Hardware-Efficient Variational Quantum Algorithms for Time Evolution

Parameterised quantum circuits are a promising technology for achieving a quantum advantage. An important application is the variational simulation of time evolution of quantum systems. To make the most of quantum hardware, variational algorithms need to be as hardware-efficient as possible. Here we present alternatives to the time-dependent variational principle that are hardware-efficient and do not require matrix inversion.

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Quantum Monte Carlo Integration: The Full Advantage in Minimal Circuit Depth

This paper proposes a method of quantum Monte-Carlo integration that retains the full quadratic quantum advantage without requiring any arithmetic or the quantum Fourier transform to be performed on the quantum computer. The heart of the proposed method is a Fourier series decomposition of the sum that approximates the expectation in Monte-Carlo integration, with each component then estimated individually using quantum amplitude estimation.

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Filtering Variational Quantum Algorithms for Combinatorial Optimization

To make combinatorial optimisation more efficient, we introduce the Filtering Variational Quantum Eigensolver, which utilises filtering operators to achieve faster and more reliable convergence to the optimal solution. We explore the use of causal cones to reduce the number of qubits required on a quantum computer. Our methods perform better than the original VQE algorithm and QAOA.

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Variational Quantum Amplitude Estimation

We propose to perform amplitude estimation with the help of constant-depth quantum circuits that variationally approximate states during amplitude amplification. In the context of Monte Carlo (MC) integration, we numerically show that shallow circuits can accurately approximate many amplitude amplification steps. We combine the variational approach with maximum likelihood amplitude estimation in VQAE.

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Noise-Aware Quantum Amplitude Estimation

In this paper. we derive from simple and reasonable assumptions a Gaussian noise model for NISQ Quantum Amplitude Estimation (QAE). We provide results from QAE run on various IBM superconducting quantum computers and Honeywell’s H1 trapped-ion quantum computer to show that the proposed model is a good fit for real world experimental data.

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Fast Stabiliser Simulation with Quadratic Form Expansions

We show how, with deft management of the quadratic form expansion representation, we may simulate individual stabiliser operations in O(n2) time matching the overall complexity of other simulation techniques. Our techniques provide economies of scale in the time to simulate simultaneous measurements of all (or nearly all) qubits in the standard basis and allow single-qubit measurements with deterministic outcomes to be simulated in constant time.

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Variational Inference with a Quantum Computer

In this work, we propose quantum Born machines as variational distributions over discrete variables. Our techniques enable efficient variational inference with distributions beyond those that are efficiently representable on a classical computer.

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Diagrammatic Differentiation for Quantum Machine Learning

Diagrams are becoming a prominent tool in both machine learning (ML) and quantum computing. We adapt a key tool of ML, gradients to general diagrammatic theories. This will enable one to do (quantum) ML fully diagrammatically, substantially broadening the road towards general quantum advantage and quantum NLP in particular.

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