Related papers: Anti-concentration is (almost) all you need
We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. We show that, for local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy…
Significant progress is required in the engineering of large, interacting quantum systems in order to realize the promises of gate-model quantum computing. Designing such systems is challenging, as the dynamics of continuous variable…
In the accompanying paper of arXiv:2408.13472, we have established the method of characterizing the maximal order of asymptotic unitary designs generated by symmetric local random circuits, and have explicitly specified the order in the…
Although entangled state vectors cannot be described in terms of classically realistic variables, localized in space and time, any given entanglement experiment can be built from basic quantum circuit components with well-defined locations.…
The rapid evolution of quantum devices fuels concerted efforts to experimentally establish quantum advantage over classical computing. Many demonstrations of quantum advantage, however, rely on computational assumptions and face…
Random quantum circuits are a central concept in quantum information theory with applications ranging from demonstrations of quantum computational advantage to descriptions of scrambling in strongly-interacting systems and black holes. The…
Two schemes are presented that mitigate the effect of errors and decoherence in short depth quantum circuits. The size of the circuits for which these techniques can be applied is limited by the rate at which the errors in the computation…
We propose a set of Bell-type nonlocal games that can be used to prove an unconditional quantum advantage in an objective and hardware-agnostic manner. In these games, the circuit depth needed to prepare a cyclic cluster state and measure a…
We show that in a complex d-dimensional vector space, one can find O(d) bases whose elements form a 2-design. Such vector sets generalize the notion of a maximal collection of mutually unbiased bases (MUBs). MUBs have manifold applications…
2-designs -- ensembles of quantum pure states whose 2nd moments equal those of the uniform Haar ensemble -- are optimal solutions for several tasks in quantum information science, especially state and process tomography. We show that…
We give three new algorithms for efficient in-place estimation, without using ancilla qubits, of average fidelity of a quantum logic gate acting on a d-dimensional system using much fewer random bits than what was known so far. Previous…
We present evidence that there exist quantum computations that can be carried out in constant depth, using 2-qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically…
We derive the transformation for the optimal universal quantum anti-cloner which produces two anti-parallel outputs for a single input state. The fidelity is shown to be 2/3 which is same as the measurement fidelity. We consider a…
We consider quantum circuit models where the gates are drawn from arbitrary gate ensembles given by probabilistic distributions over certain gate sets and circuit architectures, which we call stochastic quantum circuits. Of main interest in…
Starting from the reduced dynamical model of a two-junction quantum interference device, a quantum analog of the system has been exhibited, in order to extend the well known properties of this device to the quantum regime. By finding…
We consider the problem of estimating an SU(d) quantum operation when n copies of it are available at the same time. It is well known that, if one uses a separable state as the input for the unitaries, the optimal mean square error will…
We study quantum-classical separations between classical and quantum supervised learning models based on constant depth (i.e., shallow) circuits, in scenarios with and without noises. We construct a classification problem defined by a…
While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable…
We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for…
We prove anti-concentration bounds for the inner product of two independent random vectors, and use these bounds to prove lower bounds in communication complexity. We show that if $A,B$ are subsets of the cube $\{\pm 1\}^n$ with $|A| \cdot…