Variational quantum circuits (VQCs) have shown great potential in near-term applications. However, the discriminative power of a VQC, in connection to its circuit architecture and depth, is not understood. To unleash the genuine discriminative power of a VQC, we propose a VQC system with the optimal classical post-processing -- maximum-likelihood estimation on measuring all VQC output qubits. Via extensive numerical simulations, we find that the error of VQC quantum data classification typically decay exponentially with the circuit depth, when the VQC architecture is extensive -- the number of gates does not shrink with the circuit depth. This fast error suppression ends at the saturation towards the ultimate Helstrom limit of quantum state discrimination. On the other hand, non-extensive VQCs such as quantum convolutional neural networks are sub-optimal and fail to achieve the Helstrom limit. To achieve the best performance for a given VQC, the optimal classical post-processing is crucial even for a binary classification problem. To simplify VQCs for near-term implementations, we find that utilizing the symmetry of the input properly can improve the performance, while oversimplification can lead to degradation.
We report the experimental observation, and a theoretical explanation, of collective suppression of linewidths for multiple superconducting qubits coupled to a good cavity. This demonstrates how strong qubit-cavity coupling can significantly modify the dephasing and dissipation processes that might be expected for individual qubits, and can potentially improve coherence times in many-body circuit QED.
Parasitic crosstalk in superconducting quantum devices is a leading limitation for quantum gates. We demonstrate the suppression of static ZZ crosstalk in a two-qubit, two-coupler superconducting circuit, where the frequency of a tunable coupler can be adjusted such that the ZZ interaction from each coupler destructively interfere. We verify the crosstalk elimination with simultaneous randomized benchmarking, and use a parametrically activated iSWAP interaction to achieve a Bell state preparation fidelity of 98.5% and a $\sqrt{\textrm{iSWAP}}$ gate fidelity of 94.8% obtained via quantum proces…
Learning error suppression strategies for dynamic quantum circuits
Princeton University（普林斯顿大学）；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）；IBM Quantum, IBM Thomas J. Watson Research Center（IBM量子，IBM托马斯·J·沃森研究中心）；Microsoft Discovery & Quantum（微软探索与量子）
We propose a novel algorithm for fast training of variational classifiers by processing multiple samples parallelly. The algorithm can be adapted for any ansatz used in the variational circuit. The presented algorithm utilizes qRAM and other quantum circuits in the forward pass. Further, instead of the usual practice of computing the loss classically, we calculate the loss using a Swap-test circuit. The algorithm thus brings down the training cost of a variational classifier to O(logN)from the usual O(N)when training on a dataset of N samples. Although we discuss only binary classification in …
Circuit design for quantum machine learning remains a formidable challenge. Inspired by the applications of tensor networks across different fields and their novel presence in the classical machine learning context, one proposed method to design variational circuits is to base the circuit architecture on tensor networks. Here, we comprehensively describe tensor-network quantum circuits and how to implement them in simulations. This includes leveraging circuit cutting, a technique used to evaluate circuits with more qubits than those available on current quantum devices. We then illustrate the …
We explore how to build quantum circuits that compute the lowest energy state corresponding to a given Hamiltonian within a Symmetry subspace by explicitly encoding it into the circuit. We create an explicit unitary and a variationally trained unitary that maps any vector output by ansatz A(~α) from a defined subspace to a vector in the symmetry space. The parameters are trained varitionally to minimize the energy thus keeping the output within the labelled symmetry value. The method was tested for a spin XXZ hamiltonian using rotation and reflection symmetry and H2 hamiltonian within S_z = 0 …
Mid-circuit measurement and reset are crucial primitives in quantum computation, but such operations require strong interactions with selected qubits while maintaining isolation of neighboring qubits, which is a significant challenge in many systems. For trapped ion systems, measurement is performed with laser-induced fluorescence. Stray light from the detection beam and fluorescence from the measured ions can be significant sources of decoherence for unmeasured qubits. We present a technique using ion micromotion to reduce these sources of decoherence by over an order of magnitude. We benchma…
We generalize solid-state tight-binding techniques for the spectral analysis of large superconducting circuits. We find that tight-binding states can be better suited for approximating the low-energy excitations than charge-basis states, as illustrated for the interesting example of the current-mirror circuit. The use of tight binding can dramatically lower the Hilbert space dimension required for convergence to the true spectrum, and allows for the accurate simulation of larger circuits that are out of reach of charge basis diagonalization.
