Download Decoherence, control, and symmetry in quantum computers by Dave Morris Bacon PDF

By Dave Morris Bacon

Show description

Read Online or Download Decoherence, control, and symmetry in quantum computers PDF

Similar computers books

Real world Camera Raw with Adobe Photoshop CS: industrial strength production techniques

Name it a keep watch over factor, yet until eventually lately - or, extra specifically,until the supply of electronic uncooked digicam codecs - you simplyweren't able to make the circulation to electronic images. uncooked formats,however, replaced all of that by way of permitting you to retrieve imagesbefore any in-camera processing has been played.

Information Networking. Convergence in Broadband and Mobile Networking: International Conference, ICOIN 2005, Jeju Island, Korea, January 31- February 2, 2005. Proceedings

Welcome to ICOIN 2005,the overseas convention on info Netwo- ing, held at Ramada Plaza Jeju lodge, Jeju Island, Korea in the course of January 31– February2,2005. ICOIN2005followedthesuccessofpreviousconferences. considering the fact that 1986, the convention has supplied a technical discussion board for numerous concerns in inf- mation networking.

Simulated Evolution and Learning: First Asia-Pacific Conference, SEAL'96 Taejon, Korea, November 9–12, 1996 Seclected Papers

This ebook constitutes the completely refereed post-conference documentation of the 1st Asia-Pacific convention on Simulated Evolution and studying, SEAL'96, held in Taejon, Korea, in November 1996. The 23 revised complete papers have been chosen for inclusion during this publication at the foundation of two rounds of reviewing and enhancements.

Additional resources for Decoherence, control, and symmetry in quantum computers

Sample text

2 Fixed basis OSR A tool which we will find useful later in our derivation of master equations is the fixed basis form of the OSR[42, 10]. 3) for expanding each of the operators Ai (t) in the OSR: Ai(t) = biα (t)Fα . 14) αβ where biα (t)b∗iβ (t). 15) i Eq. 14) is the fixed basis or chi representation of the OSR. Normalization requires that b∗iα biβ F†α Fβ = χβα F†α Fβ = I. 16) iαβ αβ Taking the trace of this equation we find that χαα = d. 17) 18 The χαβ (t) matrix is a positive hermitian matrix which specifies the OSR in a given basis.

Suppose that instead of the environment being in the initial state |+ +| it is in the state |0 0|. In this case, if we us the basis |+ , |− to calculate the OSR we find that 1 A1 (t) = +|E (cos(λt)I − i sin(λt)σ z ⊗ σ z ) |0 E = √ (cos(λt)I − i sin(λt)σ z ) , 2 A2 (t) = −|E (cos(λt)I − i sin(λt)σ z ⊗ σ z ) |0 E = A1 (t). 24) 19 If we instead use the basis |0 , |1 to calculate the OSR, we find that ˜ 1 (t) = A ˜ 2 (t) = A 0|E (cos(λt)I − i sin(λt)σ z ⊗ σ z ) |0 1|E (cos(λt)I − i sin(λt)σ z ⊗ σ z ) |0 E E = (cos(λt)I − i sin(λt)σ z ) , = 0.

67) β=0 for α = 0. If we require the new basis to maintain the trace inner product, then Tr F†α Fβ = Tr ∗ gαµ gβν G†µ Gν = µ,ν ∗ gαν gβν = δαβ . 68) ν ∗ ∗ Thinking about gαν as a matrix, this implies that gαν is a unitary matrix. The non-Hamiltonian generator of the SME, Eq. 3) is defined as L [ρ] = 1 aαβ [Fα ρ, F†β ] + [Fα , ρF†β ] . 69) The change of basis, Eq. 67), transforms this generator to L [ρ] = 1 ∗ aαβ gαν gβµ [Gν ρ, G†µ ] + [Gν , ρG†µ ] . 71) where a′µν = ∗ aαβ gαν gβµ . 72) 29 ∗ Since gαν can be any unitary matrix, and aαβ is a hermitian matrix, we can choose ∗ gαν such that this matrix diagonalizes a′µν .

Download PDF sample

Rated 4.47 of 5 – based on 3 votes