Ideal Quantum Computer Research Articles

Ansatz optimization of the variational quantum eigensolver tested on the atomic Anderson model

We present a detailed analysis and optimization of the variational quantum algorithms required to find the ground state of a correlated electron model, using several types of variational ansatz. Specifically, we apply our approach to the atomic limit of the Anderson model, which is widely studied in condensed matter physics since it can simulate fundamental physical phenomena, ranging from magnetism to superconductivity. The method is developed by presenting efficient state preparation circuits that exhibit total spin, spin projection, particle number and time-reversal symmetries. These states contain the minimal number of variational parameters needed to fully span the appropriate symmetry subspace allowing to avoid irrelevant sectors of Hilbert space. Then, we show how to construct quantum circuits, providing explicit decomposition and gate count in terms of standard gate sets. We test these quantum algorithms looking at ideal quantum computer simulations as well as implementing quantum noisy simulations. We finally perform an accurate comparative analysis among the approaches implemented, highlighting their merits and shortcomings.

Navigating the noise-depth tradeoff in adiabatic quantum circuits

Adiabatic quantum algorithms solve computational problems by slowly evolving a trivial state to the desired solution. On an ideal quantum computer, the solution quality improves monotonically with increasing circuit depth. By contrast, increasing the depth in current noisy computers introduces more noise and eventually deteriorates any computational advantage. What is the optimal circuit depth that provides the best solution? Here, we address this question by investigating an adiabatic circuit that interpolates between the paramagnetic and ferromagnetic ground states of the one-dimensional quantum Ising model. We characterize the quality of the final output by the density of defects $d$, as a function of the circuit depth $N$ and noise strength $\sigma$. We find that $d$ is well-described by the simple form $d_\mathrm{ideal}+d_\mathrm{noise}$, where the ideal case $d_\mathrm{ideal}\sim N^{-1/2}$ is controlled by the Kibble-Zurek mechanism, and the noise contribution scales as $d_\mathrm{noise}\sim N\sigma^2$. It follows that the optimal number of steps minimizing the number of defects goes as $\sim\sigma^{-4/3}$. We implement this algorithm on a noisy superconducting quantum processor and find that the dependence of the density of defects on the circuit depth follows the predicted non-monotonous behavior and agrees well with noisy simulations. Our work allows one to efficiently benchmark quantum devices and extract their effective noise strength $\sigma$.

The Comparison of the computing ability of quantum and conventional computer

Contemporarily, whether quantum computing performs better than conventional computers remain an unresolved issue. In this paper, we compare the time complexity between quantum and conventional computers for a specific type of issue. Theoretically, quantum computation is better in solving nonlinear calculations, the quantitative evaluation of the computing ability should be investigated. In this paper, the Fourier transform was applied in both classical and quantum logical circuits to calculate the theoretical time complexities respectively and make a comparison after that. According to the analysis, the ideal quantum computer performed really fast as the number of tasks increased, but the gate-level accurate quantum circuit, which was a simulated circuit was running slower. The paper shows that the current technology cannot perform the perfect quantum computer, but the future of it would be very promising. Overall, these results shed light on guiding further exploration of quantum computing.

Assessing the Precision of Quantum Simulation of Many-Body Effects in Atomic Systems Using the Variational Quantum Eigensolver Algorithm

The emerging field of quantum simulation of many-body systems is widely recognized as a very important application of quantum computing. A crucial step towards its realization in the context of many-electron systems requires a rigorous quantum mechanical treatment of the different interactions. In this pilot study, we investigate the physical effects beyond the mean-field approximation, known as electron correlation, in the ground state energies of atomic systems using the classical-quantum hybrid variational quantum eigensolver algorithm. To this end, we consider three isoelectronic species, namely Be, Li−, and B+. This unique choice spans three classes—a neutral atom, an anion, and a cation. We have employed the unitary coupled-cluster ansätz to perform a rigorous analysis of two very important factors that could affect the precision of the simulations of electron correlation effects within a basis, namely mapping and backend simulator. We carry out our all-electron calculations with four such basis sets. The results obtained are compared with those calculated by using the full configuration interaction, traditional coupled-cluster and the unitary coupled-cluster methods, on a classical computer, to assess the precision of our results. A salient feature of the study involves a detailed analysis to find the number of shots (the number of times a variational quantum eigensolver algorithm is repeated to build statistics) required for calculations with IBM Qiskit’s QASM simulator backend, which mimics an ideal quantum computer. When more qubits become available, our study will serve as among the first steps taken towards computing other properties of interest to various applications such as new physics beyond the Standard Model of elementary particles and atomic clocks using the variational quantum eigensolver algorithm.

Error Mitigation and Quantum-Assisted Simulation in the Error Corrected Regime.