Sub-universal variational circuits for combinatorial optimization problems
Department of Physics, University of Colorado Boulder, Boulder, CO 80309, USA（科罗拉多大学博尔德分校物理系）；University of Technology Sydney, Centre for Quantum Software（悉尼技术大学量子软件中心）；Department of Electrical, Computer and Energy Engineering, University of Colorado Boulder, Boulder, Colorado 80309, USA（科罗拉多大学博尔德分校电气、计算机与能源工程系）
We demonstrate the simulation of a noncollinear molecule, e.g. H2O molecule using Variational Quantum Eigensolver (VQE) with high chemical accuracy. The 2D and 3D potential energy surface (PES) were reported. Taking advantage of the potential speedup in Qiskit runtime program, the optimal initial parameters for the variational quantum circuits were obtained after several consecutive iterations, thus resulting in accurate prediction of water's PES matching result obtained from exact diagonalization of the full Hamiltonian.
A hybrid variational quantum circuit approach for stabilizer states classifiers
Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS, University of Technology of Belfort-Montbéliard（贝尔福-蒙贝利亚尔技术大学）；Mathematics and Statistics Department, Auburn University（奥本大学）
We introduce a novel hybrid algorithm to simulate the real-time evolution of quantum systems using parameterized quantum circuits. The method, named "projected - Variational Quantum Dynamics" (p-VQD) realizes an iterative, global projection of the exact time evolution onto the parameterized manifold. In the small time-step limit, this is equivalent to the McLachlan's variational principle. Our approach is efficient in the sense that it exhibits an optimal linear scaling with the total number of variational parameters. Furthermore, it is global in the sense that it uses the variational principl…
As quantum computers mature, quantum error correcting codes (QECs) will be adopted in order to suppress errors to any desired level $E$ at a cost in qubit-count $n$ that is merely poly-logarithmic in $1/E$. However in the NISQ era, the complexity and scale required to adopt even the smallest QEC is prohibitive. Instead, error mitigation techniques have been employed; typically these do not require an increase in qubit-count but cannot provide exponential error suppression. Here we show that, for the crucial case of estimating expectation values of observables (key to almost all NISQ algorithms…
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…
This paper proposes a hybrid quantum-classical algorithm that learns a suitable quantum feature map that separates unlabelled data that is originally non linearly separable in the classical space using a Variational quantum feature map and q-means as a subroutine for unsupervised learning. The objective of the Variational circuit is to maximally separate the clusters in the quantum feature Hilbert space. First part of the circuit embeds the classical data into quantum states. Second part performs unsupervised learning on the quantum states in the quantum feature Hilbert space using the q-means…
Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the capacity of current quantum devices. To reduce the quantum circuit complexity, it has been suggested to incorporate a part of the electronic correlation into an effective Hamiltonian, which is often obtained from a similarity transformation of the electronic Hamiltonian. In this work, we introduce a new transformation in the form of a product of a linear com…
Utilizing counterdiabatic (CD) driving - aiming at suppression of diabatic transition - in digitized adiabatic evolution have garnered immense interest in quantum protocols and algorithms. However, improving the approximate CD terms with a nested commutator ansatz is a challenging task. In this work, we propose a technique of finding optimal coefficients of the CD terms using a variational quantum circuit. By classical optimizations routines, the parameters of this circuit are optimized to provide the coefficients corresponding to the CD terms. Then their improved performance is exemplified in…
We suggest and demonstrate a protocol which suppresses dephasing due to the low-frequency noise by qubit motion, i.e., transfer of the logical qubit of information in a system of $n \geq 2$ physical qubits. The protocol requires only the nearest-neighbor coupling and is applicable to different qubit structures. We further analyze its effectiveness against noises with arbitrary correlations. Our analysis, together with experiments using up to three superconducting qubits, shows that for the realistic uncorrelated noises, qubit motion increases the dephasing time of the logical qubit as $\sqrt{n…
We experimentally demonstrate a parametric iSWAP gate in a superconducting circuit based on a tunable coupler for achieving a continuous tunability to eliminate unwanted qubit interactions. We implement the twoqubit iSWAP gate by applying a fast-flux bias modulation pulse on the coupler to turn on parametric exchange interaction between computational qubits. The controllable interaction can provide an extra degree of freedom to verify the optimal condition for constructing the parametric gate. Aiming to fully investigate error sources of the two-qubit gates, we perform quantum process tomograp…
Quantum error correction is vital for implementing universal quantum computing. A key component is the encoding circuit that maps a product state of physical qubits into the encoded multipartite entangled logical state. Known methods are typically not 'optimal' either in terms of the circuit depth (and therefore the error burden) or the specifics of the target platform, i.e. the native gates and topology of a system. This work introduces a variational compiler for efficiently finding the encoding circuit of general quantum error correcting codes with given quantum hardware. Focusing on the noi…
We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground-states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor networks by local quantum circuits. We explore both quantum circuit matrix product states and the quantum circuit multi-scale entanglement renormalization ansatz, and introduce an adaptive method to optimize the resulting circuits to high fidelity with more than $10^4$ parameters. We benchmark their expressiveness against standard tensor networks, as well as ot…
