Related papers: How to Construct Random Unitaries
We show that several quantum circuit families can be simulated efficiently classically if it is promised that their output distribution is approximately sparse i.e. the distribution is close to one where only a polynomially small, a priori…
This paper initiates the study of hidden variables from the discrete, abstract perspective of quantum computing. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another, into a…
Randomized algorithms are crucial subroutines in quantum computing, but the requirement to execute many types of circuits on a real quantum device has been challenging to their extensive implementation. In this study, we propose an…
A quantum circuit is generalized to a nonunitary one whose constituents are nonunitary gates operated by quantum measurement. It is shown that a specific type of one-qubit nonunitary gates, the controlled-NOT gate, as well as all one-qubit…
Physical Unclonable Functions (PUFs) provide hardware-level security by exploiting intrinsic randomness to produce device-unique responses. However, machine learning and side-channel attacks increasingly undermine their classical…
Randomized benchmarking is a powerful technique to efficiently estimate the performance and reliability of quantum gates, circuits and devices. Here we propose to perform randomized benchmarking in a coherent way, where superpositions of…
Quantum tunneling across double potential barriers is studied. With the assumption that the real space is a continuum, it is rigorously proved that large barriers of arbitrary shapes can be penetrated by low-energy particles with a…
State of the art quantum computing architectures are founded on the decision to use scalable but faulty quantum hardware in conjunction with an efficient error correcting code capable of tolerating high error rates. The promised effect of…
The architecture of circuital quantum computers requires computing layers devoted to compiling high-level quantum algorithms into lower-level circuits of quantum gates. The general problem of quantum compiling is to approximate any unitary…
Certified randomness can be generated with untrusted remote quantum computers using multiple known protocols, one of which has been recently realized experimentally. Unlike the randomness sources accessible on today's classical computers,…
In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can…
Quantum algorithms for scientific computing require modules implementing fundamental functions, such as the square root, the logarithm, and others. We require algorithms that have a well-controlled numerical error, that are uniformly…
This paper positively solves the quantum subroutine problem for fully quantum oracles. The quantum subroutine problem asks whether a quantum computer with an efficiently computable oracle can be efficiently simulated by a non-oracle quantum…
The spectral gap of local random quantum circuits is a fundamental property that determines how close the moments of the circuit's unitaries match those of a Haar random distribution. When studying spectral gaps, it is common to bound these…
A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability…
The problem of the quantitative degradation of the performance of a quantum computer due to noisy unitary gates (imperfect external control) is studied. It is shown that quite general conclusions on the evolution of the fidelity can be…
We show that quantum algorithms of time $T$ and space $S\ge \log T$ with unitary operations and intermediate measurements can be simulated by quantum algorithms of time $T \cdot \mathrm{poly} (S)$ and space $ {O}(S\cdot \log T)$ with…
Cryptography depends on truly unpredictable numbers, but physical sources emit biased or correlated bits. Quantum mechanics enables the amplification of imperfect randomness into nearly perfect randomness, but prior demonstrations have…
While quantum computers have the potential to perform a wide range of practically important tasks beyond the capabilities of classical computers, realizing this potential remains a challenge. One such task is to use an untrusted remote…
We demonstrate quantum algorithms to implement pseudo-random operators that closely reproduce statistical properties of random matrices from the three universal classes: unitary, symmetric, and symplectic. Modified versions of the…