Generic Two-Qubit Photonic Gates Implemented by Number-Resolving Photodetection

We combine numerical optimization techniques [Uskov et al., Phys. Rev. A 79, 042326 (2009)] with symmetries of the Weyl chamber to obtain optimal implementations of generic linear-optical KLM-type two-qubit entangling gates. We find that while any two-qubit controlled-U gate, including CNOT and CS, can be implemented using only two ancilla resources with success probability S > 0.05, a generic SU(4) operation requires three unentangled ancilla photons, with success S > 0.0063. Specifically, we obtain a maximal success probability close to 0.0072 for the B gate. We show that single-shot implementation of a generic SU(4) gate offers more than an order of magnitude increase in the success probability and two-fold reduction in overhead ancilla resources compared to standard triple-CNOT and double-B gate decompositions.Comment: 5 pages, 3 figure

General linear-optical quantum state generation scheme: Applications to maximally path-entangled states

We introduce schemes for linear-optical quantum state generation. A quantum state generator is a device that prepares a desired quantum state using product inputs from photon sources, linear-optical networks, and postselection using photon counters. We show that this device can be concisely described in terms of polynomial equations and unitary constraints. We illustrate the power of this language by applying the Grobner-basis technique along with the notion of vacuum extensions to solve the problem of how to construct a quantum state generator analytically for any desired state, and use methods of convex optimization to identify bounds to success probabilities. In particular, we disprove a conjecture concerning the preparation of the maximally path-entangled |n,0)+|0,n) (NOON) state by providing a counterexample using these methods, and we derive a new upper bound on the resources required for NOON-state generation.Comment: 5 pages, 2 figure

Proposed Experiment in Two-Qubit Linear Optical Photonic Gates for Maximal Success Rates

Here we propose an experiment in Linear Optical Quantum Computing (LOQC) using the framework first developed by Knill, Laflamme, and Milburn. This experiment will test the ideas of the authors' previous work on imperfect LOQC gates using number-resolving photon detectors. We suggest a relatively simple physical apparatus capable of producing CZ gates with controllable fidelity less than 1 and success rates higher than the current theoretical maximum (S=2/27) for perfect fidelity. These experimental setups are within the reach of many experimental groups and would provide an interesting experiment in photonic quantum computing.Comment: 9 pages, 3 figure

Optimal Fusion Transformations for Linear Optical Cluster State Generation

We analyze the generation of linear optical cluster states (LOCS) via addition of one and two qubits. Existing approaches employ the stochastic linear optical two-qubit CZ gate with success rate of 1/9 per fusion operation. The question of optimality of the CZ gate with respect to LOCS generation remains open. We report that there are alternative schemes to the CZ gate that are exponentially more efficient and show that sequential LOCS growth is globally optimal. We find that the optimal cluster growth operation is a state transformation on a subspace of the full Hilbert space. We show that the maximal success rate of fusing n photonic qubits or m Bell pairs is 1/2^n-1 and 1/4^m-1 respectively and give an explicit optical design

Dephasing times in quantum dots due to elastic LO phonon-carrier collisions

Interpretation of experiments on quantum dot (QD) lasers presents a challenge: the phonon bottleneck, which should strongly suppress relaxation and dephasing of the discrete energy states, often seems to be inoperative. We suggest and develop a theory for an intrinsic mechanism for dephasing in QD's: second-order elastic interaction between quantum dot charge carriers and LO-phonons. The calculated dephasing times are of the order of 200 fs at room temperature, consistent with experiments. The phonon bottleneck thus does not prevent significant room temperature dephasing.Comment: 4 pages, 1 figure, accepted for Phys. Rev. Let

Imperfect Linear Optical Photonic Gates with Number-Resolving Photodetection

We use the numerical optimization techniques of Uskov et al. [PRA 81, 012303 (2010)] to investigate the behavior of the success rates for KLM style [Nature 409, 46 (2001)] two- and three-qubit entangling gates. The methods are first demonstrated at perfect fidelity, and then extended to imperfect gates. We find that as the perfect fidelity condition is relaxed, the maximum attainable success rates increase in a predictable fashion depending on the size of the system, and we compare that rate of increase for several gates.Comment: 7 pages, 7 figure