Related papers: Testing product states, quantum Merlin-Arthur game…

The task of state discrimination for a set of mutually orthogonal pure states is trivial if one has access to the corresponding sharp (projection-valued) measurement, but what if we are restricted to an unsharp measurement? Given that any…

Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by…

Evaluating quantum algorithms at utility-scale - involving more than 100 qubits - is a key step toward advancing real-world applications of quantum computing. In this study, we benchmark seven state-of-the-art quantum emulators employing…

Quantum many body physics simulations with Matrix Product States can often be accelerated if the quantum symmetries present in the system are explicitly taken into account. Conventionally, quantum symmetries have to be determined before…

Entanglement is one of the fundamental properties of a quantum state and is a crucial differentiator between classical and quantum computation. There are many ways to define entanglement and its measure, depending on the problem or…

This paper investigates the role of interaction and coins in public-coin quantum interactive proof systems (also called quantum Arthur-Merlin games). While prior works focused on classical public coins even in the quantum setting, the…

Stoquasticity, originating in sign-problem-free physical systems, gives rise to $\sf StoqMA$, introduced by Bravyi, Bessen, and Terhal (2006), a quantum-inspired intermediate class between $\sf MA$ and $\sf AM$. Unentanglement similarly…

Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing…

Quantum processing units boost entanglement at the level of hardware and enable physical simulations of highly correlated electron states in molecules and intermolecular chemical bonds. The variational quantum eigensolver provides a…

We construct a correspondence between quantum states and the observable input-output correlations they are compatible with. The problem is framed as a game involving an experimenter, claiming to be able to prepare some family of states, and…

Recall the classical hypothesis testing setting with two convex sets of probability distributions P and Q. One receives either n i.i.d. samples from a distribution p in P or from a distribution q in Q and wants to decide from which set the…

Quantum state tomography (QST) represents an essential tool for the characterization, verification, and validation (QCVV) of quantum processors. Only for a few idealized scenarios, there are analytic results for the optimal measurement set…

We examine two quantum operations, the Permutation Test and the Circle Test, which test the identity of n quantum states. These operations naturally extend the well-studied Swap Test on two quantum states. We first show the optimality of…

Entanglement and interference are among the most fundamental properties of quantum mechanics. In this work, we investigate the role and power of interference in the context of detecting entanglement. We do so from a computational complexity…

We prove a version of the quantum de Finetti theorem: permutation-invariant quantum states are well approximated as a probabilistic mixture of multi-fold product states. The approximation is measured by distinguishability under fully…

We study the estimation of the overlap between two unknown pure quantum states of a finite dimensional system, given $M$ and $N$ copies of each type. This is a fundamental primitive in quantum information processing that is commonly…

For every $\epsilon>0$, we give an $\exp(\tilde{O}(\sqrt{n}/\epsilon^2))$-time algorithm for the $1$ vs $1-\epsilon$ \emph{Best Separable State (BSS)} problem of distinguishing, given an $n^2\times n^2$ matrix $\mathcal{M}$ corresponding to…

In this paper, we introduce a class of highly entangled real quantum states that cannot be approximated by circuits with $\log$-many non-Clifford gates and prove that Bell sampling enables efficient cross-device verification (or distributed…

Sampling problems have emerged as a central avenue for demonstrating quantum advantage on noisy intermediate-scale quantum devices. However, physical noise can fundamentally alter their computational complexity, often making them…

QMA (Quantum Merlin-Arthur) is the quantum analogue of the class NP. There are a few QMA-complete problems, most notably the ``Local Hamiltonian'' problem introduced by Kitaev. In this dissertation we show some new QMA-complete problems.…