Optimizing operators

David Edward Bruschi

We propose an approach to factorize the time-evolution operator of a quantum system through a (finite) sequence of elementary operations that are time-ordered. Our proposal borrows from previous approaches based on Lie algebra techniques and other factorization procedures, and requires a set of optimization operations that provide the final result. Concretely, the algorithm produces at each step three optimal quantities, namely the optimal duration of the desired unitary operation, the optimal functional dependence of the driving function on the optimal time, and the optimal elementary Hermitian operation that induces the additional unitary operation to be implemented. The resulting sequence of unitary operations that is obtained this way is sequential with time. We compare our proposal with existing approaches, and highlight which key assumptions can be relaxed for practical implementations.

Robert Wille, Rolf Drechsler

Zhang Ya-jua

This paper exploits one optimized unitary operator to prepare a type of highly entangled state of multiple qubits—cluster state. Based on optimal control theory, the duration of optimized unitary operator has been shortened due to the application of a series of non-selective pulse. We experimentally implemented the optimized unitary operator on a NMR spectrometer. By firstly generating a pseudo-pure state, a three-qubit cluster state was produced by applying the optimized unitary operator. Our experimental results show the feasibility of the optimized unitary operator.

Belal Ehsan Baaquie

Wenjie Liu, Yue Ma, Yuchen Gu +2 more

Recently, Quantum Approximate Optimization Algorithm (QAOA) and Quantum Alternating Operator ansatz (QAOAz) are utilized to solve the Mean Variance (MV) model for the portfolio optimization problem (QAOAz-MV), which shows performance advantages over classical algorithms on this huge search space. For the more complex and comprehensive risk parity (RP) model, a novel QAOAz solution (QAOAz-RP) is proposed. We begin by defining the RP model for the portfolio optimization problem. Next, we detail the QAOAz algorithm process, where the problem Hamiltonian with the ZZZZ term is derived, the corresponding quantum circuit is ingeniously constructed using the parity check method, and the whole quantum circuit containing the ring XY-mixer is given. Finally, to improve the optimization performance of QAOAz, a Particle Swarm Optimization (PSO) optimizer is introduced to tune the parameters of the quantum circuits, which is applicable to both QAOAz-MV and QAOAz-RP. The experiment conducted on multiple financial markets (e.g. Chinese, U.S., and European) demonstrate that PSO-QAOAz-RP is significantly better for portfolio optimization than ABC-LP, GWO, GA and QAOAz-RP on eight portfolios in all metrics. PSO-QAOAz-MV also has advantage for MV model over the quantum algorithms, including QAOA (improves approximate ratio by 54.79% on average) and QAOAz (improves approximate ratio by 15.38% on average). This study not only provides a breakthrough quantum solution for portfolio optimization, but also provides a reusable technology paradigm for the deep integration of quantum computing and financial engineering. • It is the first QAOAz solution for the RP model of portfolio optimization problem. • The problem Hamiltonian and quantum circuit are derived and ingeniously constructed. • A PSO optimizer is proposed to optimize the parameters of QAOAz’s quantum circuit. • Our QAOAz-RP and PSO-QAOAz-RP outperform state-of-the-art classical algorithms. • Our PSO optimizer is effective on both MV and RP models.