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arXiv:2305.01707

Discovering Quantum Circuit Components with Program Synthesis

Leopoldo Sarra, Kevin Ellis, Florian Marquardt

Published May 2, 2023• 1 citation
arXivHTMLPDF

Abstract

Despite rapid progress in the field, it is still challenging to discover new ways to take advantage of quantum computation: all quantum algorithms need to be designed by hand, and quantum mechanics is notoriously counterintuitive. In this paper, we study how artificial intelligence, in the form of program synthesis, may help to overcome some of these difficulties, by showing how a computer can incrementally learn concepts relevant for quantum circuit synthesis with experience, and reuse them in unseen tasks. In particular, we focus on the decomposition of unitary matrices into quantum circuits, and we show how, starting from a set of elementary gates, we can automatically discover a library of new useful composite gates and use them to decompose more and more complicated unitaries.

DOI
10.48550/arxiv.2305.01707

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Despite rapid progress in the field, it is still challenging to discover new ways to take advantage of quantum computation: all quantum algorithms need to be designed by hand, and quantum mechanics is notoriously counterintuitive. In this paper, we study how artificial intelligence, in the form of program synthesis, may help to overcome some of these difficulties, by showing how a computer can incrementally learn concepts relevant for quantum circuit synthesis with experience, and reuse them in unseen tasks. In particular, we focus on the decomposition of unitary matrices into quantum circuits, and we show how, starting from a set of elementary gates, we can automatically discover a library of new useful composite gates and use them to decompose more and more complicated unitaries.
Abstract Despite rapid progress in the field, it is still challenging to discover new ways to leverage quantum computation: all quantum algorithms must be designed by hand, and quantum mechanics is notoriously counterintuitive. In this paper, we study how artificial intelligence, in the form of program synthesis, may help overcome some of these difficulties, by showing how a computer can incrementally learn concepts relevant to quantum circuit synthesis with experience, and reuse them in unseen tasks. In particular, we focus on the decomposition of unitary matrices into quantum circuits, and show how, starting from a set of elementary gates, we can automatically discover a library of useful new composite gates and use them to decompose increasingly complicated unitaries.
Quantum algorithms are notoriously hard to design and require significant human ingenuity and insight. We present a new methodology called Quantum Automated Synthesizer (QUASH) that can automatically synthesize quantum circuits using decision procedures that perform symbolic reasoning for combinatorial search. Our automated synthesis approach constructs finite symbolic abstract models of the quantum gates automatically and discovers a quantum circuit as a composition of quantum gates using these symbolic models. Our key insight is that most current quantum algorithms work on a finite number of classical inputs, and hence, their correctness proof relies only on reasoning about a finite set of quantum states that can be represented using finite symbolic systems. We demonstrate the potential of our approach by automatically synthesizing four quantum circuits and re-discovering the Bernstein-Vazirani quantum algorithm using state-of-the-art decision procedures. Our synthesis approach only requires distinguishing between a finite set of symbolic quantum states; for example, the synthesis of the Bernstein-Vazirani quantum algorithm only requires reasoning about the following qubit states: |0, |1, -i|0, i|1, |+, |-, e1/2|1i, eiπ/4|1 and a remaining symbolic state representing all other possible quantum states. Our approach leverages decision procedures and theorem provers to assist in the discovery of new quantum algorithms and is a step towards the automation of quantum algorithm design.
Abstract. In order to design a quantum circuit that performs a desired quantum computation, it is necessary to find a decomposition of the unitary matrix that represents that computation in terms of a sequence of quantum gate operations. To date, such designs have either been found by hand or by exhaustive enumeration of all possible circuit topologjks. In this paper we propose an automated approach to quantum circuit design using search heuristics based on principles abstracted from evolutionary genetics, i.e. using a genetic programming algorithm adapted specially for this problem. We demonstrate the method on the task of discovering quantum circuit designs for quantum teleportation. We show that to find a given known circuit design (one which was hand-crafted by a human), the method considers roughly an order of magnitude fewer designs than naive enumeration. In addition, the method finds novel circuit designs superior to those previously known. 1
Decoupling systems into independently evolving components has a long history of simplifying seemingly complex systems. They enable a better understanding of the underlying dynamics and causal structures while providing more efficient means to simulate such processes on a computer. Here we outline a variational decoupling algorithm for decoupling unitary quantum dynamics-allowing us to decompose a given n-qubit unitary gate into multiple independently evolving sub-components. We apply this approach to quantum circuit synthesis-the task of discovering quantum circuit implementations of target unitary dynamics. Our numerical studies illustrate significant benefits, showing that variational decoupling enables us to synthesize general two- and four-qubit gates to fidelity that conventional variational circuits cannot reach.
Abstract Gate-level quantum circuits are often derived manually from higher level algorithms. While this suffices for small implementations and demonstrations, ultimately automatic circuit design will be required to realise complex algorithms using hardware-specific operations and connectivity. Therefore, ab initio creation of circuits within a machine, either a classical computer or a hybrid quantum–classical device, is of key importance. We explore a range of established and novel techniques for the synthesis of new circuit structures, the optimisation of parameterised circuits, and the efficient removal of low-value gates via the quantum geometric tensor. Using these techniques we tackle the tasks of automatic encoding of unitary processes and translation (recompilation) of a circuit from one form to another. Using emulated quantum computers with various noise-free gate sets we provide simple examples involving up to 10 qubits, corresponding to 20 qubits in the augmented space we use. Further applications of specific relevance to chemistry modelling are considered in a sister paper, ‘Exploiting subspace constraints and ab initio variational methods for quantum chemistry’. The emulation environments used were QuEST, QuESTlink and pyQuEST. All resources will be made openly accessible and are currently available upon request.
Quantum computation established itself as a promising emerging technology and, hence, attracted considerable attention in the domain of computer-aided-design (CAD). However, quantum mechanical phenomena such as superposition, phase shifts, or entanglement lead to a logic model which poses serious challenges to the development of a proper design flow for quantum circuits. Consequently, researchers addressed synthesis of quantum circuits not as a single design step, but considered sub-tasks such as synthesis of Boolean components or synthesis of restricted subsets of quantum functionality. Generating a particularly desired quantum state is another of these sub-tasks. However, logic synthesis of quantum circuits accomplishing that has hardly been considered yet. In this work, we propose a generic method which automatically synthesizes a quantum circuit generating any desired quantum state from an initially given basis state. The proposed method allows for both, a theoretical determination of upper bounds as well as an experimental evaluation of the number of quantum gates needed for this important design step.