Related papers: On the Need for Large Quantum Depth
A conjecture of Jozsa (arXiv:quant-ph/0508124) states that any polynomial-time quantum computation can be simulated by polylogarithmic-depth quantum computation interleaved with polynomial-depth classical computation. Separately, Aaronson…
We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a…
The relationship between BQP and PH has been an open problem since the earliest days of quantum computing. We present evidence that quantum computers can solve problems outside the entire polynomial hierarchy, by relating this question to…
The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle,…
One can fix the randomness used by a randomized algorithm, but there is no analogous notion of fixing the quantumness used by a quantum algorithm. Underscoring this fundamental difference, we show that, in the black-box setting, the…
An important theoretical problem in the study of quantum computation, that is also practically relevant in the context of near-term quantum devices, is to understand the computational power of hybrid models, that combine poly-time classical…
We propose a definition of QNC, the quantum analog of the efficient parallel class NC. We exhibit several useful gadgets and prove that various classes of circuits can be parallelized to logarithmic depth, including circuits for encoding…
It is a longstanding open problem to devise an oracle relative to which BQP does not lie in the Polynomial-Time Hierarchy (PH). We advance a natural conjecture about the capacity of the Nisan-Wigderson pseudorandom generator [NW94] to fool…
We exhibit some simple gadgets useful in designing shallow parallel circuits for quantum algorithms. We prove that any quantum circuit composed entirely of controlled-not gates or of diagonal gates can be parallelized to logarithmic depth,…
This paper furthers existing evidence that quantum computers are capable of computations beyond classical computers. Specifically, we strengthen the collapse of the polynomial hierarchy to the second level if: (i) Quantum computers with…
We explore the space "just above" BQP by defining a complexity class PDQP (Product Dynamical Quantum Polynomial time) which is larger than BQP but does not contain NP relative to an oracle. The class is defined by imagining that quantum…
We study the quantum complexity class QNC^0_f of quantum operations implementable exactly by constant-depth polynomial-size quantum circuits with unbounded fan-out gates (called QNC^0_f circuits). Our main result is that the quantum OR…
Quantum computation requires large classical datasets to be embedded into quantum states in order to exploit quantum parallelism. However, this embedding requires considerable resources. It would therefore be desirable to avoid it, if…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
Quantum computers are widely believed have an advantage over classical computers, and some have even published some empirical evidence that this is the case. However, these publications do not include a rigorous proof of this advantage,…
We discuss the performance of the Search and Fourier Transform algorithms on a hybrid computer constituted of classical and quantum processors working together. We show that this semi-quantum computer would be an improvement over a pure…
Quantum algorithms are a very promising field. However, creating and manipulating these kind of algorithms is a very complex task, specially for software engineers used to work at higher abstraction levels. The work presented here is part…
Sampling from the output distributions of quantum computations comprising only commuting gates, known as instantaneous quantum polynomial (IQP) computations, is believed to be intractable for classical computers, and hence this task has…
Quantum Computers offer an intriguing challenge in modern Computer Science. With the inevitable physical limitations to Moore's Law, quantum hardware provides avenues to solve grander problems faster by utilizing Quantum Mechanical…
Quantum computing promises exponential speedups for certain problems, yet fully universal quantum computers remain out of reach and near-term devices are inherently noisy. Motivated by this, we study noisy quantum algorithms and the…