Since the publication of the Quantum Amplitude Estimation (QAE) algorithm by Brassard et al., 2002, several variations have been proposed, such as Aaronson et al., 2019, Grinko et al., 2019, and Suzuki et al., 2020. The main difference between the original and the variants is the exclusion of Quantum Phase Estimation (QPE) by the latter. This difference is notable given that QPE is the key component of original QAE, but is composed of many operations considered expensive for the current NISQ era devices. We compare two recently proposed variants (Grinko et al., 2019 and Suzuki et al., 2020) by implementing them on the IBM Quantum device using Qiskit, an open source framework for quantum computing. We analyze and discuss advantages of each algorithm from the point of view of their implementation and performance on a quantum computer.
It is hard to achieve a theoretical quantum advantage on NISQ devices. Besides the attempts to reduce error using error mitigation and dynamical decoupling, small quantum error correction and fault-tolerant schemes that reduce the high overhead of traditional schemes have also been proposed. According to the recent advancements in fault tolerance, it is possible to minimize the number of ancillary qubits using flags. While implementing those schemes is still impossible, it is worthwhile to bridge the gap between the NISQ era and the FTQC era. Here, we introduce a benchmarking method to test fa…
The ability to generate large-scale entanglement is an important progenitor of quantum information processing capability in noisy intermediate-scale quantum (NISQ) devices. In this paper, we investigate the extent to which entangled quantum states over large numbers of qubits can be prepared on current superconducting quantum devices. We prepared native-graph states on the IBM Quantum 65-qubit $\textit{ibmq_manhattan}$ device and the 53-qubit $\textit{ibmq_rochester}$ device and applied quantum readout-error mitigation (QREM). Connected entanglement graphs spanning each of the full devices wer…
Kernel methods are the basis of most classical machine learning algorithms such as Gaussian Process (GP) and Support Vector Machine (SVM). Computing kernels using noisy intermediate scale quantum (NISQ) devices has attracted considerable attention due to recent progress in the design of NISQ devices. However noise and errors on current NISQ devices can negatively affect the predicted kernels. In this paper we utilize two quantum kernel machine learning (ML) algorithms to predict the labels of a Breast Cancer dataset on two different NISQ devices: quantum kernel Gaussian Process (qkGP) and quan…
One of the greatest challenges for current quantum computing hardware is how to obtain reliable results from noisy devices. A recent paper [A. Kandala et al., Nature 567, 491 (2019)] described a method for injecting noise by stretching gate times, enabling the calculation of quantum expectation values as a function of the amount of noise in the IBM-Q devices. Extrapolating to zero noise led to excellent agreement with exact results. Here an alternative scheme is described that employs the intentional addition of identity pulses, pausing the device periodically in order to gradually subject the…
Quantum network coding has been proposed to improve resource utilization to support distributed computation but has not yet been put in to practice. We investigate a particular implementation of quantum network coding using measurement-based quantum computation on IBM Q processors. We compare the performance of quantum network coding with entanglement swapping and entanglement distribution via linear cluster states. These protocols outperform quantum network coding in terms of the final Bell pair fidelities but are unsuitable for optimal resource utilization in complex networks with contention…
The performance of quantum computers today can be studied by analyzing the effect of errors in the result of simple quantum algorithms. The modeling and characterization of these errors is relevant to correct them, for example, with quantum correcting codes. In this article we characterize the error of the five qubits quantum computer ibmqx4 (IBM Q), using a Deutsch algorithm and modeling the error by Generalized Amplitude Damping (GAD) and a unitary misalignment operation. Keywords: Quantum Deutsch's algorithm, Quantum error models, IBM Quantum Experience
In this paper, we implement a quantum algorithm -on IBM quantum devices, IBM QASM simulator and PPRC computer cluster -to find the energy values of the ground state and the first excited state of a particle in a finite square-well potential. We use the quantum phase estimation technique and the iterative one to execute the program on PPRC cluster and IBM devices, respectively. Our results obtained from executing the quantum circuits on the IBM classical devices show that our circuits succeed at simulating the system. However, duo to scattered results, we execute only the iterative phase estima…
Two qubit density matrices, which are of X-shape, are a natural generalization of Bell Diagonal States (BDSs) recently simulated on the IBM quantum device. We generalize the previous results and propose a quantum circuit for simulation of a general two qubit X-state, implement it on the same quantum device, and study its entanglement for several values of the extended parameter space. We also show that their X-shape is approximately robust against noisy quantum gates. To further physically motivate this study, we invoke the two-spin Heisenberg XYZ system and show that for a wide class of initi…
Entanglement is an important evidence that a quantum device can potentially solve problems intractable for classical computers. In this paper, we prepare connected graph states involving 8 to 16 qubits on ibmqx5, a 16-qubit superconducting quantum processor accessible via IBM cloud,using low-depth circuits. We demonstrate that the prepared state is fully entangled, i.e. the state is inseparable with respect to any fixed partition.
