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Realizing quantum speed limit in open system with a PT -symmetric trapped-ion qubit

Le Luo, Pengfei Lu, Teng Liu, Yang Liu, Xinxin Rao, Qifeng Lao, Hao Wu, Feng Zhu

Published May 8, 2023• 0 citations
Publisher

Abstract

Abstract Faster quantum gate operation time is one of the key issues in quantum information processing. It has a lower bound in a closed quantum system, so called quantum speed limit (QSL). But this limit could be significantly decreased in an open system, resulting in novel quantum computation schemes. Here we have experimentally studied the QSL in a non-Hermitian parity time symmetric (PT -symmetric) quantum system with a dissipative trapped-ion qubit. The QSL decreases with the increase of dissipation intensity, which is significantly smaller than that of closed system. The non-Hermitian QSL exhibits chiral dependence on the evolution path, for which we propose the non-Hermitian Bloch sphere and construct its corresponding SU(2) Lie group to explain it. Furthermore, the QSL with the anti-parity-time-symmetric system has been verified in our experiments. These results enable a wellcontrolled knob for speeding up quantum gate operation, paving the way towards faster quantum computation in an open system.

DOI
10.21203/rs.3.rs-2843863/v1

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Abstract Faster quantum gate operation time is one of the key issues in quantum information processing. It has a lower bound in a closed quantum system, so called quantum speed limit (QSL). But this limit could be significantly decreased in an open system, resulting in novel quantum computation schemes. Here we have experimentally studied the QSL in a non-Hermitian parity time symmetric (PT -symmetric) quantum system with a dissipative trapped-ion qubit. The QSL decreases with the increase of dissipation intensity, which is significantly smaller than that of closed system. The non-Hermitian QSL exhibits chiral dependence on the evolution path, for which we propose the non-Hermitian Bloch sphere and construct its corresponding SU(2) Lie group to explain it. Furthermore, the QSL with the anti-parity-time-symmetric system has been verified in our experiments. These results enable a wellcontrolled knob for speeding up quantum gate operation, paving the way towards faster quantum computation in an open system.
Abstract Quantum speed limit (QSL), the lower bound of the time for transferring an initial state to a target one, is of fundamental interest in quantum information processing. Despite that the speed limit of a unitary evolution could be well analyzed by either the Mandelstam–Tamm or the Margolus–Levitin bound, there are still many unknowns for the QSL in open systems. A particularly exciting result is about that the evolution time can be made arbitrarily small without violating the time-energy uncertainty principle, whenever the dynamics is governed by a parity-time ( P T ) symmetric Hamiltonian. Here we study the QSLs with both P T and anti- P T Hamiltonians, and pose the QSL as a brachistochrone problem on a non-Hermitian Bloch sphere. We then use dissipative trapped-ion qubits to construct the Hamiltonians, where the state evolutions reach the QSL governed by a generalized Margolus-Levitin bound of the non-Hermitian system. We find that the evolution time monotonously decreases with the increase of the dissipation strength and exhibits chiral dependence on the Bloch sphere. These results enable a well-controlled knob for speeding up the state manipulation in open quantum systems, which could be used for quantum control and simulation with non-unitary dynamics.
Non-Hermitian systems satisfying parity-time (PT) symmetry have aroused considerable interest owing to their exotic features. Anti-PT symmetry is an important counterpart of the PT symmetry, and has been studied in various classical systems. Although a Hamiltonian with anti-PT symmetry only differs from its PT-symmetric counterpart in a global ±i phase, the information and energy exchange between systems and environment are different under them. It is also suggested theoretically that anti-PT symmetry is a useful concept in the context of quantum information storage with qubits coupled to a bosonic bath. So far, the observation of anti-PT symmetry in individual quantum systems remains elusive. Here, we implement an anti-PT-symmetric Hamiltonian of a single qubit in a single trapped ion by a designed microwave and optical control-pulse sequence. We characterize the anti-PTphase transition by mapping out the eigenvalues at different ratios between coupling strengths and dissipation rates. The full information of the quantum state is also obtained by quantum state tomography. Our work allows quantum simulation of genuine open-system feature of an anti-PT-symmetric system, which paves the way for utilizing non-Hermitian properties for quantum information processing.
