CMPT 407/710 - Complexity Theory: Lecture 17

نویسنده

  • Valentine Kabanets
چکیده

Classically, a computation operates on a string of bits, applying a sequence of physically realizable operations (such as logical NOT, AND, and OR), and outputs an answer based on the value of the last obtained bit string. Similarly, a quantum computation operates on a register consisting of a number of quantum bits (qubits), applying a sequence of (hypothetically) physically realizable quantum operations, and outputs an answer based on some measurement applied to the resulting quantum system.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

CMPT 407/710 - Complexity Theory: Lecture 10

Why is randomness useful? Imagine you have a stack of bank notes, with very few counterfeit ones. You want to choose a genuine bank note to pay at a store. However, suppose that you don’t know how to distinguish between a “good” bank note and a “bad” one. What can you do? Well, if you pick a bank note at random, you will be lucky with high probability (here the probability of picking a good ban...

متن کامل

CMPT 407/710 - Complexity Theory: Lecture 16

The PCP theorem gives a novel characterization of the class NP in terms of probabilistically checkable proofs (PCPs). The central role in this characterization belongs to a Verifier. Here, the probabilities are taken over the random choices of the verifier, and the notation V π means that the verifier V has random access to the string π, i.e., V may request to see the ith bit of the string π, f...

متن کامل

CMPT 407 / 710 - Complexity Theory : Lecture 14

As a consequence of an AM protocol for NISO, we get the following: Theorem 1. If Graph Isomorphism is NP-complete, then PH = Σp2. Proof. Suppose that Graph Isomorphism is NP-complete. Then the problem NISO is coNPcomplete. Hence, every coNP problem is polytime reducible to NISO, which, as we know, is in AM. We use this to get the following inclusions: Σp2 = ∃ ◦ ∀ ◦ P (definition of Σ p 2) ⊆ ∃ ◦...

متن کامل

CMPT 407/710 - Complexity Theory: Lecture 20

Do we have non-relativizing techniques? Yes, we do! In fact, already the proof of the CookLevin theorem is non-black-box: to reduce the computation of a nondeterministic TM on a given input x to a 3-cnf φx, we had to “open up” the TM and look inside at the sequence of configurations the TM goes through, and moreover, exploit a very special property of a TM computation: that the computation is l...

متن کامل

CMPT 407 - Complexity Theory Lecture 5: SAT, coNP, Search-to-Decision, NTime Hierarchy

Proof. SAT is in NP (easy). To prove NP-hardness, we will show that Circuit-SAT is reducible to SAT. Let C be an arbitrary Boolean circuit with gates g1, . . . , gm, where g1, . . . , gn are input gates and gm is the output gate. For each gj, introduce a Boolean variable yj. For every i > n, define the Boolean formula gatei expressing that the value of yi is equal to the value of the gate gi. T...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2017