Abstract
Short-depth algorithms are crucial for reducing computational error on near-term quantum computers, for which decoherence and gate infidelity remain important issues. Here we present a machine-learning approach for discovering such algorithms. We apply our method to a ubiquitous primitive: computing the overlap between two quantum states ρ and σ. The standard algorithm for this task, known as the Swap Test, is used in many applications such as quantum support vector machines, and, when specialized to ρ = σ, quantifies the Renyi entanglement. Here, we find algorithms that have shorter depths than the Swap Test, including one that has a constant depth (independent of problem size). Furthermore, we apply our approach to the hardware-specific connectivity and gate sets used by Rigetti’s and IBM’s quantum computers and demonstrate that the shorter algorithms that we derive significantly reduce the error—compared to the Swap Test—on these computers.
Highlights
Quantum supremacy [1] may be coming soon [2]. While it is an exciting time for quantum computing, decoherence and gate fidelity continue to be important issues [3]. These issues limit the depth of algorithms that can be implemented on near-term quantum computers (NTQCs) and increase the computational error for short-depth algorithms
While the Swap Test appears as a subroutine in many of these applications, we show that there are more efficient circuits to perform this subroutine
We have found a constant depth algorithm for computing state overlap, which is better than the linear scaling of the Swap Test
Summary
Quantum supremacy [1] may be coming soon [2]. While it is an exciting time for quantum computing, decoherence and gate fidelity continue to be important issues [3]. Our approach is distinct from previous works in that we do not start with an ansatz or template for the quantum circuit; nor do we restrict to a discrete gate set as is usually done in algorithms based on genetic programming. Our machine-learning approach finds algorithms with a shorter depth than the Swap Test for computing the overlap. We do this by initially specializing the training data to one- and two-qubit states and manually generalizing the resulting algorithms to input states of arbitrary size. Due to its constant circuit depth, the BBA seems to be the best algorithm for quantifying state overlap on NTQCs. In what follows, we first present our machine-learning approach for discovering quantum algorithms. As a hyperparameter that one fixes while optimizing the algorithm
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