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arXiv:1803.07119 · New Journal of Physics

Supervised learning of time-independent Hamiltonians for gate design

Luca Innocenti, Leonardo Banchi, Alessandro Ferraro, Sougato Bose, Mauro Paternostro

Published Apr 17, 2020• 28 citations
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Abstract

Abstract We present a general framework to tackle the problem of finding time-independent dynamics generating target unitary evolutions. We show that this problem is equivalently stated as a set of conditions over the spectrum of the time-independent gate generator, thus translating the task into an inverse eigenvalue problem. We illustrate our methodology by identifying suitable time-independent generators implementing Toffoli and Fredkin gates without the need for ancillae or effective evolutions. We show how the same conditions can be used to solve the problem numerically, via supervised learning techniques. In turn, this allows us to solve problems that are not amenable, in general, to direct analytical solution, providing at the same time a high degree of flexibility over the types of gate-design problems that can be approached. As a significant example, we find generators for the Toffoli gate using only diagonal pairwise interactions, which are easier to implement in some experimental architectures. To showcase the flexibility of the supervised learning approach, we give an example of a non-trivial four-qubit gate that is implementable using only diagonal, pairwise interactions.

DOI
10.1088/1367-2630/ab8aaf

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Abstract We present a general framework to tackle the problem of finding time-independent dynamics generating target unitary evolutions. We show that this problem is equivalently stated as a set of conditions over the spectrum of the time-independent gate generator, thus translating the task into an inverse eigenvalue problem. We illustrate our methodology by identifying suitable time-independent generators implementing Toffoli and Fredkin gates without the need for ancillae or effective evolutions. We show how the same conditions can be used to solve the problem numerically, via supervised learning techniques. In turn, this allows us to solve problems that are not amenable, in general, to direct analytical solution, providing at the same time a high degree of flexibility over the types of gate-design problems that can be approached. As a significant example, we find generators for the Toffoli gate using only diagonal pairwise interactions, which are easier to implement in some experimental architectures. To showcase the flexibility of the supervised learning approach, we give an example of a non-trivial four-qubit gate that is implementable using only diagonal, pairwise interactions.
We present a general framework to approach the problem of finding time-independent dynamics generating target unitary evolutions. More specifically, given a target unitary gate G over a set of qubits, and a parametrized Hamiltonian of the form H ( λ ) = ∑ i λ i σ i with σi Hermitian operators over the qubits, we want to find a set of values λ0 such that exp ( i H ( λ 0 ) ) = G. We show that this problem is equivalently stated as a set of conditions over the spectrum of H ( λ ), reducing the problem to an inverse eigenvalue problem. We show how to solve this problem in some physically relevant instances, like for example to find time-independent dynamics implementing Toffoli and Fredkin gates without the need for ancillary gates or effective evolutions.
Abstract We put forward a strategy to encode a quantum operation into the unmodulated dynamics of a quantum network without the need for external control pulses, measurements or active feedback. Our optimisation scheme, inspired by supervised machine learning, consists in engineering the pairwise couplings between the network qubits so that the target quantum operation is encoded in the natural reduced dynamics of a network section. The efficacy of the proposed scheme is demonstrated by the finding of uncontrolled four-qubit networks that implement either the Toffoli gate, the Fredkin gate or remote logic operations. The proposed Toffoli gate is stable against imperfections, has a high fidelity for fault-tolerant quantum computation and is fast, being based on the non-equilibrium dynamics.
Implementing quantum operations in the form of natural Hamiltonian dynamics is desirable, since they almost require no external control or feedback. In this work, we propose a NISQ-friendly quantum-classical hybrid approach to designing a time-independent Hamiltonian that generates a given multi-qubit unitary. In particular, we execute a Variational Quantum Algorithm, whose ansatz is carefully chosen to be a sequence of appropriately parametrized unitaries describing at most two-qubit nearest neighbour interactions, dictating the target unitary. Subsequently, we apply our approach to simulate multi-qubit target gates, with and without stochastic noise. We demonstrate that our strategy allows us to implement a Toffoli gate with sufficiently high fidelity, as compared to the other similar techniques. Our approach is an example of the usage of quantum computing for the design of quantum computers.
Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the underlying combinatorial search space. Existing approaches suffer from misaligned optimization objectives, substantial training costs and limited generalization across different qubit counts. We mitigate these limitations by using supervised learning to approximate the minimum description length of residual unitaries and combining this estimate with stochastic beam search to identify near optimal gate sequences. Our method relies on a lightweight model with zero-shot generalization, substantially reducing training overhead compared to prior baselines. Across multiple benchmarks, we achieve faster wall-clock synthesis times while exceeding state-of-the-art methods in terms of success rate for complex circuits.
We present strategies for the training of a qubit network aimed at the ancilla-assisted synthesis of multi-qubit gates based on a set of restricted resources. By assuming the availability of only time-independent single and two-qubit interactions, we introduce and describe a supervised learning strategy implemented through momentum-stochastic gradient descent with automatic differentiation methods. We demonstrate the effectiveness of the scheme by discussing the implementation of nontrivial three qubit operations, including a QFT and a half-adder gate.