We present an initialisation method for variational quantum algorithms applicable to intermediate scale quantum computers. The method uses simulated annealing of the efficiently simulable Clifford parameter points as a pre-optimisation to find a low energy initial condition. We numerically demonstrate the effectiveness of the technique, and how it depends on Hamiltonian structure, number of qubits and circuit depth. While a range of different problems are considered, we note that the method is particularly useful for quantum chemistry problems. This presented method could help achieve a quantu…
We extend the ability of unitary quantum circuits by interfacing it with classical autoregressive neural networks. The combined model parametrizes a variational density matrix as a classical mixture of quantum pure states, where the autoregressive network generates bitstring samples as input states to the quantum circuit. We devise an efficient variational algorithm to jointly optimize the classical neural network and the quantum circuit for quantum statistical mechanics problems. One can obtain thermal observables such as the variational free energy, entropy, and specific heat. As a by produc…
National University of Defense Technology（国防科技大学）；National Innovation Institute of Defense Technology（国防科技创新研究院）
Quantum state tomography is a key process in most quantum experiments. In this work, we employ quantum machine learning for state tomography. Given an unknown quantum state, it can be learned by maximizing the fidelity between the output of a variational quantum circuit and this state. The number of parameters of the variational quantum circuit grows linearly with the number of qubits and the circuit depth, so that only polynomial measurements are required, even for highly-entangled states. After that, a subsequent classical circuit simulator is used to transform the information of the target …
Due to the unreliability and limited capacity of existing quantum computer prototypes, quantum circuit simulation continues to be a vital tool for validating next generation quantum computers and for studying variational quantum algorithms, which are among the leading candidates for useful quantum computation. Existing quantum circuit simulators do not address the common traits of variational algorithms, namely: 1) their ability to work with noisy qubits and operations, 2) their repeated execution of the same circuits but with different parameters, and 3) the fact that they sample from circuit…
The variational quantum eigensolver is one of the most promising approaches for performing chemistry simulations using noisy intermediate-scale quantum (NISQ) processors. The efficiency of this algorithm depends crucially on the ability to prepare multi-qubit trial states on the quantum processor that either include, or at least closely approximate, the actual energy eigenstates of the problem being simulated while avoiding states that have little overlap with them. Symmetries play a central role in determining the best trial states. Here, we present efficient state preparation circuits that r…
Variational quantum algorithms dominate gate-based applications of modern quantum processors. The so called, {\it layer-wise trainability conjecture} appears in various works throughout the variational quantum computing literature. The conjecture asserts that a quantum circuit can be trained piece-wise, e.g.~that a few layers can be trained in sequence to minimize an objective function. Here we prove this conjecture false. Counterexamples are found by considering objective functions that are exponentially close (in the number of qubits) to the identity matrix. In the finite setting, we found a…
The optimization of circuit parameters of variational quantum algorithms such as the variational quantum eigensolver (VQE) or the quantum approximate optimization algorithm (QAOA) is a key challenge for the practical deployment of near-term quantum computing algorithms. Here, we develop a hybrid quantum/classical optimization procedure inspired by the Jacobi diagonalization algorithm for classical eigendecomposition, and combined with Anderson acceleration. In the first stage, analytical tomography fittings are performed for a local cluster of circuit parameters via sampling of the observable …
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by developing two objective functions which minimise to prepare outputs of arbitrary quantum circuits. The fleeting resource of variational quantum computation is the number of expected values which must be iteratively minimised using classical-to-quantum outer loop optimisation. An efficient solution to this optimisation problem is given by the quantum circuit being…
Late Breaking Results: Hardware-Aware Compilation Reshapes Trainability in Variational Quantum Circuits
eBRAIN Lab, Division of Engineering, New York University (NYU) Abu Dhabi（纽约大学阿布扎比分校工程学院）；Center for Quantum and Topological Systems, NYUAD Research Institute, NYU Abu Dhabi（纽约大学阿布扎比分校研究学院量子与拓扑系统中心）
We propose a method for finding approximate compilations of quantum unitary transformations, based on techniques from policy gradient reinforcement learning. The choice of a stochastic policy allows us to rephrase the optimization problem in terms of probability distributions, rather than variational gates. In this framework, the optimal configuration is found by optimizing over distribution parameters, rather than over free angles. We show numerically that this approach can be more competitive than gradient-free methods, for a comparable amount of resources, both for noiseless and noisy circu…
Machine learning techniques enhanced by noisy intermediate-scale quantum (NISQ) devices and especially variational quantum circuits (VQC) have recently attracted much interest and have already been benchmarked for certain problems. Inspired by classical deep learning, VQCs are trained by gradient descent methods which allow for efficient training over big parameter spaces. For NISQ sized circuits, such methods show good convergence. There are however still many open questions related to the convergence of the loss function and to the trainability of these circuits in situations of vanishing gr…
