Related papers: Sampling of globally depolarized random quantum ci…
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…
We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…
One-parameter interpolations between any two unitary matrices (e.g., quantum gates) $U_1$ and $U_2$ along efficient paths contained in the unitary group are constructed. Motivated by applications, we propose the continuous unitary path…
In randomized benchmarking of quantum logical gates, partial twirling can be used for simpler implementation, better scaling, and higher accuracy and reliability. For instance, for two-qubit gates, single-qubit twirling is easier to realize…
This paper presents a quantum generalization of the multinomial distribution for the transition probabilities of $m$ identical photons in a $k$-port linear optical interferometer: two multinomial coefficients (one for the input…
We show the following: a randomly chosen pure state as a resource for measurement-based quantum computation, is - with overwhelming probability - of no greater help to a polynomially bounded classical control computer, than a string of…
We quantitatively analyze superradiance (collective emission) in a three-dimensional array of qubits without imposing any restrictions on the size of the sample. We show that even when the spacing between the qubits become arbitrarily…
We investigate the fidelity of Haar random bipartite pure states from a fixed reference quantum state and their bipartite entanglement. By plotting the fidelity and entanglement on perpendicular axes, we observe that the resulting plots…
In classical statistics and distribution testing, it is often assumed that elements can be sampled from some distribution $P$, and that when an element $x$ is sampled, the probability $P$ of sampling $x$ is also known. Recent work in…
We characterise the probability distributions that arise from quantum circuits all of whose gates commute, and show when these distributions can be classically simulated efficiently. We consider also marginal distributions and the…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
We show that any classical two-way communication protocol with shared randomness that can approximately simulate the result of applying an arbitrary measurement (held by one party) to a quantum state of $n$ qubits (held by another), up to…
We investigate sampling procedures that certify that an arbitrary quantum state on $n$ subsystems is close to an ideal mixed state $\varphi^{\otimes n}$ for a given reference state $\varphi$, up to errors on a few positions. This task makes…
It is known that quantum correlations exhibited by a maximally entangled qubit pair can be simulated with the help of shared randomness, supplemented with additional resources, such as communication, post-selection or non-local boxes. For…
QBism is an interpretation of quantum theory which views quantum mechanics as standard probability theory supplemented with a few extra normative constraints. The fundamental gambit is to represent states and measurements, as well as time…
We consider quantum circuits consisting of randomly chosen two-local gates and study the number of gates needed for the distribution over measurement outcomes for typical circuit instances to be anti-concentrated, roughly meaning that the…
It has been known for almost 30 years that quantum circuits with interspersed depolarizing noise converge to the uniform distribution at $\omega(\log n)$ depth, where $n$ is the number of qubits, making them classically simulable. We show…
There is a large body of evidence for the potential of greater computational power using information carriers that are quantum mechanical over those governed by the laws of classical mechanics. But the question of the exact nature of the…
An essential step in quantum key distribution is the estimation of parameters related to the leaked amount of information, which is usually done by sampling of the communication data. When the data size is finite, the final key rate depends…
The class of commuting quantum circuits known as IQP (instantaneous quantum polynomial-time) has been shown to be hard to simulate classically, assuming certain complexity-theoretic conjectures. Here we study the power of IQP circuits in…