The ability of pulse-shaping devices to generate accurately quantum optimal control is a strong limitation to the development of quantum technologies. We propose and demonstrate a systematic procedure to design robust digital control processes adapted to such experimental constraints. We show to what extent this digital pulse can be obtained from its continuous-time counterpart. A remarkable efficiency can be achieved even for a limited number of pulse parameters. We experimentally implement the protocols on IBM quantum computers for a single qubit, obtaining an optimal robust transfer in a ti…
We report the digital quantum simulation of a hamiltonian involved in the generation of quantum entanglement by gravitational means. In particular, we focus on a pair of quantum harmonic oscillators, whose interaction via a quantum gravitational field generates single-mode squeezing in both modes at the same time, a non-standard process in quantum optics. We perform a boson-qubit mapping and a digital gate decomposition specific for IBM quantum devices. We use error mitigation and post-selection to achieve high-fidelity, accessing a parameter regime out of direct experimental reach.
The intractability of deterministic solutions in solving $\mathcal{NP}$-Hard Combinatorial Optimisation Problems (COP) is well reported in the literature. One mechanism for overcoming this difficulty has been the use of efficient COP non-deterministic approaches. However, with the advent of quantum technology, these modern devices' potential to overcome this tractability limitation requires exploration. This paper juxtaposes classical and quantum optimisation algorithms' performance to solve two common COP, the Travelling Salesman Problem (TSP) and the Quadratic Assignment Problem (QAP). Two a…
The advent of Noisy Intermediate-Scale Quantum (NISQ) technology is changing rapidly the landscape and modality of research in quantum physics. NISQ devices, such as the IBM Q Experience, have very recently proven their capability as experimental platforms accessible to everyone around the globe. Until now, IBM Q Experience processors have mostly been used for quantum computation and simulation of closed systems. Here we show that these devices are also able to implement a great variety of paradigmatic open quantum systems models, hence providing a robust and flexible testbed for open quantum …
We present results on the digital quantum simulations of beam-splitter and squeezing interactions. The bosonic hamiltonians are mapped to qubits and then digitalized in order to implement them in the IBM quantum devices. We use error mitigation and post-selection to achieve high-fidelity digital quantum simulations of single-mode and two-mode interactions, as evidenced -- where possible -- by full tomography of the resulting states. We achieve fidelities above 90 \% in the case of single-mode squeezing with low squeezing values and ranging from 60 \% to 90 \% for large squeezing and in the mor…
We use quantum detector tomography to characterize the qubit readout in terms of measurement POVMs on IBM Quantum Computers IBM Q 5 Tenerife and IBM Q 5 Yorktown. Our results suggest that the characterized detector model deviates from the ideal projectors by a few percent. Further improvement on this characterization can be made by adopting two- or more-qubit detector models instead of independent single-qubit detectors for all the qubits in one device. An unexpected behavior was seen in the physical qubit labelled as qubit 3 of IBM Q 5 Tenerife, which can be a consequence of detector crosstal…
Quantum secret sharing is a way to share secret messages among the clients in a group with complete security. For the first time, Hillery et al. (Phys Rev A 59:1829, 1999) proposed the quantum version of the classical secret sharing protocol using GHZ states. Here, we implement the above quantum secret sharing protocol in 'IBM Q 5 Tenerife' quantum processor and compare the experimentally obtained results with the theoretically predicted ones. Further, a new quantum binary voting protocol is proposed and implemented in the 14-qubit 'IBM Q 14 Melbourne' quantum processor. The results are analyz…
Department of Engineering and Architecture - University of Parma（帕尔马大学工程与建筑系）；Quantum Information Science - University of Parma（帕尔马大学量子信息科学系）；Department of Engineering and Architecture - University of Parma, Italy（意大利帕尔马大学工程与建筑系）；Quantum Information Science - University of Parma, Italy（意大利帕尔马大学量子信息科学系）
Quantum compiling means fast, device-aware implementation of quantum algorithms (i.e., quantum circuits, in the quantum circuit model of computation). In this paper, we present a strategy for compiling IBM Q -aware, low-depth quantum circuits that generate Greenberger-Horne-Zeilinger (GHZ) entangled states. The resulting compiler can replace the QISKit compiler for the specific purpose of obtaining improved GHZ circuits. It is well known that GHZ states have several practical applications, including quantum machine learning. We illustrate our experience in implementing and querying a uniform q…
Wichita State University（威奇托州立大学）；Boeing Research & Technology（波音研究与技术部）
Bayesian Networks (BN) are probabilistic graphical models that are widely used for uncertainty modeling, stochastic prediction and probabilistic inference. A Quantum Bayesian Network (QBN) is a quantum version of the Bayesian network that utilizes the principles of quantum mechanical systems to improve the computational performance of various analyses. In this paper, we experimentally evaluate the performance of QBN on various IBM QX hardware against Qiskit simulator and classical analysis. We consider a 4-node BN for stock prediction for our experimental evaluation. We construct a quantum cir…
