the mit press quantum computing without magic devices sep 2008

[...]... that the physical embodiment of the bit, which the flip-flop “remembers,” is the electric charge stored on the gate of the transistor located in the upper nand gate of the flip-flop circuit If there is an accumulation of positive charge on the transistor’s gate, the Q line of the flip-flop becomes 0; and if the charge has drained from the gate, the Q line becomes 1 The Q line itself merely provides us with the. .. experiment clarifies the muddled notion of what constitutes a quantum measurement and, at the same time, is strikingly quantum computational” in its concepts and methodology The last major chapter of the book, Chapter 6 puts together all the physics and mathematics developed in the previous chapters to strike at the heart of quantum computing: the controlled-not gate We discuss here the notion of quantum gate... Table 1.2 This is indeed the table of a nand gate The important point to observe in the context of our considerations is that it is the presence or the absence of the charge on the transistor gate that determines the value of the output line If there is no accumulation of positive charge on the gate, the output line is set to 0; if there is a sufficient positive charge on the gate, the output line is set... representing bits do not have sharp edges Rather, there are transients, and these must be analyzed rigorously at the circuit design stage in order to eliminate unexpected faulty behavior On the other hand, the presence or the absence of the pebble in the box apparently represents two distinct, separate states There are no transients here The pebble either is or is not in the box Tertium non datur Yet, let us... add a pebble again to the box at the bottom, nothing much happens, because there is no other pebble in it, and so the state of the register becomes as shown below • • But fireworks fly again when we add a yet another pebble to the box at the bottom of the stack • • → bang! → •• → bang! → •• The first bang occurs because there are two pebbles in the first box The pebbles annihilate, and the energy released... state On the first application of the pulse to the clock input, A toggles to 1 on Register states the trailing edge of the pulse and stays there The state of the register becomes {C = 0, B = 0, A = 1} On the second application of the clock pulse A toggles back to 0, but this change now toggles B to 1, and so the state of the register becomes {C = 0, B = 1, A = 0} On the next trailing edge of the clock... “almost The following figure shows an example of a box and a pebble register that displays quantum some features that are reminiscent of quantum physics register The register contains three boxes stacked vertically Their position corresponds to the energy of a pebble that may be placed in a box The higher the location of the box, the higher the energy of the pebble The pebbles that are used in the register... charge drains from the gate of the transistor Consequently its channel blocks and the output of the circuit ends up being 1 On the other hand, if both inputs are set to 1, both diodes block In this case positive charge flows toward the gate of the transistor and accumulates there, and the transistor channel conducts This sets the potential on the output line to 0 The resulting truth table of the device is... cross-coupled nand gates It is easy to analyze the behavior of the circuit Let us suppose R is set to 0 and S is set to 1 If R is 0, then regardless of what the second input to the nand gate at the bottom is, its output must be 1 Therefore the second input to the nand gate at the top is 1, and so its output Q must be 0 The fact that the roles of R and S in the device are completely symmetric implies that... {101}—there may be some toggle switches to do this on the side of the package—its bits start to fluctuate randomly so that the register spends only 72% of the time in the {101} configuration and 28% of the time in every other configuration, flickering at random between them3 Let us assume that the same happens when the register is set to hold other numbers, {000}, {001}, , {111} as well; that is, the . Gabriele Jost, and Ruud van der Pas, 2008 Quantum Computing without Magic Devices Zdzislaw Meglicki The MIT Press Cambridge, Massachusetts London, England c  2008 Massachusetts Institute of Technology All. puts together all the physics and mathematics developed in the previous chapters to strike at the heart of quantum computing: the controlled-not gate. We discuss here the notion of quantum gate universality. reader will find an engaging account of the necessary theory and the experiments that confirm the theory. Along the way the reader will be introduced to many of the most interesting results of modern