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Register a new userProposed Experiment in Two-Qubit Linear Optical Photonic Gates for Maximal Success Rates
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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.
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Numerical optimization is used to design linear-optical devices that implement a desired quantum gate with perfect fidelity, while maximizing the success rate. For the 2-qubit CS (or CNOT) gate, we provide numerical evidence that the maximum success rate is $S=2/27$ using two unentangled ancilla resources; interestingly, additional ancilla resources do not increase the success rate. For the 3-qubit Toffoli gate, we show that perfect fidelity is obtained with only three unentangled ancilla photons -- less than in any existing scheme -- with a maximum $S=0.00340$. This compares well with $S=(2/27)^2/2 approx 0.00274$, obtainable by combining two CNOT gates and a passive quantum filter [PRA 68, 064303 (2003)]. The general optimization approach can easily be applied to other areas of interest, such as quantum error correction, cryptography, and metrology [arXiv:0807.4906, PRL 99 070801 (2007)].
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.
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.
Near-term quantum computers are limited by the decoherence of qubits to only being able to run low-depth quantum circuits with acceptable fidelity. This severely restricts what quantum algorithms can be compiled and implemented on such devices. One way to overcome these limitations is to expand the available gate set from single- and two-qubit gates to multi-qubit gates, which entangle three or more qubits in a single step. Here, we show that such multi-qubit gates can be realized by the simultaneous application of multiple two-qubit gates to a group of qubits where at least one qubit is involved in two or more of the two-qubit gates. Multi-qubit gates implemented in this way are as fast as, or sometimes even faster than, the constituent two-qubit gates. Furthermore, these multi-qubit gates do not require any modification of the quantum processor, but are ready to be used in current quantum-computing platforms. We demonstrate this idea for two specific cases: simultaneous controlled-Z gates and simultaneous iSWAP gates. We show how the resulting multi-qubit gates relate to other well-known multi-qubit gates and demonstrate through numerical simulations that they would work well in available quantum hardware, reaching gate fidelities well above 99 %. We also present schemes for using these simultaneous two-qubit gates to swiftly create large entangled states like Dicke and Greenberg-Horne-Zeilinger states.
We propose two optimal phase-estimation schemes that can be used for quantum-enhanced long-baseline interferometry. By using distributed entanglement, it is possible to eliminate the loss of stellar photons during transmission over the baselines. The first protocol is a sequence of gates using nonlinear optical elements, optimized over all possible measurement schemes to saturate the Cramer-Rao bound. The second approach builds on an existing protocol, which encodes the time of arrival of the stellar photon into a quantum memory. Our modified version reduces both the number of ancilla qubits and the number of gate operations by a factor of two.
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