Reinforcement learning (RL) is a promising method for quantum circuit optimisation. However, the state space that has to be explored by an RL agent is extremely large when considering all the possibilities in which a quantum circuit can be transformed through local rewrite operations. This state space explosion slows down the learning of RL-based optimisation strategies. We present for the first time how to use graph neural network (GNN) autoencoders for the optimisation of quantum circuits. We construct directed acyclic graphs from the quantum circuits, encode the graphs and use the encodings to represent RL states. We illustrate our proof of concept implementation on Bernstein-Vazirani circuits and, from preliminary results, we conclude that our autoencoder approach: a) maintains the optimality of the original RL method; b) reduces by 20 \% the size of the table that encodes the learned optimisation strategy. Our method is the first realistic first step towards very large scale RL quantum circuit optimisation.
Outcome probability estimation via classical methods is an important task for validating quantum computing devices. Outcome probabilities of any quantum circuit can be estimated using Monte Carlo sampling, where the amount of negativity present in the circuit frame representation quantifies the overhead on the number of samples required to achieve a certain precision. In this paper, we propose two classical sub-routines: circuit gate merging and frame optimisation, which optimise the circuit representation to reduce the sampling overhead. We show that the runtimes of both sub-routines scale po…
We analyse the design and optimisation of quantum logic circuits suitable for the experimental demonstration of a three-qubit quantum computation prototype based on optically-controlled, solid-state quantum logic gates. In these gates, the interaction between two qubits carried by the electron-spin of donors is mediated by the optical excitation of a control particle placed in their proximity. First, we use a geometrical approach for analysing the entangling characteristics of these quantum gates. Then, using a genetic programming algorithm, we develop circuits for the refined Deutsch-Jozsa al…
One of the main goals in quantum circuit optimisation is to reduce the number of ancillary qubits and the depth of computation, to obtain robust computation. However, most of known techniques, based on local rewriting rules, for parallelising quantum circuits will require the addition of ancilla qubits, leading to an undesired space-time tradeoff. Recently several novel approaches based on measurement-based quantum computation (MBQC) techniques attempted to resolve this problem. The key element is to explore the global structure of a given circuit, defined via translation into a corresponding …
We present a quantum circuit representation consisting entirely of qubit initialisations (I), a network of controlled-NOT gates (C) and measurements with respect to different bases (M). The ICM representation is useful for optimisation of quantum circuits that include teleportation, which is required for fault-tolerant, error corrected quantum computation. The non-deterministic nature of teleportation necessitates the conditional introduction of corrective quantum gates and additional ancillae during circuit execution. Therefore, the standard optimisation objectives, gate count and number of w…
We present a highly efficient quantum circuit for performing continuous time quantum walks (CTQWs) over an exponentially large set of combinatorial objects, provided that the objects can be indexed efficiently. CTQWs form the core mixing operation of a generalised version of the Quantum Approximate Optimisation Algorithm, which works by `steering' the quantum amplitude into high-quality solutions. The efficient quantum circuit holds the promise of finding high-quality solutions to certain classes of NP-hard combinatorial problems such as the Travelling Salesman Problem, maximum set splitting, …
We demonstrate the implementation of a novel machine learning framework for probability density estimation and classification using quantum circuits. The framework maps a training data set or a single data sample to the quantum state of a physical system through quantum feature maps. The quantum state of the arbitrarily large training data set summarises its probability distribution in a finite-dimensional quantum wave function. By projecting the quantum state of a new data sample onto the quantum state of the training data set, one can derive statistics to classify or estimate the density of …
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|in> = A|in>. 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 insufficie…
Clifford gates play a role in the optimisation of Clifford+T circuits. Reducing the count and the depth of Clifford gates, as well as the optimal scheduling of T gates, influence the hardware and the time costs of executing quantum circuits. This work focuses on circuits protected by the surface quantum error-correcting code. The result of compiling a quantum circuit for the surface code is called a topological assembly. We use queuing theory to model a part of the compiled assemblies, evaluate the models, and make the empiric observation that at least for certain Clifford+T circuits (e.g. add…
Quantum computers promise to revolutionise electronic simulations by overcoming the exponential scaling of many-electron problems. While electronic wave functions can be represented using a product of fermionic unitary operators, shallow quantum circuits for exact states have not yet been achieved. We construct universal wave functions from gate-efficient, symmetry-preserving fermionic operators by introducing an algorithm that globally optimises the wave function in the discrete ansatz design and the continuous parameter spaces. Our approach maximises the accuracy that can be obtained with ne…
Quantum computers are different from binary digital electronic computers based on transistors. Common digital computing encodes the data into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits (qubits). A circuit-based qubit quantum computer exists and is available for experiments via cloud, the IBM quantum experience project. We implemented a Quantum Tabu Search in order to obtain a quantum combinatorial optimisation, suggesting that an entanglement-metaheuristic can display optimal solutions and accelerate the optimisat…
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…
This paper presents the Maximum Amplification Optimisation Algorithm (MAOA), a novel quantum algorithm designed for combinatorial optimisation in the restricted circuit depth context of near-term quantum computing. The MAOA first produces a quantum state in which the optimal solutions to a problem are amplified to the maximum extent possible subject to a given restricted circuit depth. Subsequent repeated preparation and measurement of this maximally amplified state produces solutions of the highest quality as efficiently as possible. The MAOA performs considerably better than other near-term …
