Computational Perspectives for Quantum Phases of Matter
PI: Zhen Bi (Physics)
Tuition for the graduate student may be covered by the PI’s or the senior member’s NSFCAREER grant or startup funding.
Senior team member: Chunhao Wang (CSE)
Introduction
Phases of matter are a cornerstone concept in physics: they group together systems that share the same universal properties despite differences in microscopic details. In everyday terms, a crystal and a block of ice both belong to a solid phase because each resists shear and supports long-range positional order, whereas water exemplifies the liquid phase, flowing freely with no such rigidity. Quantum phases apply the same organizing principle to many-body systems whose degrees of freedom are quantum mechanical– spins in a magnet, electrons in a superconductor, or qubits in a quantum processor. Historically, we diagnosed these phases with experimental probes such as electrical conductivity, specific heat, etc. More recently, a complementary computational viewpoint has emerged: the complexity of preparing or simulating a quantum phase on a quantum computer often reveals deeper, more universal structures than traditional observables. Exploring this computational perspective of quantum phases is the central goal of this project.
Davies generators and mixing time Within quantum algorithm research, significant progress has been made on Gibbs-state preparation– a quantum algorithm to prepare the thermal state of an arbitrary local Hamiltonian. The workhorse is the Davies generator: a carefully designed Lindbladian (dissipative evolution) that starts from a featureless state– typically the maximally mixed state– and drives the system toward equilibrium at a chosen temperature. As Davies generators obey detailed balance and can be simulated with local couplings, they provide a resource efficient route to preparing quantum matter in thermal equilibrium on near-term hardware.
A pivotal cost metric is the mixing time– the physical duration required for the open-system dynamics to drive the state to thermal equilibrium. In practical terms, the mixing time serves as an operational complexity measure for a Gibbs state: a short mixing time means the phase can be prepared quickly and often signals that classical or tensor-network descriptions remain tractable; a long mixing time shows inherently slow thermalization and is frequently tied to hidden symmetries, frustration, or critical slow down. By analyzing how the mixing time scales with system size, temperature, and Hamiltonian parameters, this project will develop a computational perspective for comparing quantum phases and for pinpointing the dynamical signatures of phase transitions. Mixing time in 1-D transverse field Ising model The 1-D transverse-field Ising model (TFIM) is a textbook platform for exploring spontaneous symmetry breaking and quantum phase transitions. Its Hamiltonian, H = − iZiZi+1 − g iXi interpolates between a ferromagnetic phase when the transverse field g ≤ 1 and a quantum paramagnetic phase when g ≥ 1. At gc = 1 the model sits at a quantum phase transition and the associated quantum-critical fan governs f inite-temperature behaviour over a broad swath of the (g,T) plane (phase diagram on the right).
We will numerically simulate Davies open-system dynamics (algorithm of arXiv:2311.09207) for chains of length L ≤ 30:
1. construct the Davies Lindbladian and evolve mixed states;
2. extract the gap of the Davies generator and the mixing time τmix(L,g,T) to a fixed trace-distance tolerance;
3. sweep g and T to chart τmix across phases and through the quantum-critical fan.
Goals: 1) Identify scaling laws such as τmix∼Lz f(TLz) and quanPhase diagram of 1-D TFIM tify critical slowing down; 2) Use numerical trends to guide analytical work (Jordan–Wigner mapping, field-theory approximations) and, ultimately, develop general criteria that classify phases and phase transitions by computational complexity.
Computational Expertise Needed
Open-System Simulation Techniques
• Implement Lindblad/Davies dynamics with QuTiP, QuantumOptics.jl, or ITensor (MPO time evolution); use Krylov or shift-invert methods to obtain the Liouvillian gap.
The ideal Junior Researcher will pair the expertise outlined above with a working knowledge of many-body quantum physics.
Specific Short-Term Goals
1. Construction of Davies generators for 1-D transverse field Ising model with generic coupling
2. Numerical simulation of Davies evolutions
3. Analyze scaling behavior of the mixing time
Long-term goal Establish a robust portfolio of preliminary findings– combining benchmarked numerical simulations with analytical insight across diverse model systems– to serve as the cornerstone of a competitive proposal to the DOE Quantum Information Science program.
Engagement with ICDS CWisalready affiliated with ICDS, while ZB has not yet collaborated with the institute. Through this seed project, we will (i) run our open-system simulations on the Roar-GPU cluster, (ii) participate in ICDS workshops and training events, and (iii) co-supervise an ICDS Junior Researcher– steps aimed at building a long-term partnership.