Shallow quantum circuits for deeper problems

Physical Review A, vol. 108

Abstract

State-of-the-art quantum computers can only reliably execute circuits with limited qubit numbers and computational depth. This severely reduces the scope of algorithms that can be run. While numerous techniques have been invented to exploit few-qubit devices, corresponding schemes for depth-limited computations are less explored. This work investigates to what extent we can mimic the performance of a deeper quantum computation by repeatedly using a shallower device. We propose a method for this purpose, inspired by Feynman simulation, where a given circuit is chopped into two pieces. The first piece is executed and measured early on, and the second piece is run based on the previous outcome. This method is inefficient if applied in a straightforward manner due to the high number of possible outcomes. To mitigate this issue, we propose a shallow variational circuit, whose purpose is to maintain the complexity of the method within predefined tolerable limits, and provide an optimization method to find such a circuit. The composition of these components of the methods is called ``reduce'' As we discuss, this approach works for certain cases of interest. We believe this work may stimulate new research towards exploiting the potential of shallow quantum computers.

Authors 4

1. Adrián Pérez-Salinas Aachen Instituut-Lorentz 〈aQaL〉 Applied Quantum Algorithms

   Leiden University

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden, Niels Bohrweg 2, 2333 CA Leiden, Netherlands

   〈aQaL〉 Applied Quantum Algorithms, Universiteit Leiden, 2333 CA Leiden, Netherlands

   〈aQaL〉 Applied Quantum Algorithms, Universiteit Leiden, 2333 CA Leiden, Netherlands

2. Radoica Draškić Aachen 〈aQaL〉 Applied Quantum Algorithms

   Leiden University

   Affiliation as printed

   LIACS, Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, Netherlands

   〈aQaL〉 Applied Quantum Algorithms, Universiteit Leiden, 2333 CA Leiden, Netherlands

   〈aQaL〉 Applied Quantum Algorithms, Universiteit Leiden, 2333 CA Leiden, Netherlands

3. Jordi Tura Aachen Instituut-Lorentz 〈aQaL〉 Applied Quantum Algorithms

   Leiden University

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden, Niels Bohrweg 2, 2333 CA Leiden, Netherlands

   〈aQaL〉 Applied Quantum Algorithms, Universiteit Leiden, 2333 CA Leiden, Netherlands

   〈aQaL〉 Applied Quantum Algorithms, Universiteit Leiden, 2333 CA Leiden, Netherlands

4. Vedran Dunjko Aachen Instituut-Lorentz 〈aQaL〉 Applied Quantum Algorithms

   Leiden University

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden, Niels Bohrweg 2, 2333 CA Leiden, Netherlands

   LIACS, Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, Netherlands

   〈aQaL〉 Applied Quantum Algorithms, Universiteit Leiden, 2333 CA Leiden, Netherlands

   〈aQaL〉 Applied Quantum Algorithms, Universiteit Leiden, 2333 CA Leiden, Netherlands