The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the post-supremacy, noisy, intermediate scale era of quantum computing. In this work, we exploit the recently proposed digital-analog quantum computation paradigm, in which the versatility of programmable universal quantum computers and the error resilience of quantum simulators are combined to improve platforms for quantum computation. We show that the digital-analog paradigm is suited to the variational quantum approximate optimisation algorithm, due to its inherent resilience against coherent errors, by performing large-scale simulations and providing analytical bounds for its performance in devices with finite single-qubit operation times. We observe regimes of single-qubit operation speed in which the considered variational algorithm provides a significant improvement over non-variational counterparts.
We propose a method to simulate spin models in trapped ions using a digital-analog approach, consisting in a suitable gate decomposition in terms of analog blocks and digital steps. In this way, we show that the quantum dynamics of an enhanced variety of spin models could be implemented with substantially less number of gates than a fully digital approach. Typically, analog blocks are built of multipartite dynamics providing the complexity of the simulated model, while the digital steps are local operations bringing versatility to it. Finally, we describe a possible experimental implementation…
Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the evolution of classical computation, an alternative paradigm merging the flexibility of digital quantum computation with the robustness of analog quantum simulation has emerged. This universal paradigm is known as digital-analog quantum computing. Here, we introduce an efficient digital-analog quantum algorithm to compute the quantum Fourier transform, a subrout…
Quantum theory is extremely successful in explaining most physical phenomena, and is not contradicted by any experiment. Yet, the theory has many puzzling features : the occurrence of probabilities, the unclear distinction between the microscopic and the macroscopic, the unexplained absence of superpositions in positions of macroscopic objects, the dependence of the theory on an external classical time, and the experimentally verified but peculiar `influence' outside the light-cone in EPR experiments. These puzzles point towards a conflict between quantum theory and our present understanding o…
Quantum simulation can be implemented in pure digital or analog ways, each with their pros and cons. By taking advantage of the universality of a digital route and the efficiency of analog simulation, hybrid digital-analog approaches can enrich the possibilities for quantum simulation. We use a unique hybrid approach to experimentally perform a quantum simulation of phase-controlled dynamics resulting from a closed-contour interaction (CCI) within certain multi-level systems in superconducting quantum circuits. Due to symmetry constraints, such systems cannot host an inherent CCI. Nevertheless…
We solve a problem, which while not fitting into the usual paradigm, can be viewed as a quantum computation. Suppose we are given a quantum system described by an N dimensional Hilbert space with a Hamiltonian of the form $E |w >< w|$ where $| w>$ is an unknown (normalized) state. We show how to discover $| w >$ by adding a Hamiltonian (independent of $| w >$) and evolving for a time proportional to $N^{1/2}/E$. We show that this time is optimally short. This process is an analog analogue to Grover's algorithm, a computation on a conventional (!) quantum computer which locates a marked item fr…
I argue that both digital and analog information are important in the foundations of quantum physics. If it is possible for information present in one system to become present in others without being erased in the original system I will say that this information can be copied. I argue that copying is important for understanding issues like causality and that all information that can be copied is digital. I then explain that analog information that cannot be copied can be understood in terms of decision theoretic probability. Finally, I argue that these ideas can help explain the second law of …
Digital-analog quantum computation aims to reduce the currently infeasible resource requirements needed for near-term quantum information processing by replacing sequences of one- and two-qubit gates with a unitary transformation generated by the systems' underlying Hamiltonian. Inspired by this paradigm, we consider superconducting architectures and extend the cross-resonance effect, up to first order in perturbation theory, from a two-qubit interaction to an analog Hamiltonian acting on 1D chains and 2D square lattices which, in an appropriate reference frame, results in a purely two-local H…
Quantum computers based on superconducting circuits are experiencing a rapid development, aiming at outperforming classical computers in certain useful tasks in the near future. However, the currently available chip fabrication technologies limit the capability of gathering a large number of high-quality qubits in a single superconducting chip, a requirement for implementing quantum error correction. Furthermore, achieving high connectivity in a chip poses a formidable technological challenge. Here, we propose a hybrid digital-analog quantum algorithm that enhances the physical connectivity am…