We characterize for the first time the performances of IBM quantum chips as quantum batteries, specifically addressing the single-qubit Armonk processor. By exploiting the Pulse access enabled to some of the IBM Quantum processors via the Qiskit package, we investigate advantages and limitations of different profiles for classical drives used to charge these miniaturized batteries, establishing the optimal compromise between charging time and stored energy. Moreover, we consider the role played by various possible initial conditions on the functioning of the quantum batteries. As main result o…
Vertex amplitudes are elementary contributions to the transition amplitudes in the spin foam models of quantum gravity. The purpose of this article is make the first step towards computing vertex amplitudes with the use of quantum algorithms. In our studies we are focused on a vertex amplitude of 3+1 D gravity, associated with a pentagram spin-network. Furthermore, all spin labels of the spin network are assumed to be equal $j=1/2$, which is crucial for the introduction of the \emph{intertwiner qubits}. A procedure of determining modulus squares of vertex amplitudes on universal quantum comput…
Based on the connection between the categorical derivation of classical programs from specifications and the category-theoretic approach to quantum physics, this paper contributes to extending the laws of classical program algebra to quantum programming. This aims at building correct-by-construction quantum circuits to be deployed on quantum devices such as those available at the IBM Q Experience. Quantum circuit reversibility is ensured by minimal complements, extended recursively. Measurements are postponed to the end of such recursive computations, termed "quantamorphisms", thus maximising …
Spin-1 tunneling and splitting of energy levels as a result of tunneling are observed explicitly on IBM's quantum computer, ibmq-bogota. The spin-1 is realized with two spins-1/2. We detect oscillations of spin-1 between the states $|1\rangle$, $|-1\rangle$ in the result of tunneling on the basis of studies of the time dependence of the mean value of z-component of spin-1 on the quantum device. The energy level splitting is observed quantifying on the IBM's quantum computer the eigenvalues of Hamiltonian which describes the spin tunneling.
Near-term quantum devices are subject to errors and decoherence error is one of the non-negligible sources. Dynamical decoupling (DD) is a well-known technique to protect idle qubits from decoherence error. However, the optimal approach to inserting DD sequences still remains unclear. In this paper, we identify different conditions that lead to idle qubits and evaluate strategies for DD insertion under these specific conditions. Specifically, we divide the idle qubit into crosstalk-idle or idle-idle qubit depending on its coupling with other qubits and report the DD insertion strategies for th…
Hardware-Efficient Error Mitigation and Shot-Efficient Sampling on IBM Quantum Hardware
Quantum Information and Computation Centre, Department of Physics and Department of Computer Science and Engineering, Indian Institute of Technology Jodhpur（印度焦特普尔理工学院）
Designing quantum algorithms for simulating quantum systems has seen enormous progress, yet few studies have been done to develop quantum algorithms for open quantum dynamics despite its importance in modeling the system-environment interaction found in most realistic physical models. In this work we propose and demonstrate a general quantum algorithm to evolve open quantum dynamics on quantum computing devices. The Kraus operators governing the time evolution can be converted into unitary matrices with minimal dilation guaranteed by the Sz.-Nagy theorem. This allows the evolution of the initi…
It is well known that Grover's algorithm asymptotically transforms an equal superposition state into an eigenstate (of a given basis). Here, we demonstrate a verification algorithm based on weak measurement which can achieve the same purpose even if the qubit is not in an equal superposition state. The proposed algorithm highlights the distinguishability between any arbitrary single qubit superposition state and an eigenstate. We apply this algorithm to propose the scheme of a Quantum Locker, a protocol in which any legitimate party can verify his/her authenticity by using a newly developed qu…
Logical error estimation from syndrome data of surface-code experiments
Duke Quantum Center, Duke University（杜克量子中心，杜克大学）；Department of Electrical and Computer Engineering, Duke University（电气与计算机工程系，杜克大学）；Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid（马德里自治大学-西班牙国家科研委员会理论物理研究所，马德里自治大学）；Department of Electrical & Computer Engineering, University of Southern California（电气与计算机工程系，南加州大学）；Center for Quantum Information Science & Technology, University of Southern California（量子信息与科技中心，南加州大学）；Quantum Elements, Inc.（量子元素公司）；Department of Physics & Astronomy, University of Southern California（物理与天文学系，南加州大学）；Department of Chemistry, University of Southern California（化学系，南加州大学）；Department of Physics, Duke University（物理系，杜克大学）；Department of Chemistry, Duke University（化学系，杜克大学）
Simulating quantum systems is believed to be one of the first applications for which quantum computers may demonstrate a useful advantage. For many problems in physics, we are interested in studying the evolution of the electron-phonon Hamiltonian, for which efficient digital quantum computing schemes exist. Yet to date, no accurate simulation of this system has been produced on real quantum hardware. In this work, we consider the absolute resource cost for gate-based quantum simulation of small electron-phonon systems as dictated by the number of Trotter steps and bosonic energy levels necess…
When noisy intermediate scalable quantum (NISQ) devices are applied in information processing, all of the stages through preparation, manipulation, and measurement of multipartite qubit states contain various types of noise that are generally hard to be verified in practice. In this work, we present a scheme to deal with unknown quantum noise and show that it can be used to mitigate errors in measurement readout with NISQ devices. Quantum detector tomography that identifies a type of noise in a measurement can be circumvented. The scheme applies single-qubit operations only, that are with rela…
Readout errors are among the most dominant errors on current noisy intermediate-scale quantum devices. Recently, an efficient and scaleable method for mitigating such errors has been developed, based on classical bit-flip correction. In this talk, we compare the performance of this method for IBM's and Rigetti's quantum devices, demonstrating how the method improves the noisy measurements of observables obtained on the quantum hardware. Moreover, we examine the variance amplification to the data after applying of our mitigation procedure, which is common to all mitigation strategies. We derive…
Superconducting quantum computing technology has ushered in a new era of computational possibilities. While a considerable research effort has been geared toward improving the quantum technology and building the software stack to efficiently execute quantum algorithms with reduced error rate, effort toward optimizing how quantum output states are defined and classified for the purpose of reducing the error rate is still limited. To this end, this paper proposes DisQ, a quantum output state classification approach which reduces error rates of quantum programs on NISQ devices.
Quantum state preparation by adiabatic evolution is currently rendered ineffective by the long implementation times of the underlying quantum circuits, comparable to the decoherence time of present and near-term quantum devices. These implementation times can be significantly reduced by realizing the evolution with a minimal number of customized gates. Employing a realistic model of a two-qubit processor, we carried out classical device-level simulations of the adiabatic evolution of a two-spin system implemented with customized two-qubit gates. These device-level simulations were compared wit…
Quantum teleportation enables networking participants to move an unknown quantum state between the nodes of a quantum network, and hence constitutes an essential element in constructing large-sale quantum processors with a quantum modular architecture. Herein, we propose two protocols for teleporting qubits through an N-node quantum network in a highly-entangled box-cluster state or chain-type cluster state. The proposed protocols are systematically scalable to an arbitrary finite number N and applicable to arbitrary size of modules. The protocol based on a box-cluster state is implemented on …
Realizing a conceptual quantum algorithm on an actual physical device necessitates the algorithm's quantum circuit description to undergo certain transformations in order to adhere to all constraints imposed by the hardware. In this regard, the individual high-level circuit components are first synthesized to the supported low-level gate-set of the quantum computer, before being mapped to the target's architecture---utilizing several optimizations in order to improve the compilation result. Specialized tools for this complex task exist, e.g., IBM's Qiskit, Google's Cirq, Microsoft's QDK, or Ri…
Random unitary matrices sampled from the uniform Haar ensemble have a number of important applications both in cryptography and in the simulation of a variety of fundamental physical systems. Since the Haar ensemble is very expensive to sample, pseudorandom ensembles in the form of t-designs are frequently used as an efficient substitute, and are sufficient for most applications. We investigate t-designs generated using a measurement-based approach on superconducting quantum computers. In particular, we implemented an exact single-qubit 3-design on IBM quantum processors by performing measurem…
The advent of noisy intermediate-scale quantum (NISQ) devices offers crucial opportunities for the development of quantum algorithms. Here we evaluate the noise tolerance of two quantum neural network (QNN) architectures on IBM's NISQ devices, namely, dissipative QNN (DQNN) whose building-block perceptron is a completely positive map, and the quantum approximate optimization algorithm (QAOA). We compare these two approaches to learning an unknown unitary. While both networks succeed in this learning task, we find that a DQNN learns an unknown unitary more reliably than QAOA and is less suscept…
Topological data analysis is a rapidly developing area of data science where one tries to discover topological patterns in data sets to generate insight and knowledge discovery. In this project we use quantum walk algorithms to discover features of a data graph on which the walk takes place. This can be done faster on quantum computers where all paths can be explored using superposition. We begin with simple walks on a polygon and move up to graphs described by higher dimensional meshes. We use insight from the physics description of quantum walks defined in terms of probability amplitudes to …
