Related papers: Random Unitaries in Constant (Quantum) Time

We consider the task of constructing pseudorandom unitaries (PRUs) with scalable security, i.e. families in which the security parameter may vary independently of the dimension (or input bit-length). It is not known whether scalable PRUs…

Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…

A fundamental question in the theory of quantum computation is to understand the ultimate space-time resource costs for performing a universal set of logical quantum gates to arbitrary precision. Here we demonstrate that non-Abelian anyons…

We construct $\varepsilon$-approximate unitary $k$-designs on $n$ qubits in circuit depth $O(\log k \log \log n k / \varepsilon)$. The depth is exponentially improved over all known results in all three parameters $n$, $k$, $\varepsilon$.…

Quantum computational pseudorandomness has emerged as a fundamental notion that spans connections to complexity theory, cryptography and fundamental physics. However, all known constructions of efficient quantum-secure pseudorandom objects…

Quantum computers are poised to radically outperform their classical counterparts by manipulating coherent quantum systems. A realistic quantum computer will experience errors due to the environment and imperfect control. When these errors…

Unitary $2$-designs are random unitaries simulating up to the second order statistical moments of the uniformly distributed random unitaries, often referred to as Haar random unitaries. They are used in a wide variety of theoretical and…

We present the first computationally-efficient algorithm for average-case learning of shallow quantum circuits with many-qubit gates. Specifically, we provide a quasi-polynomial time and sample complexity algorithm for learning unknown…

Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…

Random many-body states are both a useful tool to model certain physical systems and an important asset for quantum computation. Realising them, however, generally requires an exponential (in system size) amount of resources. Recent…

Unitary $T$-designs play an important role in quantum information, with diverse applications in quantum algorithms, benchmarking, tomography, and communication. Until now, the most efficient construction of unitary $T$-designs for $n$-qudit…

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…

While quantum state tomography is notoriously hard, most states hold little interest to practically-minded tomographers. Given that states and unitaries appearing in Nature are of bounded gate complexity, it is natural to ask if efficient…

Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any…

A unitary $t$-design is a powerful tool in quantum information science and fundamental physics. Despite its usefulness, only approximate implementations were known for general $t$. In this paper, we provide for the first time quantum…

Local random circuits scramble efficiently and accordingly have a range of applications in quantum information and quantum dynamics. With a global $U(1)$ charge however, the scrambling ability is reduced; for example, such random circuits…

Quantum physical unclonable functions, or QPUFs, are rapidly emerging as theoretical hardware solutions to provide secure cryptographic functionalities such as key-exchange, message authentication, entity identification among others. Recent…

The relevance of shallow-depth quantum circuits has recently increased, mainly due to their applicability to near-term devices. In this context, one of the main goals of quantum circuit complexity is to find problems that can be solved by…

The unitary design formation in random circuits has attracted considerable attention due to its wide range of practical applications and relevance to fundamental physics. While the formation rates in Haar random circuits have been…

Unitary t-designs are some of the most versatile tools in quantum information theory. Their applications range from randomized benchmarking and shadow tomography, to more fundamental ones such as emulating quantum chaos and establishing…