Many quantum algorithms, such as Harrow-Hassidim-Lloyd (HHL) algorithm, depend on oracles that efficiently encode classical data into a quantum state. The encoding of the data can be categorized into two types; analog-encoding where the data are stored as amplitudes of a state, and digital-encoding where they are stored as qubit-strings. The former has been utilized to process classical data in an exponentially large space of a quantum system, where as the latter is required to perform arithmetics on a quantum computer. Quantum algorithms like HHL achieve quantum speedups with a sophisticated …
Measurement-free Preparation of Surface-Code States with Digital-Analog Counterdiabatic Drivings
Intelligent Data Analysis Laboratory (IDAL), Departament d’Enginyeria Electrònica, ETSE-UV, Universitat de València（瓦伦西亚大学电子工程系智能数据分析实验室）；Kipu Quantum（基普量子）
We propose a superconducting circuit architecture suitable for digital-analog quantum computing (DAQC) based on an enhanced NISQ family of nearest-neighbor interactions. DAQC makes a smart use of digital steps (single qubit rotations) and analog blocks (parametrized multiqubit operations) to outperform digital quantum computing algorithms. Our design comprises a chain of superconducting charge qubits coupled by superconducting quantum interference devices (SQUIDs). Using magnetic flux control, we can activate/deactivate exchange interactions, double excitation/de-excitations, and others. As a …
We propose a digital-analog quantum simulation of generalized Dicke models with superconducting circuits, including Fermi-Bose condensates, biased and pulsed Dicke models, for all regimes of light-matter coupling. We encode these classes of problems in a set of superconducting qubits coupled with a bosonic mode implemented by a transmission line resonator. Via digital-analog techniques, an efficient quantum simulation can be performed in state-of-the-art circuit quantum electrodynamics platforms, by suitable decomposition into analog qubit-bosonic blocks and collective single-qubit pulses thro…
In recent years, there has been a significant progress in the development of digital quantum processors. The state-of-the-art quantum devices are imperfect, and fully-algorithmic fault-tolerant quantum computing is a matter of future. Until technology develops to the state with practical error correction, computational approaches other than the standard digital one can be used to avoid execution of the most noisy quantum operations. We demonstrate how a hybrid digital-analog approach allows simulating dynamics of a transverse-field Ising model without standard two-qubit gates, which are curren…
Quantum simulations consist in the intentional reproduction of physical or unphysical models into another more controllable quantum system. Beyond establishing communication vessels between unconnected fields, they promise to solve complex problems which may be considered as intractable for classical computers. From a historic perspective, two independent approaches have been pursued, namely, digital and analog quantum simulations. The former usually provide universality and flexibility, while the latter allows for better scalability. Here, we review recent literature merging both paradigms in…
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 multi-qubit entangling blocks in an approach we call digital-analog quantum computing (DAQC). Along these lines, although the techniques may be extended to…
This paper is concerned with complexity theoretic aspects of a general formulation of quantum game theory that models strategic interactions among rational agents that process and exchange quantum information. In particular, we prove that the computational problem of finding an approximate Nash equilibrium in a broad class of quantum games is, like the analogous problem for classical games, included in (and therefore complete for) the complexity class PPAD. Our main technical contribution, which facilitates this inclusion, is an extension of prior methods in computational game theory to strate…
We consider the problem of mapping digital data encoded on a quantum register to analog amplitudes in parallel. It is shown to be unlikely that a fully unitary polynomial-time quantum algorithm exists for this problem; NP becomes a subset of BQP if it exists. In the practical point of view, we propose a nonunitary linear-time algorithm using quantum decoherence. It tacitly uses an exponentially large physical resource, which is typically a huge number of identical molecules. Quantumness of correlation appearing in the process of the algorithm is also discussed.
Digital quantum simulation (DQS) of continuous-variable quantum systems in the position basis requires efficient implementation of diagonal unitaries approximating the time evolution operator generated by the potential energy function. In this work, we provide efficient implementations suitable for potential functions approximable by piecewise polynomials, with either uniform or adaptively chosen subdomains. For a fixed precision of approximation, we show how adaptive grids can significantly reduce the total gate count at the cost of introducing a small number of ancillary qubits. We demonstra…
Quantum field theories are the cornerstones of modern physics, providing relativistic and quantum mechanical descriptions of physical systems at the most fundamental level. Simulating real-time dynamics within these theories remains elusive in classical computing. This provides a unique opportunity for quantum simulators, which hold the promise of revolutionizing our simulation capabilities. Trapped-ion systems are successful quantum-simulator platforms for quantum many-body physics and can operate in digital, or gate-based, and analog modes. Inspired by the progress in proposing and realizing…
