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International Journal of Quantum Information

Approximate supervised learning of quantum gates via ancillary qubits

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

Published Sep 12, 2018• 1 citation
Publisher

Abstract

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.

DOI
10.1142/s021974991840004x

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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.
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.
Fault-tolerant quantum computing requires encoding the quantum information into logical qubits and performing the quantum information processing in a code-space. Quantum error correction codes, then, can be employed to diagnose and remove the possible errors in the quantum information, thereby avoiding the loss of information. Although a series of single- and two-qubit gates can be employed to construct a quantum error correcting circuit, however this decomposition approach is not practically desirable because it leads to circuits with long operation times. An alternative approach to designing a fast quantum circuit is to design quantum gates that act on a multi-qubit gate. Here I devise quantum control schemes to design high-fidelity single-shot multi-qubit (up to three) quantum gates. Quantum control task is to steer quantum dynamics towards closely realizing specific quantum operation by varying the external control parameters (external field) such that the resultant evolution closely approximates the desired evolution. A set of instructions that determines the control parameters, and hence the effectiveness of the control scheme, is called a policy. Machine learning algorithms can be employed to find successful policies for designing quantum gates. In particular, we employ supervised machine learning techniques to generate these successful policies. Finding successful policies is a feasibility problem for which optimization algorithms can be employed. Greedy algorithms are at the heart of machine learning techniques. They converge faster onto a successful policy and require less-computational resource than non-greedy algorithms. However, there is no guarantee that greedy algorithms succeed to a feasible solution when there exist constraints on i) gate operation time ii) computational resources, and iii) experimental resources. Our results show the failure of standard greedy machine learning algorithms and the superiority of non-greedy machine learning algorithms over greedy ones for designing quantum logic gates, when there exist constraints on the quantum system. We have also observed the failure of existing greedy and non-greedy techniques for designing high-fidelity three-qubit gates. Hence, we devised our machine learning technique called Subspace-Selective Self-adaptive Differential Evolution (SuSSADE). Each three-qubit gate designed by SuSSADE operates as fast as an entangling two-qubit gate under the same experimental constraints.
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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.