Related papers: Complexity and hardness of random peaked circuits
In its many variants, randomized benchmarking (RB) is a broadly used technique for assessing the quality of gate implementations on quantum computers. A detailed theoretical understanding and general guarantees exist for the functioning and…
Recent years have enjoyed a strong interest in exploring properties and applications of random quantum circuits. In this work, we explore the ensemble of $t$-doped Clifford circuits on $n$ qubits, consisting of Clifford circuits…
We investigate the complexity of explicit construction problems, where the goal is to produce a particular object of size $n$ possessing some pseudorandom property in time polynomial in $n$. We give overwhelming evidence that $\bf{APEPP}$,…
Random circuits giving rise to unitary designs are key tools in quantum information science and many-body physics. In this work, we investigate a class of random quantum circuits with a specific gate structure. Within this framework, we…
The Poisson equation occurs in many areas of science and engineering. Here we focus on its numerical solution for an equation in d dimensions. In particular we present a quantum algorithm and a scalable quantum circuit design which…
We develop efficient randomized algorithms to solve the black-box reconstruction problem for polynomials over finite fields, computable by depth three arithmetic circuits with alternating addition/multiplication gates, such that output gate…
Variational quantum algorithms, which utilize Parametrized Quantum Circuits (PQCs), are promising tools to achieve quantum advantage for optimization problems on near-term quantum devices. Their PQCs have been conventionally constructed…
We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathfrak{C}$ be a class of polynomial-size concepts, and suppose that $\mathfrak{C}$ can be PAC-learned with…
The present era of quantum processors with hundreds to thousands of noisy qubits has sparked interest in understanding the computational power of these devices and how to leverage it to solve practically relevant problems. For applications…
The applications of random quantum circuits range from quantum computing and quantum many-body systems to the physics of black holes. Many of these applications are related to the generation of quantum pseudorandomness: Random quantum…
Results on the hardness of approximate sampling are seen as important stepping stones towards a convincing demonstration of the superior computational power of quantum devices. The most prominent suggestions for such experiments include…
Motivated by realistic hardware considerations of the pre-fault-tolerant era, we comprehensively study the impact of uncorrected noise on quantum circuits. We first show that any noise `truncates' most quantum circuits to effectively…
We show that under mild assumptions for a problem whose solutions admit a dynamic programming-like recurrence relation, we can still find a solution under additional packing constraints, which need to be satisfied approximately. The number…
Quantum data loading plays a central role in quantum algorithms and quantum information processing. Many quantum algorithms hinge on the ability to prepare arbitrary superposition states as a subroutine, with claims of exponential speedups…
Quantum random number generators can provide genuine randomness by appealing to the fundamental principles of quantum mechanics. In general, a physical generator contains two parts---a randomness source and its readout. The source is…
In this work, we show that learning the output distributions of brickwork random quantum circuits is average-case hard in the statistical query model. This learning model is widely used as an abstract computational model for most generic…
There is a large body of work studying what forms of computational hardness are needed to realize classical cryptography. In particular, one-way functions and pseudorandom generators can be built from each other, and thus require equivalent…
The component-by-component construction is the standard method of finding good lattice rules or polynomial lattice rules for numerical integration. Several authors have reported that in numerical experiments the generating vector sometimes…
Whether parameterized quantum circuits (PQCs) can be systematically constructed to be both trainable and expressive remains an open question. Highly expressive PQCs often exhibit barren plateaus, while several trainable alternatives admit…
While recent breakthroughs have proven the ability of noisy intermediate-scale quantum (NISQ) devices to achieve quantum advantage in classically-intractable sampling tasks, the use of these devices for solving more practically relevant…