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By Michael A. Nielsen
Probably the most pointed out books in physics of all time, Quantum Computation and Quantum info continues to be the simplest textbook during this intriguing box of technology. This tenth anniversary variation comprises an creation from the authors environment the paintings in context. This entire textbook describes such amazing results as speedy quantum algorithms, quantum teleportation, quantum cryptography and quantum error-correction. Quantum mechanics and laptop technological know-how are brought ahead of relocating directly to describe what a quantum computing device is, the way it can be utilized to unravel difficulties swifter than 'classical' desktops and its real-world implementation. It concludes with an in-depth therapy of quantum details. Containing a wealth of figures and routines, this recognized textbook is perfect for classes at the topic, and should curiosity starting graduate scholars and researchers in physics, computing device technology, arithmetic, and electric engineering.
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Additional info for Quantum Computation and Quantum Information: 10th Anniversary Edition
Sample text
This lesson – that the effects of realistic noise must be taken into account in evaluating the efficiency of a computational model – was one of the great early challenges of quantum computation and quantum information, a challenge successfully met by the development of a theory of quantum error-correcting codes and fault-tolerant quantum computation. Thus, unlike analog computation, quantum computation can in principle tolerate a finite amount of noise and still retain its computational advantages.
What do we mean by ‘efficient’ versus ‘inefficient’ simulations of a quantum computer? Many of the key notions needed to answer this question were actually invented before the notion of a quantum computer had even arisen. In particular, the idea of efficient and inefficient algorithms was made mathematically precise by the field of computational complexity. Roughly speaking, an efficient algorithm is one which runs in time polynomial in the size of the problem solved. In contrast, an inefficient algorithm requires superpolynomial (typically exponential) time.
1 to 11 . . 1 with the bottom-most wire being the least significant bit. Note that eiπ/4 is the square root of i, so that the π/8 gate is the square root of the phase gate, which itself is the square root of the Pauli-Z gate. Hadamard Pauli-X Pauli-Y Pauli-Z Phase π/8 1 1 1 √ 2 1 −1 0 1 1 0 0 −i i 0 1 0 0 −1 1 0 0 i 1 0 0 eiπ/4 Nomenclature and notation ⎡ 1 ⎢0 ⎣0 0 ⎡ 1 ⎢0 ⎣0 0 ⎡ 1 ⎢0 ⎣0 0 ⎡ 1 ⎢0 ⎣0 0 controlled- swap • controlled-Z = Z controlled-phase ⎡ • Toffoli • ⊕ 1 ⎢0 ⎢0 ⎢ ⎢0 ⎢ ⎢0 ⎢ ⎢0 ⎣ 0 0 ⎡ • Fredkin (controlled-swap) × × measurement ❴✤✤ ❴ ❴ ❴ ❴ ❴ L ❴ ❴ ✤✤ ✙ ✤✤ ✤✤✤ ✙✙ ✤✤ ✤✤ ✙✙ ❴ ❴ ❴ ❴ ❴✙ ❴ ❴ ❴ ✤ 1 ⎢0 ⎢0 ⎢ ⎢0 ⎢ ⎢0 ⎢ ⎢0 ⎣ 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 ⎤ 0 0⎥ 1⎦ 0 ⎤ 0 0⎥ 0⎦ 1 ⎤ 0 0 ⎥ 0 ⎦ −1 ⎤ 0 0⎥ 0⎦ i xxxi 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 ⎤ 0 0⎥ 0⎥ ⎥ 0⎥ ⎥ 0⎥ ⎥ 0⎥ ⎦ 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 ⎤ 0 0⎥ 0⎥ ⎥ 0⎥ ⎥ 0⎥ ⎥ 0⎥ ⎦ 0 1 Projection onto |0 and |1 qubit wire carrying a single qubit (time goes left to right) classical bit wire carrying a single classical bit n qubits wire carrying n qubits I Fundamental concepts 1 Introduction and overview Science offers the boldest metaphysics of the age.