ABSTRACT
The three-spin-1/2 decoherence-free subsystem defines a logical qubit protected from collective noise and supports exchange-only universal gates. Such logical qubits are well suited for implementation with electrically defined quantum dots. Exact exchange-only entangling logical gates exist but are challenging to construct and understand. We use a decoupling strategy to obtain straightforward approximate entangling gates. A benefit of the strategy is that, if the physical spins are aligned, then it can implement evolution under entangling Hamiltonians. Hamiltonians expressible as linear combinations of logical Pauli products not involving σ y can be implemented directly. Self-inverse gates that are constructible from these Hamiltonians, such as the controlled-not (cnot) gate, can be implemented without the assumption on the physical spins. We compare the control complexity of implementing cnot to previous methods and find that the complexity for fault-tolerant fidelities is competitive.
ABSTRACT
General relativity predicts the gravitational wave signatures of coalescing binary black holes. Explicit waveform predictions for such systems, required for optimal analysis of observational data, have so far been achieved primarily using the post-Newtonian (PN) approximation. The quality of this treatment is unclear, however, for the important late-inspiral portion. We derive late-inspiral waveforms via a complementary approach, direct numerical simulation of Einstein's equations. We compare waveform phasing from simulations of the last approximately 14 cycles of gravitational radiation from equal-mass, nonspinning black holes with the corresponding 2.5PN, 3PN, and 3.5PN orbital phasing. We find phasing agreement consistent with internal error estimates for either approach, suggesting that PN waveforms for this system are effective until the last orbit prior to final merger.
