M. Stay
May25-04, 01:33 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>I\'m trying to figure out how to simulate the evolution of two systems\nof qubits, originally separate, but now brought together. I can get\nthe Hamiltonian for the combined system without interactions:\nH_1 (X) I + I (X) H_2 (where I is the suitable identity)\nbut any interactions between them need to conserve energy, and I\'m not\nsure how to do that. It seems like the only allowed things would be\nto do something like rotate the basis between energy states with the\nsame energy, but that seems to ignore the difficulty of distinguishing\nstates that are nearly degenerate.\n\nFor instance, say I have one system A in a ground state that\'s easily\nconstructed but very unlikely. There are zillions of ways for it to\nbe in an excited state with energy E. I put this in contact with a\nsystem B in the superposition of two states whose energy difference is\nE. I\'d expect it to evolve into a superposition of states:\n1) A in ground state, B in low state\n2) A in ground state, B in high state\n3) the new possibility due to interaction: A in excited state, B in\nlow state\n\nIt shouldn\'t be able to go to A excited, B high state, because the\nenergy to excite A has to come from B. Most descriptions of absorbing\na photon that I\'ve seen assume the absorbtion is from an external\nfield rather than from another subsystem.\n\nIt also seems like it ought to take a long time if E is small.\n\nAny suggestions?\n--\nMike Stay\nstaym@clear.net.nz\nhttp://www.cs.auckland.ac.nz/~msta039\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>I'm trying to figure out how to simulate the evolution of two systems
of qubits, originally separate, but now brought together. I can get
the Hamiltonian for the combined system without interactions:
H_1 (X) I + I (X) H_2 (where I is the suitable identity)
but any interactions between them need to conserve energy, and I'm not
sure how to do that. It seems like the only allowed things would be
to do something like rotate the basis between energy states with the
same energy, but that seems to ignore the difficulty of distinguishing
states that are nearly degenerate.
For instance, say I have one system A in a ground state that's easily
constructed but very unlikely. There are zillions of ways for it to
be in an excited state with energy E. I put this in contact with a
system B in the superposition of two states whose energy difference is
E. I'd expect it to evolve into a superposition of states:
1) A in ground state, B in low state
2) A in ground state, B in high state
3) the new possibility due to interaction: A in excited state, B in
low state
It shouldn't be able to go to A excited, B high state, because the
energy to excite A has to come from B. Most descriptions of absorbing
a photon that I've seen assume the absorbtion is from an external
field rather than from another subsystem.
It also seems like it ought to take a long time if E is small.
Any suggestions?
--
Mike Stay
staym@clear.net.nz
http://www.cs.auckland.ac.nz/~msta039
of qubits, originally separate, but now brought together. I can get
the Hamiltonian for the combined system without interactions:
H_1 (X) I + I (X) H_2 (where I is the suitable identity)
but any interactions between them need to conserve energy, and I'm not
sure how to do that. It seems like the only allowed things would be
to do something like rotate the basis between energy states with the
same energy, but that seems to ignore the difficulty of distinguishing
states that are nearly degenerate.
For instance, say I have one system A in a ground state that's easily
constructed but very unlikely. There are zillions of ways for it to
be in an excited state with energy E. I put this in contact with a
system B in the superposition of two states whose energy difference is
E. I'd expect it to evolve into a superposition of states:
1) A in ground state, B in low state
2) A in ground state, B in high state
3) the new possibility due to interaction: A in excited state, B in
low state
It shouldn't be able to go to A excited, B high state, because the
energy to excite A has to come from B. Most descriptions of absorbing
a photon that I've seen assume the absorbtion is from an external
field rather than from another subsystem.
It also seems like it ought to take a long time if E is small.
Any suggestions?
--
Mike Stay
staym@clear.net.nz
http://www.cs.auckland.ac.nz/~msta039