Quantum Wires Physics C191 Fall 2005 Youming Yang Scott Beamer GuanXiong Mao It is reasonable to assume that in the future any sophisticated quantum computational device of merit would to process many qubits necessarily be large Thus it is also reasonable to assume that such devices would require the ability to transport data and therefore qubits from one location to another The Kane proposal not only addresses this issue of transport but is also a holistic approach to quantum computing which allows for the implementation of the universal gates of quantum computing and also builds on the solid state foundation which has had decades of research and improvement That is the Kane proposal embraces the past few decades worth of development in the semiconductor industry and utilizes that framework to create a quantum computing system that is not only easily relatively implemented but also readily scalable Also like any architecture it must be relatively invulnerable to both decoherence and error buildup within the internal circuitry In this paper we ll examine how to resolve the latter problem which is often a nastier problem that can still be reasonably resolved given careful circuit design In doing so we will discuss how to build up individual error correcting elements together to form error correction procedures and examine what elements an overall error correction scheme needs to be successful as well as how that affects the design and ultimately architecture of the entire setup Youming Yang In the Kane proposal phosphorous ions are embedded into a substrate at specific intervals minimum spacing 15nm large enough to not interfere with each other when performing one qubit operations These qubits are controlled with classical metal wires placed above the ions When various alternating current signals are applied to these electrodes a field is created over the ions which can perform all the basic single qubit gates Wires are also placed above vacant areas between ions in order to facilitate two qubit gates maximum spacing 100nm These additional electrodes placed between the ions which are used to hold and shift electrons are used to implement the two qubit gates necessary for quantum computation A nominal value of ion spacing of 60nm is used by most of our sources Due to the nature of the solid state implementation interacting with spins of electrons surrounded by a lattice of atoms decoherence must be limited by operating in a very cold environment near absolute zero At this temperature there are very few components that can usefully interact with the qubit and still leave its data intact The main motivation for mentioning such a demanding operating environment is to point out the fact that a simple and literal ballistic qubit transport process where a qubit is physically displaced from one location to another is quite impractical Not only would it necessitate a device which can kinetically interact with the qubit but it would also require giving the qubit kinetic energy to transport it from one location to the next Such physical transport mechanisms aside from being foreign to the solid state world are also overshadowed by much simpler approaches as we shall see next Where the beauty of the Kane implementation comes in is its capability of effectively using a two qubit gate as a quantum wire By placing the phosphorous ions adjacently as described above it is possible to have a qubit s data be transported from one location to the other through acting the SWAP gate from qubit to qubit Essentially the electron whose spin contains the data is moved from phosphorous atom phosphorous atom using the gates allowing for transport of data Of course the fidelity or quality of the data which goes as an inverse exponential in time is exponentially dependent on how long it exists in qubit form and thus how long it couples and evolves with the environment Because the swap gates take roughly Overview of Wires one microsecond to execute per qubit and with the ions being 60nm apart the maximum theoretical wire length that qubits can be sent using the SWAP gate technique is roughly 6 micrometers Beyond this the qubit s data degradation will be too high beyond 10 4 to be considered acceptable by the Threshold Theorem Of course this is a strict theoretical limitation and no amount of carefulness on the implementation side can resolve this issue There is however another method whereby quantum teleportation can be utilized to transport qubits over longer distances In this method an EPR generator creates entangled qubit pairs and sends them to two locations one which contains the data to be transported and the other to the location the data is to be transported to During this transport the EPR pair couples to the environment and degrades in fidelity just as a normal qubit would However due to special characteristics of EPR pairs a process known as purification can be utilized to create an asymptotically perfect subset of EPR pairs from a larger original set of imperfect corrupted pairs After two presumably perfect EPR pairs are at either destination the process teleportation can be performed By enacting a CNOT data qubit being control on one EPR qubit and then measuring and sending the both measurements classically to the other EPR qubit the original data qubit can be reconstructed at the second EPR qubit s location An additional benefit of using transportation is having the option of sending EPR pairs to the two locations before there is even a need to transport data This data pre pipelining means that the time delay of transmitting information is only limited by the latency of a standard teleportation process which can for all intensive purposes be taken as a constant 20 microseconds Thus in the time it takes the short wire to transport data a mere micrometer the long wire implementation could have theoretically transported that data across centimeters As great as teleportation sounds there are still limitations that necessitate using both short purely SWAP based wires and long wires Of course it can be seen that for sake of latency alone it s more beneficial to use short wires for very short distances below 1 micrometer But also because the purification process generates a subset of asymptotically perfect EPR pairs this creates for a data quality fidelity that is independent of the number of swaps performed to teleport the pairs That is regardless of the distance of transport for long wires the