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Europhysics Letters (EPL)

Adiabatic speedup via zero-energy-change control in a spin system

Licheng Zhang, Feng-Hua Ren, Yifei Chen, Run-Hong He, Yongjian Gu, Zhao-Ming Wang

Published Feb 6, 2019• 8 citations
Publisher

Abstract

Adiabatic evolution is required in performing quantum information processing tasks and adiabatic speedup is often used to avoid decoherence problems for a long evolution time.Here, we add a leakage elimination operator (LEO) Hamiltonian to the evolution and adiabatic speedup can be obtained.LEO Hamiltonians can be realized by a sequence of periodic zero-energy-change pulses.By using the Feshbach P -Q partitioning technique, we obtain the exact control parameters to realize adiabatic speedup for different types of pulses.Furthermore, we show that this control scheme is fault-tolerant against pulse strength and pulse frequency for specified thresholds.

DOI
10.1209/0295-5075/125/10010

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Adiabatic evolution is required in performing quantum information processing tasks and adiabatic speedup is often used to avoid decoherence problems for a long evolution time.Here, we add a leakage elimination operator (LEO) Hamiltonian to the evolution and adiabatic speedup can be obtained.LEO Hamiltonians can be realized by a sequence of periodic zero-energy-change pulses.By using the Feshbach P -Q partitioning technique, we obtain the exact control parameters to realize adiabatic speedup for different types of pulses.Furthermore, we show that this control scheme is fault-tolerant against pulse strength and pulse frequency for specified thresholds.
Adiabatic evolution is used in a variety of quantum information processing tasks. However, the elimination of errors is not as well developed as it is for circuit model processing. Here, we present a strategy to improve the performance of a quantum adiabatic process by adding leakage elimination operators (LEOs) to the evolution. These are a sequence of pulse controls acting in an adiabatic subspace to eliminate errors by suppressing unwanted transitions. Using the Feshbach PQPQPQ partitioning technique, we obtain an analytical solution for a set of pulse controls. The effectiveness of the LEO is independent of the specific form of the pulse but depends on the average frequency of the control function. By observing that the evolution of the target eigenstate is governed by a periodic function appearing in the integral of the control function, we show that control parameters can be chosen in such a way that the instantaneous eigenstates of the system are unchanged, yet a speedup can be achieved by suppressing transitions. Furthermore, we give the exact expression of the control function for a counter unitary transformation to be used in experiments which provides a clear physical meaning for the LEO, aiding in the implementation.
The adiabatic quantum information processing task requires that the evolution of a system must be kept in its instantaneous eigenstate. However, normally the adiabaticity will be ruined due to the interaction between the system and the noisy environment in its long evolution time. Here, in this paper, we show that zero-area pulse control can be used to realize the adiabatic process in a nonadiabatic regime. A concrete example is provided where one spin chain is cut into two chains. The pulse function is applied in the laboratory frame and suitable pulse conditions are obtained numerically. We find that compared with the pulse conditions obtained in the adiabatic frame, the results are similar for low-energy-level systems but tend to deviate when the system's energy level increases. We then obtain the pulse conditions theoretically by writing the control Hamiltonian in the adiabatic frame. It is found that a sequence of pulses with intensities tuned by a time-dependent energy difference is required to guarantee an effective adiabatic speedup.
The slow evolution required for adiabaticity in adiabatic quantum computation renders the system vulnerable to environmental noise. Leakage elimination operator (LEO) control provides an effective strategy to realize adiabatic speedup over a short timescale, thus mitigating the noise impact. Despite extensive theoretical investigations, the realization of LEO-based adiabatic speedup on realistic superconducting quantum processors remains absent. In this work, we present such a realization on IBM superconducting quantum processors. We first characterize the trade-off between adiabaticity and noise accumulation by varying the total evolution time on both the Qiskit simulator and the ibm_marrakesh processor, employing a comprehensive noise model that closely reproduces the experimental results. We then implement ideal LEO pulse derived for a closed system and achieve a significant enhancement of adiabatic fidelity within a short evolution time. To further improve the adiabatic fidelity, we refine the ideal LEO pulse via Bayesian optimization based on the comprehensive noise model. The optimized pulse yields a modest fidelity gain in simulation, yet on hardware it falls short of the ideal pulse under the present experimental conditions. Our work validates the feasibility of LEO-based adiabatic speedup on a superconducting quantum processor and highlights the potential of LEO for noise-aware adiabatic dynamics.
Adiabatic quantum computation requires keeping a system in a particular eigenstate. However, unwanted transitions can occur due to the interaction of the system with a noisy environment. The adiabatic evolution of the system will then be ruined. To reduce the effect of the environment, quantum control methods can be used. This allows one to speed up the adiabatic process. Here we present an effective control scheme to allow for a speedup of the adiabatic process by using a sequence of pulses on the system. Using the hierarchical functional derivative (HFD) approach, we calculate the fidelity evolution, which is a measure of the adiabaticity in an open system. By carefully choosing the pulse intensity and duration, an accelerated adiabatic path can be obtained for both a weak-coupling and a strong non-Markovian environment.
Quantum communication through spin chains has been extensively investigated. In this scenario, state transfer through linearly arranged spins connected by uniform nearest-neighbor couplings qualifies as a natural choice, with minimal control requirements. However, quantum states usually cannot be perfectly transferred through a uniformly coupled chain due to the dispersion of the chain. Here, we propose an effective quantum control technique to realize almost exact state transfer (AEST) in a quantum spin chain. The strategy is to add a leakage elimination operator Hamiltonian to the evolution, which implements a sequence of pulse control acting on a perfect state transfer subspace. By using the one-component Feshbach PQ partitioning technique, we obtain the conditions over the required pulses. AEST through a spin chain can then be obtained under a suitable pulse intensity and duration.
Effective quantum control is essential for quantum computing and information processing, yet level leakage remains a bottleneck limiting control fidelity. The leakage elimination operator (LEO) approach is highly effective at suppressing leakage from a target subspace to other subspaces. Analytical control conditions under the high-frequency driving limit have been derived via the Feshbach PQ partitioning technique. However, the driving intensity is subject to fundamental physical bounds, and low-frequency driving is experimentally more feasible. In this work, we reformulate LEO within the Magnus framework and extend it beyond the high-frequency limit. We show that the analytical control conditions obtained from the Feshbach PQ partitioning technique are equivalent to the zeroth-order Magnus expansion. We then analyze the higher-order Magnus corrections. By minimizing the leakage, we obtain a modified pulse condition suitable for the low-frequency regime. As an illustrative example, we study near-perfect state transfer through a one-dimensional spin chain under LEO control. We find that the second-order Magnus correction improves the transmission fidelity at low-frequency driving, while the improvement becomes negligible at high frequencies. Our results provide an effective route for designing control pulses in the low-frequency regime, with potential applications in superconducting qubits, trapped ions, and solid-state spin systems.