Elizabeth Champion

Analog quantum simulation of the Lipkin-Meshkov-Glick model in a transmon qudit

  1. Elizabeth Champion,
  2. Annie Schwartz,
  3. Muhammad A. Ijaz,
  4. Xiaohui Xu,
  5. Steve Campbell,
  6. Gabriel T. Landi,
  7. and Machiel S. Blok
The simulation of large-scale quantum systems is one of the most sought-after applications of quantum computers. Of particular interest for near-term demonstrations of quantum computational
advantage are analog quantum simulations, which employ analog controls instead of digitized gates. Most analog quantum simulations to date, however, have been performed using qubit-based processors, despite the fact that many physical systems are more naturally represented in terms of qudits (i.e., d-level systems). Motivated by this, we present an experimental realization of the Lipkin-Meshkov-Glick (LMG) model using an analog simulator based on a single superconducting transmon qudit with up to d=9 levels. This is accomplished by moving to a rotated frame in which evolution under any time-dependent local field and one-axis twisting can be realized by the application of multiple simultaneous drives. Combining this analog drive scheme with universal control and single-shot readout of the qudit state, we provide a detailed study of five finite-size precursors of quantum criticality in the LMG model: dynamical phase transitions, closing of the energy gap, Kibble-Zurek-like dynamics, statistics of the order parameter, and excited-state phase transitions. For each experiment we devise a protocol for extracting the relevant properties which does not require any prior knowledge of the system eigenstates, and can therefore be readily extended to higher dimensions or more complicated models. Our results cement high-dimensional transmon qudits as an exciting path towards simulating many-body physics.
arxiv pdf

Multi-frequency control and measurement of a spin-7/2 system encoded in a transmon qudit

  1. Elizabeth Champion,
  2. Zihao Wang,
  3. Rayleigh Parker,
  4. and Machiel Blok
Qudits hold great promise for efficient quantum computation and the simulation of high-dimensional quantum systems. Utilizing a local Hilbert space of dimension d > 2 is known to speed
up certain quantum algorithms relative to their qubit counterparts given efficient local qudit control and measurement. However, the direct realization of high-dimensional rotations and projectors has proved challenging, with most experiments relying on decompositions of SU(d) operations into series of rotations between two-level subspaces of adjacent states and projective readout of a small number of states. Here we employ simultaneous multi-frequency drives to generate rotations and projections in an effective spin-7/2 system by mapping it onto the energy eigenstates of a superconducting circuit. We implement single-shot readout of the 8 states using a multi-tone dispersive readout (F_assignment = 88.3%) and exploit the strong nonlinearity in a high EJ/EC transmon to simultaneously address each transition and realize a spin displacement operator. By combining the displacement operator with a virtual SNAP gate, we realize arbitrary single-qudit unitary operations in O(d) physical pulses and extract spin displacement gate fidelities ranging from 0.997 to 0.989 for virtual spins of size j = 1 to j = 7/2. These native qudit operations could be combined with entangling operations to explore qudit-based error correction or simulations of lattice gauge theories with qudits. Our multi-frequency approach to qudit control and measurement can be readily extended to other physical platforms that realize a multi-level system coupled to a cavity and can become a building block for efficient qudit-based quantum computation and simulation.
arxiv pdf