I offer a case that quantum query complexity still has loads of enticing and fundamental open
problems—from relativized QMA versus QCMA and BQP versus IP, to time/space tradeoffs …

This article surveys the state of the art in quantum computer algorithms, including both black-
box and non-black-box results. It is infeasible to detail all the known quantum algorithms, so …

A random access memory (RAM) uses n bits to randomly address N= 2 n distinct memory
cells. A quantum random access memory (QRAM) uses n qubits to address any quantum …

This concise, accessible text provides a thorough introduction to quantum computing-an
exciting emergent field at the interface of the computer, engineering, mathematical and …

We examine the number of queries to input variables that a quantum algorithm requires to
compute Boolean functions on {0, 1} N in the black-box model. We show that the exponential …

A thorough exposition of quantum computing and the underlying concepts of quantum
physics, with explanations of the relevant mathematics and numerous examples. The …

Pseudorandom functions (PRFs) are one of the foundational concepts in theoretical
computer science, with numerous applications in complexity theory and cryptography. In this …

We propose a new method for proving lower bounds on quantum query algorithms. Instead
of a classical adversary that runs the algorithm with one input and then modifies the input we …

We provide algorithms for efficiently moving and addressing quantum memory in parallel.
These imply that the standard circuit model can be simulated with a low overhead by a more …

A random access memory, or RAM, is a device that, when interrogated, returns the content of
a memory location in a memory array. A quantum RAM, or qRAM, allows one to access …