51 Search Results

Abstract A leading approach to algorithm design aims to minimize the number of operations in an algorithm’s compilation. One intuitively expects that reducing the number of operations may decrease the chance of errors. This paradigm is particularly prevalent in quantum computing, where gates are hard to implement and noise rapidly decreases a quantum computer’s potential to outperform classical computers. Here, we find that minimizing the number of operations in a quantum algorithm can be counterproductive, leading to a noise sensitivity that induces errors when running the algorithm in non-ideal conditions. To show this, we develop a framework to characterize themore » resilience of an algorithm to perturbative noises (including coherent errors, dephasing, and depolarizing noise). Some compilations of an algorithm can be resilient against certain noise sources while being unstable against other noises. We condense these results into a tradeoff relation between an algorithm’s number of operations and its noise resilience. We also show how this framework can be leveraged to identify compilations of an algorithm that are better suited to withstand certain noises.« less

Abstract We show that the quantum approximate optimization algorithm (QAOA) for higher-order, random coefficient, heavy-hex compatible spin glass Ising models has strong parameter concentration across problem sizes from 16 up to 127 qubits for p  = 1 up to p  = 5, which allows for computationally efficient parameter transfer of QAOA angles. Matrix product state (MPS) simulation is used to compute noise-free QAOA performance. Hardware-compatible short-depth QAOA circuits are executed on ensembles of 100 higher-order Ising models on noisy IBM quantum superconducting processors with 16, 27, and 127 qubits using QAOA angles learned from a single 16-qubit instance using the JuliQAOA tool.more » We show that the best quantum processors find lower energy solutions up to p  = 2 or p  = 3, and find mean energies that are about a factor of two off from the noise-free distribution. We show that p  = 1 QAOA energy landscapes remain very similar as the problem size increases using NISQ hardware gridsearches with up to a 414 qubit processor.« less

Abstract Periodically driven quantum systems exhibit a diverse set of phenomena but are more challenging to simulate than their equilibrium counterparts. Here, we introduce the Quantum High-Frequency Floquet Simulation (QHiFFS) algorithm as a method to simulate fast-driven quantum systems on quantum hardware. Central to QHiFFS is the concept of a kick operator which transforms the system into a basis where the dynamics is governed by a time-independent effective Hamiltonian. This allows prior methods for time-independent simulation to be lifted to simulate Floquet systems. We use the periodically driven biaxial next-nearest neighbor Ising (BNNNI) model, a natural test bed for quantummore » frustrated magnetism and criticality, as a case study to illustrate our algorithm. We implemented a 20-qubit simulation of the driven two-dimensional BNNNI model on Quantinuum’s trapped ion quantum computer. Our error analysis shows that QHiFFS exhibits not only a cubic advantage in driving frequency ω but also a linear advantage in simulation time t compared to Trotterization.« less

Optical communication is the standard for high-bandwidth information transfer in today’s digital age. The increasing demand for bandwidth has led to the maturation of coherent transceivers that use phase- and amplitude-modulated optical signals to encode more bits of information per transmitted pulse. Such encoding schemes achieve higher information density, but also require more complicated receivers to discriminate the signaling states. In fact, achieving the ultimate limit of optical communication capacity, especially in the low light regime, requires coherent joint detection of multiple pulses. Despite their superiority, such joint detection receivers are not in widespread use because of the difficulty ofmore » constructing them in the optical domain. In this work we describe how optomechanical transduction of phase information from coherent optical pulses to superconducting qubit states followed by the execution of trained short-depth variational quantum circuits can perform joint detection of communication codewords with error probabilities that surpass all classical, individual pulse detection receivers. Importantly, we utilize a model of optomechanical transduction that captures non-idealities such as thermal noise and loss in order to understand the transduction performance necessary to achieve a quantum advantage with such a scheme. We also execute the trained variational circuits on an IBM-Q device with the modeled transduced states as input to demonstrate that a quantum advantage is possible even with current levels of quantum computing hardware noise.« less

Variational Quantum Algorithms (VQAs) and Quantum Machine Learning (QML) models train a parametrized quantum circuit to solve a given learning task. The success of these algorithms greatly hinges on appropriately choosing an ansatz for the quantum circuit. Perhaps one of the most famous ansatzes is the one-dimensional layered Hardware Efficient Ansatz (HEA), which seeks to minimize the effect of hardware noise by using native gates and connectives. The use of this HEA has generated a certain ambivalence arising from the fact that while it suffers from barren plateaus at long depths, it can also avoid them at shallow ones. Inmore » this work, we attempt to determine whether one should, or should not, use a HEA. We rigorously identify scenarios where shallow HEAs should likely be avoided (e.g., VQA or QML tasks with data satisfying a volume law of entanglement). More importantly, we identify a Goldilocks scenario where shallow HEAs could achieve a quantum speedup: QML tasks with data satisfying an area law of entanglement. We provide examples for such scenario (such as Gaussian diagonal ensemble random Hamiltonian discrimination), and we show that in these cases a shallow HEA is always trainable and that there exists an anti-concentration of loss function values. Our work highlights the crucial role that input states play in the trainability of a parametrized quantum circuit, a phenomenon that is verified in our numerics.« less

