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Locally observable conditions for the successful implementation of entangling multi-qubit quantum gates

Hofmann, H F, Okamoto, R, Takeuchi, S

Published Sep 1, 2005• 0 citations
OpenAlex

Abstract

The information obtained from the operation of a quantum gate on only two complementary sets of input states is sufficient to estimate the quantum process fidelity of the gate. In the case of entangling gates, these conditions can be used to predict the multi qubit entanglement capability from the fidelities of two non-entangling local operations. It is then possible to predict highly non-classical features of the gate such as violations of local realism from the fidelities of two completely classical input-output relations, without generating any actual entanglement.

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The information obtained from the operation of a quantum gate on only two complementary sets of input states is sufficient to estimate the quantum process fidelity of the gate. In the case of entangling gates, these conditions can be used to predict the multi qubit entanglement capability from the fidelities of two non-entangling local operations. It is then possible to predict highly non-classical features of the gate such as violations of local realism from the fidelities of two completely classical input-output relations, without generating any actual entanglement.
The information obtained from the operation of a quantum gate on only two complementary sets of input states is sufficient to estimate the quantum process fidelity of the gate. In the case of entangling gates, these conditions can be used to predict the multi qubit entanglement capability from the fidelities of two non-entangling local operations. It is then possible to predict highly non-classical features of the gate such as violations of local realism from the fidelities of two completely classical input-output relations, without generating any actual entanglement.
We define scalable benchmarks for two important quantum subroutines, namely the quantum Fourier transform (QFT) and the multi-controlled-Z gate. Our benchmarks are based on applying the subroutines to a set of states that are sufficient for lower-bounding the process fidelity from the set of measured output state fidelities. By randomly sampling from the set of input states, the lower boundonthe process fidelity can be estimated. We implement the QFT and multi-controlled-Z circuits with up to 20 and 12 qubits, respectively, on the Quantinuum H1-1 quantum computer. Our circuits make use of parameterized-angle entangling gates, which for these circuits reduces the number of two-qubit gates significantly.
Quantum entanglement, a fundamental phenomenon in quantum mechanics, presents a unique challenge to traditional computational methods. This paper explores the potential of utilizing entanglement to enhance quantum computation, specifically focusing on the development of a novel prediction algorithm predicated on the non-local nature of entangled states. We propose a method that leverages the inherent properties of entanglement to predict the state of quantum systems with improved accuracy. This research aims to address limitations in current quantum algorithms by providing a new approach to quantum state determination. The core mechanism involves the construction of a predictive model, utilizing entanglement's non-classical behavior, to accurately forecast quantum system properties. This work explores the potential implications of this algorithm for enhancing quantum computing capabilities and highlights its unique advantages.
Accurate characterization of two-qubit gates will be critical for any realization of quantum computation. We discuss a range of measurements for characterizing two-qubit gates. These measures are architecture-independent and span a range of complexity from simple measurement routines to full quantum-state and process tomography. Simple indicative measures, which flag but do not quantify gate operation in the quantum regime, include the fringe visibility, parity, Bell-state fidelity, and entanglement witnesses. Quantitative measures of gate output states include linear entropy and tangle; measures of, and error bounds to, whole-gate operation are provided by metrics such as process fidelity, process distance, and average gate fidelity. We discuss which measures are appropriate, given the stage of development of the gate, and highlight connections between them.
We propose a scheme to implement a two-qubit controlled-phase gate for single atomic qubits, which works in principle with nearly ideal success probability and fidelity. Our scheme is based on the cavity input-output process and the single-photon polarization measurement. We show that, even with the practical imperfections such as atomic spontaneous emission, weak atom-cavity coupling, violation of the Lamb-Dicke condition, cavity photon loss, and detection inefficiency, the proposed gate is feasible for generation of a cluster state in that it meets the scalability criterion and it operates in a conclusive manner. We demonstrate a simple and efficient process to generate a cluster state with our high probabilistic entangling gate.