The quantum speed limit (QSL) refers to the maximum speed of a quantum system to evolve from an initial state to its orthogonal states. The bound on the QSL for Hermitian systems, for example the Mandelstam-Tamm (MT) and Margolus-Levitin (ML) as well as Sun-Zheng(SZ) bound, was studied respectively from the perspectives of average value and variance of the system Hamiltonian as well as the geometry of the system. While the compactness of the MT-type, ML-type and SZ-type bounds has been examined well for Hermitian systems, a compact QSL for non-Hermitian systems has not been well studied. In this work, based on the biorthogonal basis theory we derive two distinct and tighter bounds on the QSL for non-Hermitian systems, which correspond to the MT and ML bounds for Hermitian systems. We show that the shortest evolution time corresponding to the two bounds of the non-Hermitian system can be attained by certain initial states, showing the compactness and tightness of our bounds. These initial states dubbed fastest initial states(FIS) are different from that in Hermitian systems. A bound close to QSL for non-FIS is presented and comparison of our bound with others in literature is performed. To illustrate our results, we present a minimal non-Hermitian system to show QSL, and the condition for the shortest evolution time is derived analytically using the present theory.
Entanglement generation is a cornerstone of quantum information science, yet its speed in Hermitian systems is fundamentally constrained by the coupling strength, a restriction known as the quantum speed limit. Here we demonstrate that this bound can be beaten by exploiting the unique topology of non-Hermitian systems near exceptional points (EPs). Using a pair of trapped ions, we engineer a parity-time symmetric Hamiltonian where the coalescence of eigenstates near the EP distorts the Hilbert space geometry, providing a shortcut for quantum state evolution. We observe that, as the system approaches the EP, the time required to generate a maximally entangled state is markedly reduced with respect to the limits imposed by the equivalent Hermitian interaction. We further uncover a fundamental physical trade-off whereby the acceleration of entanglement is intrinsically coupled to a reduction in the success probability, revealing the information cost of non-Hermitian speedup. Our results suggest that tailored dissipation, rather than being a source of decoherence, can serve as a powerful resource for accelerating quantum dynamics, offering a new paradigm for designing high-speed quantum gates and sensors in hardware-constrained platforms.
Abstract The quantum speed limit (QSL) is a fundamental lower bound on the evolution time for quantum systems, and its tightness has been observed to be dependent on the properties of the physical process. However, experimental studies exploring the QSL in open quantum systems are still missing. Here, we studied geometric quantum speed limits of a qubit subject to decoherence in an ensemble of chloroform molecules in a Nuclear Magnetic Resonance experiment. We controlled the system-reservoir interaction and the spin relaxation rates by adding a paramagnetic salt, allowing the observation of both Markovian and non-Markovian open system dynamics for the qubit. We used two distinguishability measures of quantum states to assess the speed of the qubit evolution: the quantum Fisher information (QFI) and Wigner-Yanase skew information (WY). For non-Markovianity and low salt concentrations, we found crossovers between QSLs related to those metrics. The WY metric sets the tighter QSL for high concentrations and Markovian dynamics. We also show that QSLs are sensitive even to small fluctuations in spin magnetization.
In this study, we investigate qubit dynamics under PT and Anti-PT-symmetric non-Hermitian Hamiltonians, focusing on phase evolution, decoherence, quantum speed limits (QSL), and Rényi entanglement entropies. Using similarity transformations and Dyson maps, we analyze the reduced density matrix evolution in bosonic environments. Anti-PT-symmetric systems show enhanced robustness against decoherence, with slower entropy growth and longer coherence times compared to PT-symmetric counterparts. QSL behavior is non-monotonic, reflecting rapid initial evolution followed by a gradual decrease. Higher-order Rényi entropies reveal that Anti-PT-symmetric qubits preserve quantum information more effectively, offering advantages for memory and cryptographic applications.