Quantum compilation provides a method to translate quantum algorithms at a high level of abstraction into their implementations as quantum circuits on real hardware. One approach to quantum compiling is to design a parameterised circuit and to use techniques from optimisation to find the parameters that minimise the distance between the parameterised circuit and the target circuit of interest. While promising, such an approach typically runs into the obstacle of barren plateaus - i.e. large regions of parameter space in which the gradient vanishes. A number of recent works focusing on so-called quantum assisted quantum compiling have developed new techniques to induce gradients in some particular cases. Here we develop and implement a set of related techniques such that they can be applied to classically assisted quantum compiling. We consider both approximate state preparation and approximate circuit preparation and show that, in both cases, we can significantly improve convergence with the approach developed in this work.
Quantum compilation provides a method to translate quantum algorithms at a high level of abstraction into their implementations as quantum circuits on real hardware. One approach to quantum compiling is to design a parameterised circuit and to use techniques from optimisation to find the parameters that minimise the distance between the parameterised circuit and the target circuit of interest. While promising, such an approach typically runs into the obstacle of barren plateaus - i.e. large regions of parameter space in which the gradient vanishes. A number of recent works focusing on so-called quantum assisted quantum compiling have developed new techniques to induce gradients in some particular cases. Here we develop and implement a set of related techniques such that they can be applied to classically assisted quantum compiling. We consider both approximate state preparation and approximate circuit preparation and show that, in both cases, we can significantly improve convergence with the approach developed in this work.
Optimisation via parameterised quantum circuits is the prevalent technique of near-term quantum algorithms. However, the omnipresent phenomenon of barren plateaus parameter regions with vanishing gradients - sets a persistent hurdle that drastically diminishes its success in practice. In this work, we introduce an approach - based on nonunitary operations - that favours jumps out of a barren plateau into a fertile valley. These operations are constructed from conic extensions of parameterised unitary quantum circuits, relying on mid-circuit measurements and a small ancilla system. We further reduce the problem of finding optimal jump directions to a low-dimensional generalised eigenvalue problem. As a proof of concept we incorporate jumps within state-of-theart implementations of the Quantum Approximate Optimisation Algorithm (QAOA). We demonstrate the extensions' effectiveness on QAOA through extensive simulations, showcasing robustness against barren plateaus and highly improved sampling probabilities of optimal solutions.
Barren Plateaus are a formidable challenge for hybrid quantum-classical algorithms that lead to flat plateaus in the loss function landscape making it difficult to take advantage of the expressive power of parameterized quantum circuits with gradient-based methods. Like in classical neural network models, parameterized quantum circuits suffer the same vanishing gradient issue due to large parameter spaces with non-convex landscapes. In this review, we present an overview of the different genesis for barren plateaus, mathematical formalisms of common themes around barren plateaus, and dives into gradients. The central objective is to provide a conceptual perspective between classical and quantum interpretations of vanishing gradients as well as dive into techniques involving cost functions, entanglement, and initialization strategies to mitigate barren plateaus. Addressing barren plateaus paves the way towards feasibility of many classically intractable applications for quantum simulation, optimization, chemistry, and quantum machine learning.
Abstract In recent years, variational quantum circuits (VQCs) have been widely explored to advance quantum circuits against classic models on various domains, such as quantum chemistry and quantum machine learning. Similar to classic machine-learning models, VQCs can be trained through various optimization approaches, such as gradient-based or gradient-free methods. However, when employing gradient-based methods, the gradient variance of VQCs may dramatically vanish as the number of qubits or layers increases. This issue, a.k.a. barren plateaus (BPs), seriously hinders the scaling of VQCs on large datasets. To mitigate the barren plateaus, extensive efforts have been devoted to tackling this issue through diverse strategies. In this survey, we conduct a systematic literature review of recent works from both investigation and mitigation perspectives. Furthermore, we propose a new taxonomy to categorize most existing mitigation strategies into five groups and introduce them in detail. Also, we compare the concurrent survey papers about BPs. Finally, we provide insightful discussion on future directions for BPs.
Realizing successful quantum algorithms on current generation of quantum hardware depends on developing appropriate parametrized quantum circuits, which are the quantum computing counterpart to classical neural networks. A key consideration in this context is the algorithm’s trainability that can be hindered by the existence of so-called barren plateaus. In this case, the algorithm suffers from exponentially vanishing gradients as the number of qubits increases, resulting in a flat optimization landscape and making an efficient training intractable. Due to its serious impact on the success of such algorithms, this problem has gained substantial attention in recent years of quantum computing research. Theoretical and heuristic approaches have been proposed to investigate, avoid and mitigate this issue. In this work, we explore this phenomenon in detail and study the underlying mathematical concepts in depth, investigating the factors that influence the structure of the optimization landscape. Using corresponding mathematical tools, we diagnose whether a given variational circuit will exhibit barren plateaus when going beyond tens of qubits. Additionally, a review of mitigation strategies will be provided. The theory will then be applied to a use case that involves image classification to evaluate whether the model is affected by this phenomenon and which hyperparameters improve or degrade the overall performance.
This paper considers the problem of quantum compilation from an optimization perspective by fixing a circuit structure of CNOTs and rotation gates then optimizing over the rotation angles. We solve the optimization problem classically and consider algorithmic tools to scale it to higher numbers of qubits. We investigate stochastic gradient descent and two sketchand-solve algorithms. For all three algorithms, we compute the gradient efficiently using matrix-vector instead of matrix-matrix computations. Allowing for a runtime on the order of one hour, our implementation using either sketch-and-solve algorithm is able to compile 9 qubit, 27 CNOT circuits; 12 qubit, 24 CNOT circuits; and 15 qubit, 15 CNOT circuits. Without our algorithmic tools, standard optimization does not scale beyond 9 qubit, 9 CNOT circuits, and, beyond that, is theoretically dominated by barren plateaus.
We explore a method for automatically recompiling a quantum circuit A into a target circuit B , with the goal that both circuits have the same action on a specific input i.e. B ∣ i n ⟩ = A ∣ i n ⟩ . This is of particular relevance to hybrid, NISQ-era algorithms for dynamical simulation or eigensolving. The user initially specifies B as a blank template: a layout of parameterised unitary gates configured to the identity. The compilation then proceeds using quantum hardware to perform an isomorphic energy-minimisation task, and an optional gate elimination phase to compress the circuit. If B is insufficient for perfect recompilation then the method will result in an approximate solution. We optimise using imaginary time evolution, and a recent extension of quantum natural gradient for noisy settings. We successfully recompile a 7 -qubit circuit involving 186 gates of multiple types into an alternative form with a different topology, far fewer two-qubit gates, and a smaller family of gate types. Moreover we verify that the process is r o b u s t , finding that per-gate noise of up to 1 % can still yield near-perfect recompilation. We test the scaling of our algorithm on up to 20 qubits, recompiling into circuits with up to 400 parameterized gates, and incorporate a custom adaptive timestep technique. We note that a classical simulation of the process can be useful to optimise circuits for today's prototypes, and more generally the method may enable `blind' compilation i.e. harnessing a device whose response to control parameters is deterministic but unknown.The code and resources used to generate our results are openly available online \cite{githubLink} \cite{mmaGithubLink}. A simple Mathematica demonstration of our algorithm can be found at questlink.qtechtheory.org.