A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations to a universal set by the addition of "magic" quantum states. In this context, we develop a general framework to discuss the value of the available, nonideal magic resources, relative to those ideally required. We single out a quantity, the quantum-assisted robustness of magic (QROM), which measures the overhead of simulating the ideal resource with the nonideal ones through quasiprobability-based methods. This extends error mitigation techniques, originally developed for noisy intermediate-scale quantum devices, to the case where qubits are logically encoded. The QROM shows how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit and enables the construction of explicit protocols, interpolating between classical simulation and an ideal quantum computer.

The long journey from prototype to the ideal quantum computer

The long journey from prototype to the ideal quantum computer

Сравнение производительности пакетов симуляции квантовых вычислений QuEST и Intel-QS

In the nearest future quantum computers will be suitable for practical use. The development of quantum algorithms can be carried out using classical computers and specialized software that allows simulating of a quantum circuit functioning. Simulation results can be used to analyze the algorithm and also contribute to co-design when developing quantum architectures. However, when planning and performing numerical experiments, it is necessary to understand the capabilities of simulators and the limitations on the parameters of the quantum circuit imposed by the characteristics of the available classical computational resources (computers). This paper presents the results of computational experiments on simulating the operation of quantum circuits on an ideal quantum computer using the QuEST and Intel-QS packages, as well as our own "naïve" implementation. Restrictions on the size of a simulated quantum system N are shown when using computing systems of various classes — a virtual machine, a computing server, a computing server with a graphics accelerator (GPU), a supercomputer (the maximum achieved size is N = 33). The performance and scalability characteristics of the considered implementations on shared and distributed memory are given (the observed scaling efficiency is 30 % and 70 %, respectively). For the QuEST package and our own implementation the performance is presented for systems with graphics accelerator (GPU).

Report cools down quantum computing hype

A report released Dec. 4 by the National Academies of Sciences, Engineering, and Medicine throws some cold water on the hype smoldering around quantum computing. The report finds no commercially viable applications for near-term quantum computers that cannot already be tackled with conventional computers. Unlike conventional computers, which represent information digitally as 1s and 0s in electronic bits, quantum computers use qubits. During quantum calculations, qubits can hold more information than a simple 1 or 0, existing in a combination of states called a superposition. Because of these superpositions, quantum computers should be able to solve certain problems exponentially faster than classical supercomputers and perform calculations that cannot be performed by conventional devices. With an ideal quantum computer, chemists could accurately simulate complex chemical bonds and predict the structures of new drugs, semiconductors, and efficient catalysts. Physicists and computer scientists are sure that, once high-performance quantum computers can be built,

Efficient classical simulation of the Deutsch\u2013Jozsa and Simon\u2019s algorithms

A long-standing aim of quantum information research is to understand what gives quantum computers their advantage. This requires separating problems that need genuinely quantum resources from those for which classical resources are enough. Two examples of quantum speed-up are the Deutsch–Jozsa and Simon’s problem, both efficiently solvable on a quantum Turing machine, and both believed to lack efficient classical solutions. Here we present a framework that can simulate both quantum algorithms efficiently, solving the Deutsch–Jozsa problem with probability 1 using only one oracle query, and Simon’s problem using linearly many oracle queries, just as expected of an ideal quantum computer. The presented simulation framework is in turn efficiently simulatable in a classical probabilistic Turing machine. This shows that the Deutsch–Jozsa and Simon’s problem do not require any genuinely quantum resources, and that the quantum algorithms show no speed-up when compared with their corresponding classical simulation. Finally, this gives insight into what properties are needed in the two algorithms and calls for further study of oracle separation between quantum and classical computation.

Model dynamics for quantum computing

A model master equation suitable for quantum computing dynamics is presented. In an ideal quantum computer (QC), a system of qubits evolves in time unitarily and, by virtue of their entanglement, interfere quantum mechanically to solve otherwise intractable problems. In the real situation, a QC is subject to decoherence and attenuation effects due to interaction with an environment and with possible short-term random disturbances and gate deficiencies. The stability of a QC under such attacks is a key issue for the development of realistic devices. We assume that the influence of the environment can be incorporated by a master equation that includes unitary evolution with gates, supplemented by a Lindblad term. Lindblad operators of various types are explored; namely, steady, pulsed, gate friction, and measurement operators. In the master equation, we use the Lindblad term to describe short time intrusions by random Lindblad pulses. The phenomenological master equation is then extended to include a nonlinear Beretta term that describes the evolution of a closed system with increasing entropy. An external Bath environment is stipulated by a fixed temperature in two different ways. Here we explore the case of a simple one-qubit system in preparation for generalization to multi-qubit, qutrit and hybrid qubit–qutrit systems. This model master equation can be used to test the stability of memory and the efficacy of quantum gates. The properties of such hybrid master equations are explored, with emphasis on the role of thermal equilibrium and entropy constraints. Several significant properties of time-dependent qubit evolution are revealed by this simple study.