Excited state properties play a pivotal role in various chemical and physical phenomena, such as charge separation and light emission. However, the primary focus of most existing quantum algorithms has been the ground state, as seen in quantum phase estimation and the variational quantum eigensolver (VQE). Although VQE-type methods have been extended to explore excited states, these methods grapple with optimization challenges. In contrast, the quantum Krylov subspace (QKS) method has been introduced to address both ground and excited states, positioning itself as a cost-effective alternative to quantum phase estimation. However, conventional QKS methodologies depend on a pre-generated subspace throughmore » either real or imaginary-time evolutions. This subspace is inherently expansive and can be plagued with issues like slow convergence or numerical instabilities, often leading to relatively deep circuits. In our research, we present an economic QKS algorithm, which we term the quantum Davidson (QDavidson) algorithm. This innovation hinges on the iterative expansion of the Krylov subspace and the incorporation of a pre-conditioner within the Davidson framework. By using the residues of eigenstates to expand the Krylov subspace, we manage to formulate a compact subspace that aligns closely with the exact solutions. This iterative subspace expansion paves the way for a more rapid convergence in comparison to other QKS techniques, such as the quantum Lanczos. We employ the novel QDavidson algorithm to delve into the excited state properties of various systems, spanning from the Heisenberg spin model to real molecules, utilizing quantum simulators. Compared to the existing QKS methods, the QDavidson algorithm not only converges swiftly but also demands a significantly shallower circuits. This efficiency establishes the QDavidson method as a pragmatic tool for elucidating both ground and excited state properties on quantum computing platforms.« less

We study the problem of learning the parameters for the Hamiltonian of a quantum many-body system, given limited access to the system. In this work, we build upon recent approaches to Hamiltonian learning via derivative estimation. We propose a protocol that improves the scaling dependence of prior works, particularly with respect to parameters relating to the structure of the Hamiltonian (e.g., its locality k). Furthermore, by deriving exact bounds on the performance of our protocol, we are able to provide a precise numerical prescription for theoretically optimal settings of hyperparameters in our learning protocol, such as the maximum evolution timemore » (when learning with unitary dynamics) or minimum temperature (when learning with Gibbs states). Thanks to these improvements, our protocol has practical scaling for large problems: we demonstrate this with a numerical simulation of our protocol on an 80-qubit system.« less

Variational Quantum Algorithms (VQAs) are often viewed as the best hope for near-term quantum advantage. However, recent studies have shown that noise can severely limit the trainability of VQAs, e.g., by exponentially flattening the cost landscape and suppressing the magnitudes of cost gradients. Error Mitigation (EM) shows promise in reducing the impact of noise on near-term devices. Thus, it is natural to ask whether EM can improve the trainability of VQAs. In this work, we first show that, for a broad class of EM strategies, exponential cost concentration cannot be resolved without committing exponential resources elsewhere. This class of strategiesmore » includes as special cases Zero Noise Extrapolation, Virtual Distillation, Probabilistic Error Cancellation, and Clifford Data Regression. Second, we perform analytical and numerical analysis of these EM protocols, and we find that some of them (e.g., Virtual Distillation) can make it harder to resolve cost function values compared to running no EM at all. As a positive result, we do find numerical evidence that Clifford Data Regression (CDR) can aid the training process in certain settings where cost concentration is not too severe. Our results show that care should be taken in applying EM protocols as they can either worsen or not improve trainability. On the other hand, our positive results for CDR highlight the possibility of engineering error mitigation methods to improve trainability.« less

Quantum machine learning—and specifically Variational Quantum Algorithms (VQAs)—offers a powerful, flexible paradigm for programming near-term quantum computers, with applications in chemistry, metrology, materials science, data science, and mathematics. Here, one trains an ansatz, in the form of a parameterized quantum circuit, to accomplish a task of interest. However, challenges have recently emerged suggesting that deep ansatzes are difficult to train, due to flat training landscapes caused by randomness or by hardware noise. This motivates our work, where we present a variable structure approach to build ansatzes for VQAs. Our approach, called VAns (Variable Ansatz), applies a set of rules tomore » both grow and (crucially) remove quantum gates in an informed manner during the optimization. Consequently, VAns is ideally suited to mitigate trainability and noise-related issues by keeping the ansatz shallow. We employ VAns in the variational quantum eigensolver for condensed matter and quantum chemistry applications, in the quantum autoencoder for data compression and in unitary compilation problems showing successful results in all cases.« less

Previously proposed quantum algorithms for solving linear systems of equations cannot be implemented in the near term due to the re quired circuit depth. Here, we propose a hybrid quantum-classical algorithm, called Variational Quantum Linear Solver (VQLS), for solving linear systems on near-term quantum computers. VQLS seeks to variationally prepare |x$$\rangle$$ such that A|x$$\rangle$$ ∝ |b$$\rangle$$. We derive an operationally meaningful termination condition for VQLS that allows one to guarantee that a desired solution precision ϵ is achieved. Specifically, we prove that C $⩾$ ϵ²/κ², where C is the VQLS cost function and κ is the condition number of A.more » We present efficient quantum circuits to estimate C, while providing evidence for the classical hardness of its estimation. Using Rigetti’s quantum computer, we success fully implement VQLS up to a problem size of 1024 × 1024. Finally, we numerically solve nontrivial problems of size up to 2⁵⁰ × 2⁵⁰. For the specific examples that we consider, we heuristically find that the time complexity of VQLS scales efficiently in ϵ, κ, and the system size N.« less