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arXiv:1611.00204 · Annalen der Physik

Reliability of Digitized Quantum Annealing and the Decay of Entanglement

John P. S. Peterson, Roberto S. Sarthour, Alexandre M. Souza, Ivan S. Oliveira, Frederico Brito, Fernando de Melo

Published Jun 3, 2018• 2 citations
arXivHTMLPDF

Abstract

Abstract A banged‐digital‐analog simulation of a quantum annealing protocol is performed in a two‐qubit nuclear magnetic resonance (NMR) quantum computer. The experimental simulation employs up to 235 Trotter steps, with more than 2000 gates (pulses), and a protocol success above 80% is obtained. Given the exquisite control of the NMR quantum computer, the simulation is also performed with different noise levels. Thus, the reliability of the quantum annealing process is is analyzed, and it is related to the level of entanglement produced during the protocol. Although the presence of entanglement is not a sufficient signature for a better‐than‐classical simulation, the level of entanglement achieved relates to the fidelity of the protocol.

DOI
10.1002/andp.201800007

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•Jan 1, 2018•0 citations
Abstract A banged‐digital‐analog simulation of a quantum annealing protocol is performed in a two‐qubit nuclear magnetic resonance (NMR) quantum computer. The experimental simulation employs up to 235 Trotter steps, with more than 2000 gates (pulses), and a protocol success above 80% is obtained. Given the exquisite control of the NMR quantum computer, the simulation is also performed with different noise levels. Thus, the reliability of the quantum annealing process is is analyzed, and it is related to the level of entanglement produced during the protocol. Although the presence of entanglement is not a sufficient signature for a better‐than‐classical simulation, the level of entanglement achieved relates to the fidelity of the protocol.
The method of quantum annealing (QA) is a promising way for solving many optimization problems in both classical and quantum information theory. The main advantage of this approach, compared with the gate model, is the robustness of the operations against errors originated from both external controls and the environment. In this work, we succeed in demonstrating experimentally an application of the method of QA to a simplified version of the traveling salesman problem by simulating the corresponding Schr\"odinger evolution with a NMR quantum simulator. The experimental results unambiguously yielded the optimal traveling route, in good agreement with the theoretical prediction.
Simulations of nuclear magnetic resonance (NMR) experiments can be an important tool for extracting information about molecular structure and optimizing experimental protocols but are often intractable on classical computers for large molecules such as proteins and for protocols such as zero-field NMR. We demonstrate the first quantum simulation of an NMR spectrum, computing the zero-field spectrum of the methyl group of acetonitrile using four qubits of a trapped-ion quantum computer. We reduce the sampling cost of the quantum simulation by an order of magnitude using compressed sensing techniques. We show how the intrinsic decoherence of NMR systems may enable the zero-field simulation of classically hard molecules on relatively near-term quantum hardware and discuss how the experimentally demonstrated quantum algorithm can be used to efficiently simulate scientifically and technologically relevant solid-state NMR experiments on more mature devices. Our work opens a practical application for quantum computation.
Nuclear magnetic resonance (NMR) was successfully employed to test several protocols and ideas in quantum information science. In most of these implementations, the existence of entanglement was ruled out. This fact introduced concerns and questions about the quantum nature of such bench tests. In this paper, we address some issues related to the non-classical aspects of NMR systems. We discuss some experiments where the quantum aspects of this system are supported by quantum correlations of separable states. Such quantumness, beyond the entanglement-separability paradigm, is revealed via a departure between the quantum and the classical versions of information theory. In this scenario, the concept of quantum discord seems to play an important role. We also present an experimental implementation of an analogue of the single-photon Mach-Zehnder interferometer employing two nuclear spins to encode the interferometric paths. This experiment illustrates how non-classical correlations of separable states may be used to simulate quantum dynamics. The results obtained are completely equivalent to the optical scenario, where entanglement (between two field modes) may be present.
Abstract This work provides a simple approximate method of creating a Greenberger–Horne–Zeilinger (GHZ) state with high fidelity, using nuclear magnetic resonance (NMR) techniques, and reports on the decoherence process for these GHZ states, which is observed with a pair of encoder and decoder quantum circuits. The prepared GHZ states are verified by measuring the quantum correlations, which are well known as GHZ correlations. The results of the decoherence experiments, show that the GHZ states decay faster than bipartite entangled states such as Bell states by a factor of 1.3, and it appears that two different decoherence processes exist. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006
Digital–analog quantum computing (DAQC) offers a promising approach to addressing the challenges of building a practical quantum computer. By efficiently allocating resources between digital and analog quantum circuits, DAQC paves the way for achieving optimal performance. We propose an algorithm designed to enhance the performance of quantum annealing. This method employs a quantum gate to estimate the goodness of the final annealing state and find the ground state of combinatorial optimization problems. We explore two strategies for integrating the quantum annealing circuit into the DAQC framework: (1) state preparation, and (2) embedding within the quantum gate. While the former strategy does not yield performance improvements, we discover that the latter enhances performance within a specific range of annealing time. Algorithms demonstrating enhanced performance utilize the imaginary part of the inner product of two states from different quantum annealing settings. This measure reflects not only the energy of the classical cost function but also the trajectory of the quantum dynamics. This study provides an example of how processing quantum data using a quantum circuit can outperform classical data processing, which discards quantum information.
Quantum simulation is one of the most relevant applications of quantum computation for the near future, due to its scientific impact and also because quantum simulation algorithms are typically less demanding than generalized quantum computations. Ultimately, the success of a quantum simulation depends on the amount and reliability of information one is able to extract from the results. In such a context, this work reviews the theory behind quantum simulation, with a focus on digital quantum simulation. The concepts of efficiency and reliability in quantum simulations are discussed, particularly for implementations of digital simulation algorithms in state-of-the-art quantum computers. A review of approaches for quantum characterization, verification and validation techniques (QCVV) is also presented. A digital quantum simulation of the Schrödinger equation for a single particle in 1 spatial dimension was experimentally implemented and analyzed, along with a quantum state tomography procedure for characterization of the final quantum state and evaluation of simulation reliability. From the literature, it is shown that digital quantum simulation is theoretically sound and experimentally feasible, with several applications in a wide range of physics-related fields. Nonetheless, a number of conditions arise that must be observed for a truly efficient implementation of a digital quantum simulation, from theoretical conception to experimental circuit design. The review of QCVV techniques highlights the need for characterization and validation techniques that could be efficiently implemented for current models of quantum computation, particularly in instances where classical verification is not tractable. However, there are proposals for efficient verification procedures when a set of parameters defining the final result of the simulation is known. The experimental simulation demonstrated partial success in comparison with an ideal quantum simulation. From the results it is apparent that better coherence times, better reliability and finer control are as decisive for the advancement of quantum computing power as the more-publicized number of qubits of a given device.