Practical Experimental Certification of Computational Quantum Gates Using a Twirling Procedure

Because of the technical difficulty of building large quantum computers, it is important to be able to estimate how faithful a given implementation is to an ideal quantum computer. The common approach of completely characterizing the computation process via quantum process tomography requires an exponential amount of resources, and thus is not practical even for relatively small devices. We solve this problem by demonstrating that twirling experiments previously used to characterize the average fidelity of quantum memories efficiently can be easily adapted to estimate the average fidelity of the experimental implementation of important quantum computation processes, such as unitaries in the Clifford group, in a practical and efficient manner with applicability in current quantum devices. Using this procedure, we demonstrate state-of-the-art coherent control of an ensemble of magnetic moments of nuclear spins in a single crystal solid by implementing the encoding operation for a 3-qubit code with only a 1% degradation in average fidelity discounting preparation and measurement errors. We also highlight one of the advances that was instrumental in achieving such high fidelity control.

Quantum computer simulation using the CUDA programming model

Quantum computing emerges as a field that captures a great theoretical interest. Its simulation represents a problem with high memory and computational requirements which makes advisable the use of parallel platforms. In this work we deal with the simulation of an ideal quantum computer on the Compute Unified Device Architecture (CUDA), as such a problem can benefit from the high computational capacities of Graphics Processing Units (GPU). After all, modern GPUs are becoming very powerful computational architectures which is causing a growing interest in their application for general purpose. CUDA provides an execution model oriented towards a more general exploitation of the GPU allowing to use it as a massively parallel SIMT (Single-Instruction Multiple-Thread) multiprocessor. A simulator that takes into account memory reference locality issues is proposed, showing that the challenge of achieving a high performance depends strongly on the explicit exploitation of memory hierarchy. Several strategies have been experimentally evaluated obtaining good performance results in comparison with conventional platforms.

Topologically protected quantum states and quantum computing in Josephson junctions arrays

We review recent results on a new class of Josephson arrays which have nontrivial topology and exhibit novel quantum states at low temperatures. One of these states is characterized by long-range order in a two-Cooper-pair condensate and by a discrete topological order parameter. The second state is insulating and can be considered as being the result of an evolution of the former state due to Bose-condensation of usual superconductive vortices with a flux quantum Φ0. The quantum phase transition between these two states is controlled by variation of the external magnetic field. Both the superconductive and insulating states are characterized by the presence of 2K-degenerate ground states, with K being the number of topologically different cycles existing in the plane of the array. This degeneracy is “protected” from the external perturbations (and noise) by the topological order parameter and spectral gap. We show that under ideal conditions the low-order effect of the external perturbations on this degeneracy is exactly zero and that deviations from ideality lead to only exponentially small effects of perturbations. We argue that this system provides a physical implementation of an ideal quantum computer with a built-in error correction. A number of relatively simple “echo-like” experiments possible on small-size arrays are discussed.

Discrete non-Abelian gauge theories in Josephson-junction arrays and quantum computation

We discuss real-space lattice models equivalent to gauge theories with a discrete non-Abelian gauge group. We construct the Hamiltonian formalism which is appropriate for their solid-state physics implementation and outline their basic properties. The unusual physics of these systems is due to local constraints on the degrees of freedom which are variables localized on the links of the lattice. We discuss two types of constraints that become equivalent after a duality transformation for Abelian theories but are qualitatively different for non-Abelian ones. We emphasize highly nontrivial topological properties of the excitations (fluxons and charges) in these non-Abelian discrete lattice gauge theories. We show that an implementation of these models may provide one with the realization of an ideal quantum computer, that is the computer that is protected from the noise and allows a full set of precise manipulations required for quantum computations. We suggest a few designs of the Josephson-junction arrays that provide the experimental implementations of these models and discuss the physical restrictions on the parameters of their junctions.

Possible realization of an ideal quantum computer in Josephson junction array

We introduce a class of Josephson arrays which have nontrivial topology and exhibit a novel state at low temperatures. This state is characterized by long-range order in a two Cooper pair condensate and by a discrete topological order parameter. These arrays have degenerate ground states with this degeneracy ``protected'' from the external perturbations (and noise) by the topological order parameter. We show that in ideal conditions the low order effect of the external perturbations on this degeneracy is exactly zero and that deviations from ideality lead to only exponentially small effects of perturbations. We argue that this system provides a physical implementation of an ideal quantum computer with a built-in error correction and show that even a small array exhibits interesting physical properties such as superconductivity with double charge, $4e,$ and extremely long decoherence times.