Wasserstein Complexity of Quantum Circuits
- URL: http://arxiv.org/abs/2208.06306v1
- Date: Fri, 12 Aug 2022 14:44:13 GMT
- Title: Wasserstein Complexity of Quantum Circuits
- Authors: Lu Li, Kaifeng Bu, Dax Enshan Koh, Arthur Jaffe, Seth Lloyd
- Abstract summary: Given a unitary transformation, what is the size of the smallest quantum circuit that implements it?
This quantity, known as the quantum circuit complexity, is a fundamental property of quantum evolutions.
We show that our new measure also provides a lower bound for the experimental cost of implementing quantum circuits.
- Score: 10.79258896719392
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Given a unitary transformation, what is the size of the smallest quantum
circuit that implements it? This quantity, known as the quantum circuit
complexity, is a fundamental property of quantum evolutions that has widespread
applications in many fields, including quantum computation, quantum field
theory, and black hole physics. In this letter, we obtain a new lower bound for
the quantum circuit complexity in terms of a novel complexity measure that we
propose for quantum circuits, which we call the quantum Wasserstein complexity.
Our proposed measure is based on the quantum Wasserstein distance of order one
(also called the quantum earth mover's distance), a metric on the space of
quantum states. We also prove several fundamental and important properties of
our new complexity measure, which stand to be of independent interest. Finally,
we show that our new measure also provides a lower bound for the experimental
cost of implementing quantum circuits, which implies a quantum limit on
converting quantum resources to computational resources. Our results provide
novel applications of the quantum Wasserstein distance and pave the way for a
deeper understanding of the resources needed to implement a quantum
computation.
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