Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator (1708.01044v2)

Abstract: A quantum simulator is a restricted class of quantum computer that controls the interactions between quantum bits in a way that can be mapped to certain difficult quantum many-body problems. As more control is exerted over larger numbers of qubits, the simulator can tackle a wider range of problems, with the ultimate limit being a universal quantum computer that can solve general classes of hard problems. We use a quantum simulator composed of up to 53 qubits to study a non-equilibrium phase transition in the transverse field Ising model of magnetism, in a regime where conventional statistical mechanics does not apply. The qubits are represented by trapped ion spins that can be prepared in a variety of initial pure states. We apply a global long-range Ising interaction with controllable strength and range, and measure each individual qubit with near 99% efficiency. This allows the single-shot measurement of arbitrary many-body correlations for the direct probing of the dynamical phase transition and the uncovering of computationally intractable features that rely on the long-range interactions and high connectivity between the qubits.

• The paper demonstrates a quantum quench in a 53-qubit system leading to clear observation of a nonequilibrium dynamical phase transition.
• It employs a linear chain of trapped 171Yb⁺ ions with power-law decaying Ising interactions to capture single-shot many-body correlation measurements.
• The findings challenge traditional thermalization theories and pave the way for exploring long-range quantum interactions and critical phenomena.

Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator

The paper, "Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator," by J. Zhang et al., presents a significant advancement in the paper of quantum many-body systems using quantum simulation techniques. Employing a 53-qubit quantum simulator, the authors explore a nonequilibrium dynamical phase transition (DPT) within the transverse field Ising model (TFIM), highlighting regions where traditional statistical mechanics does not suffice.

Simulation and Experimental Setup

The quantum simulator is constructed using a linear chain of up to 53 trapped $^{171}\text{Yb}^+$ ions, each representing a qubit. This system is subjected to a variety of initial states followed by the application of long-range Ising interactions and a transverse magnetic field. The Ising couplings exhibit an approximate power-law decay with distance between ions, characterized by an exponent between 0.8 and 1.0. The spin state of each qubit is individually prepared, manipulated, and measured with near 99% efficiency, allowing for single-shot measurements of many-body correlation functions.

Dynamical Phase Transition Investigation

A central focus of this research is the quantum quench process, whereby the Hamiltonian of the system is suddenly altered, compelling the system into a nonequilibrium state. The dynamics of the system post-quench are probed through the TFIM, an archetype for quantum phase transitions. The authors monitor the average magnetization and higher-order spin correlation functions throughout the evolution to identify the anticipated DPT. By varying the strength of the transverse field, two distinct regimes emerge: one exhibiting preserved $\mathbb{Z}_2$ symmetry breaking and the other restoring symmetry, with an intermediate regime indicating a robust non-zero magnetization plateau.

Methodological and Theoretical Insights

The experimental results are reinforced through numerical simulations and analytical treatments. Exact diagonalization offers insights into systems with fewer spins, while the thermodynamically extensive observed DPT, particularly for the supercritical case with long-range interactions, prompts hypotheses about the crossover behavior and critical phenomena characteristic of such quantum systems.

Key Observations

For the regime explored, a fundamental observation is the non-thermalization tendency of the spin system under paper. Traditional expectations of thermalization are not met, especially in the intermediate regime where the transverse field strength is comparable to the long-range interaction energy scale. This departure from thermalization is primarily attributed to the long-range nature of the Ising couplings, suggesting avenues for further theoretical investigation into long-range quantum interactions and their unique dynamics.

Implications and Future Directions

The presented work is a decisive step towards utilizing quantum simulators to delve into complex quantum phenomena that exceed the capabilities of classical simulation techniques. The achievement of controlling and measuring a 53-qubit system paves the way for more extensive studies involving quantum criticality, entanglement dynamics, and the exploration of quantum chaotic behavior in isolated systems. Moreover, the demonstrated single-shot measurement of complex correlators presents a tangible path to potentially solve currently intractable problems in quantum chemistry, condensed matter physics, and materials science.

Future developments may focus on refining control over interaction parameters, exploring alternative quantum phase models, and enhancing qubit coherence times. As the field progresses, these simulators could transition from simulating specific Hamiltonians to addressing broader algorithmic challenges and eventually contributing to quantum supremacy in computational tasks. This research demonstrates the feasibility and utility of large-scale quantum simulators in exploring deeply entangled many-body systems, heralding a new era in quantum simulation and computation.