Digital-analog is a universal quantum computing paradigm which employs the natural entangling Hamiltonian of the system and single-qubit gates as resources. Here, we study the stability of these protocols against Hamiltonian characterization errors. For this, we bound the maximum separation between the target and the implemented Hamiltonians. Additionally, we obtain an upper bound for the deviation in the expected value of an observable. We further propose a protocol for mitigating calibration errors which resembles dynamical-decoupling techniques. These results open the possibility of scaling digital-analog to intermediate and large scale systems while having an estimation on the errors committed.
Digital-analog is a universal quantum computing paradigm which employs the natural entangling Hamiltonian of the system and single-qubit gates as resources. Here, we study the stability of these protocols against Hamiltonian characterization errors. For this, we bound the maximum separation between the target and the implemented Hamiltonians. Additionally, we obtain an upper bound for the deviation in the expected value of an observable. We further propose a protocol for mitigating calibration errors which resembles dynamical-decoupling techniques. These results open the possibility of scaling digital-analog to intermediate and large scale systems while having an estimation on the errors committed.
Digital-analog is a universal quantum computing paradigm which employs the natural entangling Hamiltonian of the system and single-qubit gates as resources.Here, we study the stability of these protocols against Hamiltonian characterization errors.For this, we bound the maximum separation between the target and the implemented Hamiltonians.Additionally, we obtain an upper bound for the deviation in the expected value of an observable.We further propose a protocol for mitigating calibration errors which resembles dynamical-decoupling techniques.These results open the possibility of scaling digital-analog to intermediate and large scale systems while having an estimation on the errors committed.
Digital-analog is a quantum computational paradigm that employs the natural interaction Hamiltonian of a system as the entangling resource, combined with single qubit gates, to implement universal quantum operations. As in the case of its digital gate-based counterpart, designing digital-analog circuits that employ optimal quantum resources often requires an exceedingly large classical computational time. In this work we find a suboptimal solution to this exponentially large problem, showing that it can be solved within polynomial computational time. In particular, we provide an exact solution for the problem of expressing arbitrary two-body Hamiltonians as the sum of local unitary transformations of an arbitrary Ising Hamiltonian, with the total number of required terms being at most quadratic in system size. This allows us to design a digital-analog simulation protocol that avoids employing numerical optimization over a large parameter space at the preprocessing stage, minimizing computational resources and allowing for further scaling.
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 M-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.
Quantum simulation and computing traditionally has been based on two main paradigms, namely, digital and analog. In the digital paradigm, usually single and two-qubit gates (where qubit is an acronym for quantum bit) are employed as building blocks for scalable, universal quantum computing, although errors add up fast and error correction will be ultimately needed for scaling up. In the analog paradigm, large analog blocks are normally employed for a unitary dynamics that carries out the computation, enabling quantum operations on many qubits with reduced errors, but with the drawback of a limited choice of evolutions and lack of universality. In the past decade, a new paradigm has emerged, showing interesting possibilities for quantum simulation and computing in the near and mid term. This is the paradigm of digital-analog quantum technologies, which proposes to combine the best of both paradigms: large analog blocks, provided by native interactions of the employed quantum platform, enabling scalability, combined with digital gates, allowing for more versatility and, ultimately, universality. In this Perspective, I give an overview of the evolution of the field along the past decade, and an outlook for its future possibilities.
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.