1 a 6 1 a 7 1 page 11 of 35 an introduction to

This preview shows page 11 - 13 out of 35 pages.

0 0 0 0 0 1 0 0 + a 6 0 0 0 0 0 0 1 0 + a 7 0 0 0 0 0 0 0 1 Page 11 of 35
Image of page 11

Subscribe to view the full document.

An Introduction to Quantum Algorithms 2.5 Quantum logic gates As mentioned earlier, each possible bit configuration in the quantum superposition is denoted by the tensor product of its counterpart qubits. Consider | 101 i , the bit string that represents the integer value 5: | 101 i = | 1 i ⊗ | 0 i ⊗ | 1 i = 0 1 1 0 0 1 = 0 0 0 0 0 1 0 0 T As with single qubits, the squared absolute value of the amplitude associated with a given bit string is the probability of observing that bit string upon collapsing the register to a classical state, and the the sqares of the absolute values of the amplitudes of all 2 n possible bit configuations of an n -bit register sum to unity: 2 n - 1 X i =0 | a i | 2 = 1 Quantum registers are a relatively straightforward extension of quantum bits. 2.5 Quantum logic gates Understanding how quantum registers work mathematically and how they differ from classical registers, it is now possible to think about how the state of a quantum register can evolve over time, changing to reach some ultimate goal. In classical computing, one way of thinking about algorithm design and computation is via universal Turing machines. Quantum universal Turing machines were first described by David Deutsch in 1985 [16], but designing algorithms for quantum Turing machines is even more difficult and tedious than doing so for classical Turing machines; both a quantum Turing machine’s tape and its read-write head exist in superpositions of an exponential number states! As in classical computer science, instead of using the Turing machine as a computational model, operations on a quantum computer are most often described using quantum circuits made up of qubits and quantum logic gates, a concept also introduced by Deutsch a few years after his specification of the quantum analog to a Turing machine [ 17 ]. In classical computer science but arguably even more so in quantum computing, although circuits are computationally equivalent to Turing machines, they are usually much simpler to depict, manipulate and understand. In classical computing, binary values, as stored in a register, pass through logic gates that, given a certain binary input, produce a certain binary output. Mathematically, classical logic gates are described using boolean algebra. Quantum logic gates act in a similar way, in that quantum logic gates applied to quantum registers map the quantum superposition to another, together allowing the evolution of the system to some desired Page 12 of 35
Image of page 12
An Introduction to Quantum Algorithms 2.5 Quantum logic gates final state, a correct answer.
Image of page 13
You've reached the end of this preview.
  • Fall '13
  • Xue
  • Hilbert space, Quantum algorithms

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern