Holographic dynamics simulations with a trapped ion quantum computer

Abstract

Using a trapped ion quantum computer, we experimentally demonstrate a tensor-network-based algorithm that simulates the dynamics of infinite-size quantum sys-tems by re-using qubits in the middle of the calculation.

Qubit-efficient simulation of thermal states with quantum tensor networks

“…The sto-qMPS ansatz can also be particularly helpful in certain quantum dynamics simulations, where a moderately-accurate approximation to an initial thermal state is useful, for example, in simulating the effect of temperature on chemical reaction kinetics or computing the temperature-dependence of conductivity in a correlated electron system. In these applications, the qubitefficient sto-qMPS ansatz can serve as an initial state for qubit-efficient holographic quantum dynamics techniques [17] to simulate near-thermal equilibrium dynamics. In this context, generic dynamics will be thermalizing and quickly erase any small errors in the initial state (yet it is still important to be able to produce a state with a known, and tunable initial temperature).…”

“…qMPS methods enable qubit-efficient access to a subset of MPS with exponentially-large bond dimension (in qubit number), including classically intractable cases such as 2d and 3d ground-states with symmetrybreaking [5] or (non-chiral) topological order [16], and finite-time quantum dynamics from any qMPS [2,17].…”

Measuring NISQ Gate-Based Qubit Stability Using a 1+1 Field Theory and Cycle Benchmarking

“…J is the nearest neighbor (hopping) coupling and controls the movement of the spins and creation of spin pairs, while h T is the on-site energy. This model has been used in a variety of contexts related to quantum computing [31,32,30,33,34,2,35,36,37,3,38,39,40,41,42,43,44,10,45,46,47,48,49,50].…”

“…Because it is known that, in general, two qubit gates contribute a substantially larger error on QC hardware platforms than do single qubit gates, our group conducted an in-depth stability analysis of these two-qubit gates on ibmq boeblingen by measuring the process infidelities using CB and comparing them to the results obtained from RB measurements based on the IBM quantum processor qubit re-calibrations. Because of its wide applicability in quantum field theories and many-body interactions [31,32,30,33,34,2,35,36,37,3,38,39,40,41,42,43,44,10,45,46,47,48,40,49,50] we used two-qubit gates in the Transverse Field Ising Model (TFIM) for our study of the two-qubit gate error properties.…”

Simulating Large PEPs Tensor Networks on Small Quantum Devices

“…Such capability has recently become available on some quantum processors 5 , allowing one to simulate quantum systems consisting of more qubits than are present on the physical device. Several recent works have taken this approach, simulating both static and dynamical one-dimensional (1D) matrix product states (MPS) of quasi-infinite length using a constant number of qubits [6][7][8] . Since most physical quantum states of interest are not maximally entangled, it should not be necessary to use N qubits to simulate most relevant N-qubit states.…”