Supplementary Information to“Balancing the quantum speed limit and instantaneous energy cost in adiabatic quantum evolution”

I.SUPPLEMENTARY NOTE 1:THEORETICAL MATERIALS.The quantum speed limit(QSL)is essential for quantum computing and quantum communication,referring to the minimum time required for a quantum system to evolve from one state to another.Two well-known forms of the QSL are the Mandelstam-Tamm(MT)relation TqsL≥πh/2△E[S1]and the Margolus-Levitin(ML)relation TqsL≥πh/2(E)[S2]where Tqst is denoted as the QSL time,h is the reduced Planck's constant,△E is the energy uncertainty(standard deviation)of the system,and(E)is the average energy of the system above its ground state.Both of relations provide a lower bound on the evolution time.

Balancing the Quantum Speed Limit and Instantaneous Energy Cost in Adiabatic Quantum Evolution

Adiabatic time-optimal quantum controls are extensively used in quantum technologies to break the constraints imposed by short coherence times.However,practically it is crucial to consider the trade-off between the quantum evolution speed and instantaneous energy cost of process because of the constraints in the available control Hamiltonian.Here,we experimentally show that using a transmon qubit that,even in the presence of vanishing energy gaps,it is possible to reach a highly time-optimal adiabatic quantum driving at low energy cost in the whole evolution process.This validates the recently derived general solution of the quantum Zermelo navigation problem,paving the way for energy-efficient quantum control which is usually overlooked in conventional speed-up schemes,including the well-known counter-diabatic driving.By designing the control Hamiltonian based on the quantum speed limit bound quantified by the changing rate of phase in the interaction picture,we reveal the relationship between the quantum speed limit and instantaneous energy cost.Consequently,we demonstrate fast and high-fidelity quantum adiabatic processes by employing energy-efficient driving strengths,indicating a promising strategy for expanding the applications of time-optimal quantum controls in superconducting quantum circuits.

考虑负荷聚合商的源荷双侧合作协同运行策略

为应对可再生能源出力间歇性对电能供需实时平衡带来的挑战,利用供给侧与需求侧相互配合的运营模式,进而提出考虑负荷聚合商参与的源荷合作博弈优化模型。首先,构建考虑负荷聚合商的源荷合作运行基本框架,以解决源侧可再生能源出力波动性带来的电能供需供应难题。其次,计及源侧发电成本、弃风成本,荷侧需求响应成本,构建源荷双侧支付函数模型;并以源荷合作运行总成本最低为目标函数,以保证各参与主体的运行经济性。再次,基于Shapley值分配法,提出合作运行联盟内源荷双侧的成本分配策略,从而保证合作运行联盟的稳定性。最后利用算例仿真验证所提源荷合作运行策略的可行性与有效性。结果表明:所提策略可减小负荷峰谷差、减少火电机组出力、提高可再生能源消纳量、降低源荷双侧运行成本,对系统的经济环境效益具有积极作用。