilibrium scenario. In particular, when the initial state is prepared in the unbroken phase and the system is either quenched to the broken or unbroken phase, we analytically demonstrate that the rate function and the average Lo Schmidt echo can distinguish between the quench occurred in the broken or the unbroken phase for the nearest-neighbour XY model with uniform and alternating magnetic fields, thereby indicating the exceptional point. Furthermore, we exhibit that such quantities are capable of identifying the exceptional point even in models like the non-Hermitian XYZ model with magnetic field which can only be solved numerically.

Quantum dense coding (DC), first introduced by Bennett and Weisner for qubit systems, was generalized to the continuous variable (CV) paradigm by Braunstein and van Look for a single sender and a single receiver. In this talk, I will discuss the continuous variable dense coding (CV-DC) scheme for multiple senders sharing a multimode entangled state with a single receiver. I will present our framework for generating a multimode-dense coding network using quantum optical fields and demonstrate the quantum advantage of the protocol using paradigmatic classes of three- and four-mode states. The protocol is scalable to arbitrary numbers of senders. The encoding operations comprise local displacements while the decoding involves homodyne measurements of the modes. Our protocol involves simple optical elements such as beam splitters and mirrors, thereby exhibiting its potentiality for experimental realization.