QUANTUM ERROR CORRECTION generate, create qrcode none on .net projects QR Code Features This spect qr-codes for .NET acular expansion of the scope of quantum states might not come as a complete surprise to the nonphysicist reader. I have stressed all along that the quantum state of a Qbit or a collection of Qbits is not a property carried by those Qbits, but a way of concisely summarizing everything we know that has happened to them, to enable us to make statistical predictions about the information we might then be able to extract from them.

If quantum states are not properties inherent in the system they describe, but states of the knowledge we have managed to acquire about the prior history of the system if they somehow incorporate fundamental aspects of how we exchange information with the world outside of us then they might indeed have an applicability going beyond the particular kinds of systems we have applied them to up until now. Indeed, nowhere in this exposition of quantum computation has it been necessary to refer to the individual character of the Qbits. Whether they are spinning electrons, polarized photons, atoms in cavities, or any number of other things, the quantum-mechanical description of their computational behavior has been exactly the same.

So insofar as the assignment of quantum states to physical systems is a general feature of how we come to grips with the external world, it might not be unreasonable to assign a quantum state . e to whate ver part of the world comes into interactive contact with the Qbit or Qbits their environment. We will not make any speci c assumptions about the character of that environment or of the quantum state . e associat qrcode for .NET ed with it, beyond noting that, unlike the state of a single Qbit, the state of the environment is likely to be a state in a space of enormously many dimensions if there is any complexity to the environment that couples, however weakly, to the Qbit. If, in spite of this recommended point of view, you still feel uncomfortable applying quantum states to noncomputational degrees of freedom, then I invite you to regard .

e as the s tate of some enormous collection of extra Qbits, from which one would like the computation to be completely decoupled, but which, for reasons beyond our control, somehow manage to interact weakly with the Qbits we are actually interested in. I offer this invitation as a conceptual aid to computer scientists uncomfortable with my claim that quantum states apply to the description of arbitrary physical systems. But I also note that in recent years a few physicists have suggested that the entire world should indeed be viewed as an enormous collection of Qbits a position that has not attracted many adherents to date.

Returning from grand world views to the practical reality of errors in a quantum computation, we shall regard a single Qbit, initially in the state . x (x = 0 o .NET qr codes r 1), as being part of a larger system consisting of the Qbit plus its environment, initially in the state . e . x . In the QR Code 2d barcode for .NET ideal case, as the Qbit evolves under 1-Qbit unitary gates or interacts with other Qbits under 2-Qbit unitary gates, it stays unentangled with.

5.3 THE PHYSICS OF ERROR GENERATION its enviro Denso QR Bar Code for .NET nment. The environmental component of the state is then irrelevant to the computational process and can be ignored, as we have been doing up to now.

Unfortunately, however, interactions with the environment will in general transform and entangle the states of the Qbit and its environment. The most general way in which this can come about can be expressed in the form . e . 0 . e 0 . 0 + . e 1 . 1 , . e . 1 . e 2 . 0 + . e 3 . 1 , (5.7). where e is the initially uncorrelated state of the environment and e 0 , . . .

, . e 3 are po VS .NET QRCode ssible nal environmental states. The environmental nal states are not necessarily orthogonal or normalized, and are constrained only by the requirement that the two states on the right side of (5.

7) should be orthogonal, since the Qbit environment interaction is required, like any other physical interaction, to lead to a unitary development in time. This corruption of a computation by the entanglement of the state of Qbits with the state of their environment is called decoherence. It is the primary enemy of quantum computation.

Included in (5.7) are cases like the oversimpli ed one we examined in Section 5.2, in which the Qbit remains isolated from the environment (.

e i = ai e , i = 0, Denso QR Bar Code for .NET . .

., 3) but still suffers in that isolation an unintended unitary evolution. But (5.

7) also includes the case of major practical interest. This is the case in which the interaction with the environment has a small but otherwise quite general entangling effect on the Qbit: . e 0 . e 3 . e ; e 1 e 1 , e 2 e 2 1. (5.8).

In dealing QR Code JIS X 0510 for .NET with such entangling interactions with the environment, it is useful to introduce projection operators.
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