R. Cleve, "An introduction to quantum complexity theory," in Quantum computa- tion and quantum information theory: Collected papers and notes (Villa Gualino, Torino, Italy, 1999) ed. by C. Macchiavello, G. M. Palma, and A. Zeilinger (World Scientific, Singapore, 2000), pp 103-128; ...
The book starts with a broad introduction to the field and progresses to advanced results. Contents include: definition of Turing machines and basic time and space complexity classes, probabilistic algorithms, interactive proofs, cryptography, quantum computation, lower bounds for concrete computational ...
Quantum information processing is now a well-evolved field of study with roots to quantum physics that has significantly evolved from pioneering works over
The field of quantum computing has grown from concept to demonstration devices over the past 20 years. Universal quantum computing offers efficiency in approaching problems of scientific and commercial interest, such as factoring large numbers, searching databases, simulating intractable models from quantum...
You’ve probably been hearing a lot lately about the quantum-computing threat to cryptography. If so, you probably also have a lot of questions about what this “quantum threat” is and how it will impact your cryptographic solutions. Let’s take a look at some of the most common ...
The foundations of quantum complexity theory are laid up in the paper of Bernstein and Vazirani [BV97]. This paper defines the fundamental complexity classes for quantum computation, such as BQP, and it establishes the fact that BPP ⊆ BQP ⊆ P#P. The result that put quantum computation ...
For an introduction to quantum machine learning, see also [332]. The method of fidelity-based probabilistic quantum learning for control of quantum systems is studied in [333]. In [334], the problem of human-level control through deep reinforcement learning is studied. For a study on the ...
4 Quantum Foam 5 The Standard Model • 5.1 Down the Slippery Slope 6 Does the Universe Expand? Chaos Theory 7 Introduction 8 Self-similarity • 8.0 Koch Proof • 8.1 Jessica Rabbit Explains • 8.2 Something About the Sequence • 8.3 Ulam's Rose? Get a grip! • 8.4 How to Make...
complexity regime? How would we be able to check this? Thus, the fundamental question is whether there exists a verification procedure for quantum mechanical predictions which is efficient for arbitrarily large systems. In trying to answer this question we return to complexity theory. The primary ...
Quantum technologies hold the promise of not only faster algorithmic processing of data, via quantum computation, but also of more secure communications, in the form of quantum cryptography. In recent years, a number of protocols have emerged which seek