By taking into account the physical nature of quantum errors it is possible to improve the efficiency of quantum error correction. Here we consider an optimisation to conventional quantum error correction which involves exploiting asymmetries in the rates of X and Z errors by reducing the rate of X correction. As an example, we apply this optimisation to the [[7,1,3]] code and make a comparison with conventional quantum error correction. After two levels of concatenated error correction we demonstrate a circuit depth reduction of at least 43% and reduction in failure rate of at least 67%. This…
Of late, we are witnessing spectacular developments in Quantum Information Processing with the availability of Noisy Intermediate-Scale Quantum devices of different architectures and various software development kits to work on quantum algorithms. Different problems, which are hard to solve by classical computation, but can be sped up (significantly in some cases) are also being populated. Leveraging these aspects, this paper examines unsupervised graph clustering by quantum algorithms or, more precisely, quantum-assisted algorithms. By carefully examining the two cluster Max-Cut problem withi…
The Quantum Approximate Optimisation Algorithm is a $p$ layer, time-variable split operator method executed on a quantum processor and driven to convergence by classical outer loop optimisation. The classical co-processor varies individual application times of a problem/driver propagator sequence to prepare a state which approximately minimizes the problem's generator. Analytical solutions to choose optimal application times (called angles) have proven difficult to find, whereas outer loop optimisation is resource intensive. Here we prove that optimal Quantum Approximate Optimisation Algorithm…
The de novo design of drug molecules is recognized as a time-consuming and costly process, and computational approaches have been applied in each stage of the drug discovery pipeline. Variational autoencoder is one of the computer-aided design methods which explores the chemical space based on existing molecular dataset. Quantum machine learning has emerged as an atypical learning method that may speed up some classical learning tasks because of its strong expressive power. However, near-term quantum computers suffer from limited number of qubits which hinders the representation learning in hi…
Classical autoencoders are neural networks that can learn efficient low dimensional representations of data in higher dimensional space. The task of an autoencoder is, given an input $x$, is to map $x$ to a lower dimensional point $y$ such that $x$ can likely be recovered from $y$. The structure of the underlying autoencoder network can be chosen to represent the data on a smaller dimension, effectively compressing the input. Inspired by this idea, we introduce the model of a quantum autoencoder to perform similar tasks on quantum data. The quantum autoencoder is trained to compress a particul…
Quantum autoencoder is an efficient variational quantum algorithm for quantum data compression. However, previous quantum autoencoders fail to compress and recover high-rank mixed states. In this work, we discuss the fundamental properties and limitations of the standard quantum autoencoder model in more depth, and provide an information-theoretic solution to its recovering fidelity. Based on this understanding, we present a noise-assisted quantum autoencoder algorithm to go beyond the limitations, our model can achieve high recovering fidelity for general input states. Appropriate noise chann…
It is challenging to transform an arbitrary quantum circuit into a form protected by surface code quantum error correcting codes (a variant of topological quantum error correction), especially if the goal is to minimise overhead. One of the issues is the efficient placement of magic state distillation sub circuits, so-called distillation boxes, in the space-time volume that abstracts the computation's required resources. This work presents a general, systematic, online method for the synthesis of such circuits. Distillation box placement is controlled by so-called schedulers. The work introduc…
We introduce qprof, a new and extensible quantum program profiler able to generate profiling reports of various quantum circuits. We describe the internal structure and working of qprof and provide three practical examples on practical quantum circuits with increasing complexity. This tool will allow researchers to visualise their quantum implementation in a different way and reliably localise the bottlenecks for efficient code optimisation.
We propose a Hybrid classical-quantum Autoencoder (HAE) model, which is a synergy of a classical autoencoder (AE) and a parametrized quantum circuit (PQC) that is inserted into its bottleneck. The PQC augments the latent space, on which a standard outlier detection method is applied to search for anomalous data points within a classical dataset. Using this model and applying it to both standard benchmarking datasets, and a specific use-case dataset which relates to predictive maintenance of gas power plants, we show that the addition of the PQC leads to a performance enhancement in terms of pr…
Quantum computations are expressed in general as quantum circuits, which are specified by ordered lists of quantum gates. The resulting specifications are used during the optimisation and execution of the expressed computations. However, the specification format makes it difficult to verify that optimised or executed computations still conform to the initial gate list specifications: showing the computational equivalence between two quantum circuits expressed by different lists of quantum gates is exponentially complex in the worst case. In order to solve this issue, this work presents a deriv…
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…
Noisy, intermediate-scale quantum (NISQ) computers are expected to execute quantum circuits of up to a few hundred qubits. The circuits have to conform to NISQ architectural constraints regarding qubit allocation and the execution of multi-qubit gates. Quantum circuit compilation (QCC) takes a nonconforming circuit and outputs a compatible circuit. Can classical optimisation methods be used for QCC? Compilation is a known combinatorial problem shown to be solvable by two types of operations: 1) qubit allocation, and 2) gate scheduling. We show informally that the two operations form a discrete…
Quantum walk-based optimisation for capacitated vehicle routing with homogeneous and heterogeneous fleets
Pawsey Supercomputing Research Centre（Pawsey超级计算研究中心）；Centre for Quantum Information, Simulation and Algorithms, The University of Western Australia（西澳大利亚大学量子信息、模拟与算法中心）；PrioriAnalytica
