Reduce&chop: Shallow circuits for deeper problems

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 in 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 pre-defined tolerable limits, and provide a novel optimisation method to find such circuit. The composition of these components of the methods is called reduce\&chop. 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.

arXiv comment12 pages + 4 pages appendix, 7 + 1 figures; accepted version in Physical Review A

References in corpus (21)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• A variational eigenvalue solver on a quantum processor
• Variational Quantum Algorithms
• Quantum computational advantage using photons
• Barren plateaus in quantum neural network training landscapes
• Noisy intermediate-scale quantum (NISQ) algorithms
• Efficient simulation of one-dimensional quantum many-body systems
• Improved Simulation of Stabilizer Circuits
• Characterizing Quantum Supremacy in Near-Term Devices
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Measurement-based quantum computation
• Extending the computational reach of a noisy superconducting quantum processor
• Hybrid quantum-classical algorithms and quantum error mitigation
• Quantum autoencoders for efficient compression of quantum data
• General parameter-shift rules for quantum gradients
• Simulation of quantum circuits by low-rank stabilizer decompositions
• Simulating Large Quantum Circuits on a Small Quantum Computer
• Qibo: a framework for quantum simulation with hardware acceleration
• Time-domain characterization and correction of on-chip distortion of control pulses in a quantum processor
• Classical algorithms for quantum mean values
• High Dimensional Quantum Machine Learning With Small Quantum Computers

Cited by in corpus (4)

• Hybrid quantum cycle generative adversarial network for small molecule generation
• Realizing a Continuous Set of Two-Qubit Gates Parameterized by an Idle Time
• Error mitigation and circuit division for early fault-tolerant quantum phase estimation
• Making the cut: two methods for breaking down a quantum algorithm