Gates for the Kane Quantum Computer in the Presence of Dephasing

In this paper we investigate the effect of dephasing on proposed quantum gates for the solid-state Kane quantum computing architecture. Using a simple model of the decoherence, we find that the typical error in a CNOT gate is $8.3 \times 10^{-5}$. We also compute the fidelities of Z, X, Swap, and Controlled Z operations under a variety of dephasing rates. We show that these numerical results are comparable with the error threshold required for fault tolerant quantum computation.Comment: 9 pages, 9 figure

Robust two-qubit gates for donors in silicon controlled by hyperfine interactions

We present two strategies for performing two-qubit operations on the electron spins of an exchange-coupled pair of phosphorus donors in silicon, using the ability to set the donor nuclear spins in arbitrary states. The effective magnetic detuning of the two electron qubits is provided by the hyperfine interaction when the $^{31}$P nuclei are prepared in opposite spin states. This can be exploited to switch on and off SWAP operations with modest tuning of the electron exchange interaction. Furthermore, the hyperfine detuning enables high-fidelity conditional rotation gates based on selective resonant excitation. The latter requires no dynamic tuning of the exchange interaction at all, and offers a very attractive scheme to implement two-qubit logic gates under realistic experimental conditions.Comment: 8 pages, 3 figure

Optimising Matrix Product State Simulations of Shor's Algorithm

We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on $r$, the solution to the underlying order-finding problem of Shor's algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping.Comment: 8 pages, 2 figures, 2 tables. v2 using PDFLaTeX compiler. v3 to include extra references. v4 for publication in Quantu

Legislating by Proxy: Did President Obama Amend the Texas Labor Code When He Signed the Lilly Ledbetter Fair Pay Act?

Does the Texas Labor Code permit Congress to amend Texas law by proxy? Specifically, does the Texas Commission on Human Rights Act automatically incorporate Title VII amendments? This is the question posed to Texas courts and federal courts interpreting the limitations period for filing employment discrimination claims with the Texas Workforce Commission. Despite almost two decades of court precedent interpreting Texas\u27s equal employment opportunity law, the answer is anything but clear. With the passage of the Lilly Ledbetter Fair Pay Act, Texas courts must decide whether the law automatically incorporates the federal act or not. Given Title VII\u27s deference to state law, the answer might seem simple. But, relying on the Texas Labor Code\u27s correlative policy statement, when interpreting vagaries in Texas equal employment opportunity law, Texas courts have historically looked to federal case law interpreting Title VII for guidance. Does this practice mean that the Texas Labor Code must now automatically incorporate the Lilly Ledbetter Fair Pay Act because federal case law will now include it? This is the dilemma facing Texas courts. This Comment will discuss how courts, including some outside of Texas, have handled this question. Using these court opinions, this Comment will show why the Texas Labor Code does not support automatic incorporation. Additionally, this Comment recommends a legislative solution. By amending the correlative policy statement that Texas courts have used as justification for seeking guidance from federal case law, the Texas legislature can easily head off future automatic incorporation questions, sparing judicial resources and adding stability to Texas\u27s equal employment opportunity law

Weak measurement and control of entanglement generation

In this paper we show how weak joint measurement and local feedback can be used to control entanglement generation between two qubits. To do this, we make use of a decoherence free subspace (DFS). Weak measurement and feedback can be used to drive the system into this subspace rapidly. Once within the subspace, feedback can generate entanglement rapidly, or turn off entanglement generation dynamically. We also consider, in the context of weak measurement, some of differences between purification and generating entanglement

Robust CNOT gates from almost any interaction

There are many cases where the interaction between two qubits is not precisely known, but single qubit operations are available. In this paper we show how, regardless of an incomplete knowledge of the strength or form of the interaction between two qubits, it is often possible to construct a CNOT gate which has arbitrarily high fidelity. In particular, we show that oscillations in the strength of the exchange interaction in solid state Si and Ge structures are correctable.Comment: 5 pages, 2 figure