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arXiv:2306.02059 · APL Quantum

Enhancing quantum annealing in digital–analog quantum computing

Tadashi Kadowaki

Published Apr 2, 2024• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/5.0179540

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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.
Digital quantum computing paradigm offers highly desirable features such as universality, scalability, and quantum error correction. However, physical resource requirements to implement useful error-corrected quantum algorithms are prohibitive in the current era of NISQ devices. As an alternative path to performing universal quantum computation, within the NISQ era limitations, we propose to merge digital single-qubit operations with analog multiqubit entangling blocks in an approach we call digital-analog quantum computing (DAQC). Along these lines, although the techniques may be extended to any resource, we propose to use unitaries generated by the ubiquitous Ising Hamiltonian for the analog entangling block and we prove its universal character. We construct explicit DAQC protocols for efficient simulations of arbitrary inhomogeneous Ising, two-body, and MMM-body spin Hamiltonian dynamics by means of single-qubit gates and a fixed homogeneous Ising Hamiltonian. Additionally, we compare a sequential approach where the interactions are switched on and off (stepwise DAQC) with an always-on multiqubit interaction interspersed by fast single-qubit pulses (banged DAQC). Finally, we perform numerical tests comparing purely digital schemes with DAQC protocols, showing a remarkably better performance of the latter. The proposed DAQC approach combines the robustness of analog quantum computing with the flexibility of digital methods.
Digital-analog quantum computing (DAQC) combines digital gates with analog operations, offering an alternative paradigm for universal quantum computation. This approach leverages the higher fidelities of analog operations and the flexibility of local single-qubit gates. In this paper, we propose a quantum genetic algorithm within the DAQC framework using a Rydberg-atom emulator. The algorithm employs single-qubit operations in the digital domain and a global driving interaction based on the Rydberg Hamiltonian in the analog domain. We evaluate the algorithm performance by estimating the ground-state energy of Hamiltonians, with a focus on molecules such as H2,LiH{\mathrm{H}}_{2}, \mathrm{LiH}H2​,LiH, and BeH2{\mathrm{BeH}}_{2}BeH2​. Our results show energy estimations with less than 1% error and state overlaps nearing 1, with computation times ranging from a few minutes for H2{\mathrm{H}}_{2}H2​ (two-qubit circuits) to one to two days for LiH\mathrm{LiH}LiH and BeH2{\mathrm{BeH}}_{2}BeH2​ (six-qubit circuits). The gate fidelities of global analog operations further underscore DAQC as a promising quantum computing strategy in the noisy intermediate-scale quantum era.
Abstract Quantum computing uses quantum resources provided by the underlying quantum nature of matter to enhance classical computation. However, the current Noisy Intermediate-Scale Quantum (NISQ) era in quantum computing is characterized by the use of quantum processors comprising from a few tens to, at most, a few hundreds of physical qubits without implementing quantum error correction techniques. This limits the scalability in the implementation of quantum algorithms. Digital-analog quantum computing (DAQC) has been proposed as a more resilient alternative quantum computing paradigm to outperform digital quantum computation within the NISQ era framework. It arises from adding the flexibility provided by fast single-qubit gates to the robustness of analog quantum simulations. Here, we perform a careful comparison between the digital and digital-analog paradigms under the presence of noise sources. The comparison is illustrated by comparing the performance of the quantum Fourier transform and quantum phase estimation algorithms under a wide range of single- and two-qubit noise sources. Indeed, we obtain that when the different noise channels usually present in superconducting quantum processors are considered, the fidelity of these algorithms for the digital-analog paradigm outperforms the one obtained for the digital approach. Additionally, this difference grows when the size of the processor scales up, making DAQC a sensible alternative paradigm in the NISQ era. Finally, we show how to adaptthe DAQC paradigm to quantum error mitigation techniques for canceling different noise sources, including the bang error.
Digital-analog quantum computing (DAQC) is a universal computational paradigm that combines the evolution under an entangling Hamiltonian with the application of single-qubit gates. Since any unitary operation can be decomposed into a sequence of evolutions generated by two-body Hamiltonians, DAQC is inherently well-suited for realizing such operations. Suboptimal upper bounds for the total time required to perform these evolutions have been previously proposed. Here, we improve these limits by providing a tight bound for this crucial parameter, which shows a linear dependence with the number of couplings. This result enables a precise estimation of the time resources needed for quantum simulations and quantum algorithms implemented within the DAQC framework, facilitating a rigorous comparison with other approaches.
Digital-Analog Quantum Computation (DAQC) has recently been proposed as an alternative to the standard paradigm of digital quantum computation. DAQC creates entanglement through a continuous or analog evolution of the whole device, rather than by applying two-qubit gates. This manuscript describes an in-depth analysis of DAQC by extending its implementation to arbitrary connectivities and by performing the first systematic study of its scaling properties. We specify the analysis for three examples of quantum algorithms, showing that except for a few specific cases, DAQC is in fact disadvantageous with respect to the digital case.
Abstract Noisy Intermediate-Scale Quantum (NISQ) devices lack error correction, limiting scalability for quantum algorithms. In this context, digital-analog quantum computing (DAQC) offers a more resilient alternative quantum computing paradigm that outperforms digital quantum computation by combining the flexibility of single-qubit gates with the robustness of analog simulations. This work explores the impact of noise on both digital and DAQC paradigms and demonstrates DAQC’s effectiveness in error mitigation. We compare the quantum Fourier transform and quantum phase estimation algorithms under a wide range of single and two-qubit noise sources in superconducting processors. DAQC consistently surpasses digital approaches in fidelity, particularly as processor size increases. Moreover, zero-noise extrapolation further enhances DAQC by mitigating decoherence and intrinsic errors, achieving fidelities above 0.95 for 8 qubits, and reducing computation errors to the order of 10 −3 . These results establish DAQC as a viable alternative for quantum computing in the NISQ era.