### Molecules as quantum information devices

Molecules – and atoms – are perfect. That is, every molecule *X* is a complex, intricate quantum machine – and a perfect copy of every other *X*. Polyatomic molecular ions contain many desirable attributes of a useful quantum system – rich internal degrees of freedom, weak, highly controllable coupling to the environment, and potential scalability via strong inter-molecular interactions. To date, we cannot realize the promise of this intricate perfection – because we lack the tools to initialize and read out these quantum machines. Remarkably, we have never put a molecule with more than two atoms in a single quantum state. We hope to do so – and to realize a set of tools which will allow us to treat the molecules like the perfect quantum machines that they are.

Trapped atomic ions have become a well established quantum information platform. We have learned to initialize, manipulate, entangle, and read out substantial arrays of trapped atomic ions; each ion is a 2-state system, or Qubit. Molecular ions are far more complex than 2-state systems, and allow for agile, microwave-mediated transitions within a rich subspace of low-lying rotational and hyperfine states. Each molecular ion therefore yields the “quantum processing power” of several 2-state Qubits; for example, the ability to rapidly realize arbitrary unitary transformations within a molecule’s lowest 16 hyperfine states is exactly analagous to the ability to realize arbitrary 4-input, 4-output gates in a system of 4 discrete Qubits with controllable couplings. As with atomic ion systems, such a system can be scaled by adding more molecules; discrete molecules can be coupled via their shared motional states as in atomic ion systems. Quantum computing architectures with both identical and distinct molecular species can be considered

### How to manipulate molecules

All state manipulation is done via applied magnetic,electric, or far off resonant optical field pulses produced from agile arbitrary waveform generators. Although each molecule represents several Qubits, this architecture is very much a “gate based” QC design, in that realization of arbitrary unitary transformations within the combined Hilbert space of the entire ensemble is the design goal. While the long term goal is to explore the potential of complex molecules as quantum information systems, many intermediate goals – ultra-precise spectroscopy, implementation of quantum error correction within a single molecule, and entanglement of multiple molecules – present themselves.

### What can be done with quantum control of molecules?

Once we can initialize, manipulate, and read out the state of a molecule, what new frontiers can we address?

One tantalizing possibility is the idea of realizing quantum error correction within a single molecule. The well known Shor code, for example, can correct any of 18 plausible errors applied to the 9 physical bits used to encode a data bit. These errors – consisting of bit flip errors on bits 1..9, and sign flip errors on bits 1..9 – form a small subset of the possible unitary transformations that could act on the physical computer; it makes sense to correct these errors, and not others, because they are plausibly caused by understood physical processes, such as stray fields. A molecule exposed to electromagnetic fields likewise experiences certain unwanted unitary transformations much more rapidly than others. Can codes be designed to correct these errors? Can the coherence time of data stored in a molecule be extended by continuous feedback, done faster than errors can accumulate? These exciting questions – questions which are closely related to the frontiers of “discrete bit” quantum computing – form a major motivation of our work.