Although the performance of hybrid quantum-classical algorithms is highly dependent on the selection of the classical optimizer and the circuit ansatz, a robust and thorough assessment on-hardware of such features has been missing to date. From the optimizer perspective, the primary challenge lies in the solver's stochastic nature, and their significant variance over the random initialization. Therefore, a robust comparison requires that one perform several training curves for each solver before one can reach conclusions about their typical performance. Since each of the training curves requires the execution of thousands of quantum circuits in the quantum computer, such a robust study remained a steep challenge for most hybrid platforms available today. Here, we leverage on Rigetti's Quantum Cloud Services to overcome this implementation barrier, and we study the on-hardware performance of the data-driven quantum circuit learning (DDQCL) for three different state-of-the-art classical solvers, and on two-different circuit ansatze associated to different entangling connectivity graphs for the same task. Additionally, we assess the gains in performance from varying circuit depths. To evaluate the typical performance associated with each of these settings in this benchmark study, we use at least five independent runs of DDQCL towards the generation of quantum generative models capable of capturing the patterns of the canonical Bars and Stripes data set.
Parametrized quantum circuits initialized with random initial parameter values are characterized by barren plateaus where the gradient becomes exponentially small in the number of qubits. In this technical note we theoretically motivate and empirically validate an initialization strategy which can resolve the barren plateau problem for practical applications. The technique involves randomly selecting some of the initial parameter values, then choosing the remaining values so that the circuit is a sequence of shallow blocks that each evaluates to the identity. This initialization limits the eff…
Despite all the progress in quantum technologies over the last decade, there is still a dearth of practical applications for quantum computers with a small number of noisy qubits. The effort to show quantum supremacy has been largely focused on demonstrating computations that cannot be accomplished on a classical computer at all, a difficult and controversial target. Quantum advantage (a speedup over classical computers) is a more practical milestone for today's modest quantum processors. In this work, we proposed a scheme for quantum-computer compatible proof of work (cryptographic mechanism …
Parametrized quantum optical circuits are a class of quantum circuits in which the carriers of quantum information are photons and the gates are optical transformations. Classically optimizing these circuits is challenging due to the infinite dimensionality of the photon number vector space that is associated to each optical mode. Truncating the space dimension is unavoidable, and it can lead to incorrect results if the gates populate photon number states beyond the cutoff. To tackle this issue, we present an algorithm that is orders of magnitude faster than the current state of the art, to re…
When compared to fault-tolerant quantum computational strategies, variational quantum algorithms stand as one of the candidates with the potential of achieving quantum advantage for real-world applications in the near term. However, the optimization of the circuit parameters remains arduous and is impeded by many obstacles such as the presence of barren plateaus, many local minima in the optimization landscape, and limited quantum resources. A non-random initialization of the parameters seems to be key to the success of the parametrized quantum circuits (PQC) training. Drawing and extending id…
Isfahan University of Technology（伊斯法罕理工大学）；Shahid Bahonar University of Kerman（克尔曼沙希德·巴霍纳尔大学）；University of Basque Country UPV/EHU（巴斯克大学（UPV/EHU））
In this paper, we develop a compositional vector-based semantics of positive transitive sentences in quantum natural language processing for a non-English language, i.e. Persian, to compare the parametrized quantum circuits of two synonymous sentences in two languages, English and Persian. By considering grammar+meaning of a transitive sentence, we translate DisCoCat diagram via ZX-calculus into quantum circuit form. Also, we use a bigraph method to rewrite DisCoCat diagram and turn into quantum circuit in the semantic side.
Parametrized-circuit-free quantum regression with variance regularization
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；Faculty of Physics, M.V. Lomonosov Moscow State University（莫斯科国立大学物理系）
Estimates of loss function concentration in noisy parametrized quantum circuits
University of Trieste（的里雅斯特大学）；Istituto Nazionale di Fisica Nucleare, Trieste Section（意大利国家核物理研究所，的里雅斯特分部）；European Organization for Nuclear Research (CERN)（欧洲核子研究组织（CERN））
Motivated by the recent success of realizing the topologically ordered ground state of the exactly solvable toric code model by a quantum circuit on the real quantum device [K. J. Satzinger {\it et al}., Science \textbf{374}, 1237 (2021)], here we propose a parametrized quantum circuit (PQC) with the same real-device-performable optimal structure to represent quantum loop gas states with adjustably weighted loop configurations. Combining such a PQC with the variational quantum eigensolver, we obtain the accurate quantum circuit representation for the toric code model in an external magnetic fi…
Imperial College London（伦敦帝国理工学院）；National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies（量子科技中心）
To harness the potential of noisy intermediate-scale quantum devices, it is paramount to find the best type of circuits to run hybrid quantum-classical algorithms. Key candidates are parametrized quantum circuits that can be effectively implemented on current devices. Here, we evaluate the capacity and trainability of these circuits using the geometric structure of the parameter space via the effective quantum dimension, which reveals the expressive power of circuits in general as well as of particular initialization strategies. We assess the expressive power of various popular circuit types a…
Probabilistic Design of Parametrized Quantum Circuits through Local Gate Modifications
The Edward S. Rogers Sr. Department of Electrical \& Computer Engineering, University of Toronto 10 King's College Rd Toronto ON M5S 3G8 Canada；Department of Chemical；Physical Sciences, University of Toronto Mississauga 3359 Mississauga Road Mississauga ON L5L 1C6 Canada；Department of Computer Science, University of Toronto Toronto ON M5S 2E4 Canada；Vector Institute for Artificial Intelligence 108 College St W1140 Toronto ON M5G 0C6 Canada；The Edward S. Rogers Sr. Department of Electrical \& Computer Engineering, University of Toronto 10 King's College Rd Toronto ON M5G 0C6 Canada；Department of Chemistry, University of Calgary 2500 University Drive NW Calgary AB T2N 1N4 Canada；Department of Computer Science, University of Toronto 40 St. George Street Toronto ON M5S 2E4 Canada；The Edward S. Rogers Sr. Department of Electrical \& Computer Engineering, University of Toronto；Physical Sciences, University of Toronto Mississauga；Department of Computer Science, University of Toronto；Vector Institute for Artificial Intelligence；Department of Chemistry, University of Calgary
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Theoretical Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室理论部）；Center for Nonlinear Studies, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室非线性研究中心）
Variational quantum algorithms (VQAs) optimize the parameters $\vecθ$ of a parametrized quantum circuit $V(\vecθ)$ to minimize a cost function $C$. While VQAs may enable practical applications of noisy quantum computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming $V(\vecθ)$ is an alternating layered ansatz composed of blocks forming local 2-designs. Our first result states that defining $C$ in terms of global observables leads to exponentially vanishing gradients (i.e., barren plateaus) even when $V(\vecθ)$ is shallow. Hence, …
We explicitly construct a quantum circuit which exactly generates random three-qubit states. The optimal circuit consists of three CNOT gates and fifteen single qubit elementary rotations, parametrized by fourteen independent angles. The explicit distribution of these angles is derived, showing that the joint distribution is a product of independent distributions of individual angles apart from four angles.
Recent advancements in quantum computing have shown promising computational advantages in many problem areas. As one of those areas with increasing attention, hybrid quantum-classical machine learning systems have demonstrated the capability to solve various data-driven learning tasks. Recent works show that parameterized quantum circuits (PQCs) can be used to solve challenging reinforcement learning (RL) tasks with provable learning advantages. While existing works yield potentials of PQC-based methods, the design choices of PQC architectures and their influences on the learning tasks are gen…
Generative AI Beyond Tokens: Quantum Resource Consumption of IQP Circuits
Technical University of Applied Sciences Regensburg（雷根斯堡应用技术大学）；Universität der Bundeswehr München（联邦国防军慕尼黑大学）；Siemens AG, Foundational Technology（西门子股份公司基础技术部门）
Parametrized Quantum Circuit Learning for Quantum Chemical Applications
The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, 10 King's College Road, Toronto, Ontario, Canada M5S 3G4（电气与计算机工程系，多伦多大学）；Department of Chemical and Physical Sciences, University of Toronto Mississauga, 3359 Mississauga Road, Mississauga, Ontario, Canada L5L 1C6（化学与物理科学系，多伦多大学滑铁卢分校）
Are multi-layer parameterized quantum circuits (MPQCs) more expressive than classical neural networks (NNs)? How, why, and in what aspects? In this work, we survey and develop intuitive insights into the expressive power of MPQCs in relation to classical NNs. We organize available sources into a systematic proof on why MPQCs are able to generate probability distributions that cannot be efficiently simulated classically. We first show that instantaneous quantum polynomial circuits (IQPCs), are unlikely to be simulated classically to within a multiplicative error, and then show that MPQCs effici…
In this work we experimentally demonstrate how generative model training can be used as a benchmark for small ($<5$ qubits) quantum devices. Performance is quantified using three data analytic metrics: the Kullbeck-Leiber divergence, and two adaptations of the F1 score. Using the $2\times2$ Bars and Stripes dataset, we determine optimal circuit constructions for generative model training on superconducting qubits by including hardware connectivity constraints into circuit design. We show that on noisy hardware sparsely connected, shallow circuits out-perform denser counterparts.
In the current noisy intermediate-scale quantum (NISQ) era, quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. In quantum machine learning, the gates of a quantum circuit are parametrized, and the parameters are tuned via classical optimization based on data and on measurements of the outputs of the circuit. Parametrized quantum circuits (PQCs) can efficiently address combinatorial optimization problems, implement probabilistic generative models, and carry out inference (classification and regression). This monograph provides a self-contained i…
Parameterized quantum circuits (PQCs), as one of the most promising schemes to realize quantum machine learning algorithms on near-term quantum computers, have been designed to solve machine earning tasks with quantum advantages. In this paper, we explain why PQCs with different structures can achieve generative tasks in the discrete case from the perspective of probability estimation. Although different kinds of PQCs are proposed for generative tasks, the current methods often encounter the following three hurdles: (1) the mode contraction problem; (2) unexpected data are often generated with…
Hybrid quantum-classical algorithms provide ways to use noisy intermediate-scale quantum computers for practical applications. Expanding the portfolio of such techniques, we propose a quantum circuit learning algorithm that can be used to assist the characterization of quantum devices and to train shallow circuits for generative tasks. The procedure leverages quantum hardware capabilities to its fullest extent by using native gates and their qubit connectivity. We demonstrate that our approach can learn an optimal preparation of the Greenberger-Horne-Zeilinger states, also known as "cat states…
Molecular quantum simulations with the variational quantum eigensolver (VQE) rely on ansatz states that approximate the molecular ground states. These ansatz states are generally defined by parametrized fermionic excitation operators and an initial reference state. Efficient ways to perform fermionic excitations are vital for the realization of the VQE on noisy intermediate-scale quantum computers. Here, we address this issue by first demonstrating circuits that perform qubit excitations, excitations that do not account for fermionic anticommutation relations. We then extend the functionality …
Generative learning of time series with holographic quantum circuit sampling
University of Southern California（南加州大学）；Applied Quantum Software（应用量子软件）；Triaxiom Capital, LLC（Triaxiom资本有限责任公司）；Department of Physics and Astronomy, University of Southern California（南加州大学物理与天文学系）
Variational quantum algorithms, which utilize Parametrized Quantum Circuits (PQCs), are promising tools to achieve quantum advantage for optimization problems on near-term quantum devices. Their PQCs have been conventionally constructed from parametrized rotational angles of single-qubit gates around predetermined set of axes, and two-qubit entangling gates, such as CNOT gates. We propose a method to construct a PQC by continuous parametrization of both the angles and the axes of its single-qubit rotation gates. The method is based on the observation that when rotational angles are fixed, opti…
We propose a hybrid quantum-classical approach to model continuous classical probability distributions using a variational quantum circuit. The architecture of the variational circuit consists of two parts: a quantum circuit employed to encode a classical random variable into a quantum state, called the quantum encoder, and a variational circuit whose parameters are optimized to mimic a target probability distribution. Samples are generated by measuring the expectation values of a set of operators chosen at the beginning of the calculation. Our quantum generator can be complemented with a clas…
Machine learning is seen as a promising application of quantum computation. For near-term noisy intermediate-scale quantum (NISQ) devices, parametrized quantum circuits (PQCs) have been proposed as machine learning models due to their robustness and ease of implementation. However, the cost function is normally calculated classically from repeated measurement outcomes, such that it is no longer encoded in a quantum state. This prevents the value from being directly manipulated by a quantum computer. To solve this problem, we give a routine to embed the cost function for machine learning into a…
Optical quantum circuits can be optimized using gradient descent methods, as the gates in a circuit can be parametrized by continuous parameters. However, the parameter space as seen by the cost function is not Euclidean, which means that the Euclidean gradient does not generally point in the direction of steepest ascent. In order to retrieve the steepest ascent direction, in this work we implement Natural Gradient descent in the optical quantum circuit setting, which takes the local metric tensor into account. In particular, we adapt the Natural Gradient approach to a complex-valued parameter…
