[Paper Review] Single-qubit rotations in parameterized quantum circuits

S. E. Rasmussen, Niels Jakob Søe Loft+3 more|arXiv (Cornell University)|May 27, 2020

Quantum Computing Algorithms and Architecture10 references2 citations

TL;DR

This paper demonstrates that single-qubit rotations in parameterized quantum circuits can be reduced without sacrificing expressibility or entangling capability. It further shows that a parameterized photonic quantum circuit without any single-qubit rotations achieves expressibility and entangling performance comparable to the best standard parameterized circuits, suggesting significant optimization potential in variational quantum algorithms.

ABSTRACT

With the advent of hybrid quantum classical algorithms using parameterized quantum circuits the question of how to optimize these algorithms and circuits emerges. In this paper we show that the number of single-qubit rotations in parameterized quantum circuits can be decreased without compromising the expressibility or entangling capability of the circuit. We also compare expressibility and entangling capability across different number of qubits in parameterized quantum circuits. We also consider a parameterized photonics quantum circuit, without any single-qubit rotations, which yields an expressibility and entangling capability comparable to the best regular parameterized quantum circuits.

Motivation & Objective

• To investigate whether single-qubit rotations can be minimized in parameterized quantum circuits without degrading performance.
• To analyze how expressibility and entangling capability vary with the number of qubits in parameterized circuits.
• To evaluate the performance of a parameterized photonic quantum circuit that omits single-qubit rotations entirely.
• To compare the expressibility and entangling capability of rotation-free photonic circuits against standard parameterized circuits.

Proposed method

• The authors analyze the expressibility and entangling capability of parameterized quantum circuits using different numbers of single-qubit rotations.
• They derive and compare the unitary evolution of circuits with and without single-qubit rotations to assess their functional equivalence in state space coverage.
• They design and simulate a parameterized photonic quantum circuit that relies solely on entangling gates and phase shifts, excluding all single-qubit rotations.
• They evaluate expressibility via the fidelity of the state distribution to the Haar measure and entangling capability via entanglement entropy metrics.
• They perform comparative analysis across varying qubit counts to assess scalability and performance trade-offs.
• They use numerical simulations to validate that rotation-free photonic circuits achieve comparable expressibility and entangling capability to standard circuits.

Experimental results

Research questions

• RQ1 Can the number of single-qubit rotations in parameterized quantum circuits be reduced without compromising expressibility or entangling capability?
• RQ2 How does the expressibility and entangling capability of parameterized circuits scale with the number of qubits when single-qubit rotations are minimized?
• RQ3 Can a parameterized photonic quantum circuit without any single-qubit rotations achieve expressibility and entangling capability comparable to standard parameterized circuits?
• RQ4 What is the performance trade-off between circuit depth and expressibility when eliminating single-qubit rotations?

Key findings

• The number of single-qubit rotations in parameterized quantum circuits can be significantly reduced without degrading the circuits' expressibility or entangling capability.
• Circuits with fewer single-qubit rotations maintain high expressibility across different qubit counts, indicating robustness to rotation reduction.
• A parameterized photonic quantum circuit that excludes all single-qubit rotations achieves expressibility and entangling capability comparable to the best standard parameterized circuits.
• The performance of the rotation-free photonic circuit remains strong even as the number of qubits increases, suggesting scalability.
• The results indicate that single-qubit rotations are not essential for high expressibility, challenging the conventional design of variational quantum algorithms.
• The study reveals that entangling gates and phase shifts alone can effectively generate a rich and diverse set of quantum states.