Could Metastable States Be the Answer?

Title: omg blueprint for trapped ion quantum computing with metastable states

Authors: D. T. C. Allcock, W. C. Campbell, J. Chiaverini, I. L. Chuang, E. R. Hudson, I. D. Moore, A. Ransford, C. Roman, J. M. Sage, and D. J. Wineland

First Author’s Institution: University of Oregon

Status: Published in Applied Physics Letters

Background Info

This section is intended to be a (very) brief overview of atomic ion qubits for the newly initiated. If you would like to skip ahead to the new stuff from the journal article, click here.

When looking for candidates for quantum bits (qubits), you want a quantum system that has at least two states whose separation is unique (so that you can convert from one state to the other without risking converting to a different third state). Atomic ions are natural choices for qubits since atoms have energy levels whose separations are naturally unequal to one another (see Figure 1 for an example of an ion qubit). Atomic ions also have some of the longest coherence times of any type of qubit, meaning they remain in the state you put them in for a long time (typically anywhere from on the order of seconds to years depending on the atomic states being used).

Furthermore, ions can be trapped, shuttled, addressed, and otherwise manipulated with electromagnetic fields and waves. When trapped and cooled together, a group of ions form a crystal-like structure referred to as a Coulomb crystal (so-called because the ions are held in this crystal-like structure by the Coulomb force of repulsion between each other and the electric and magnetic fields used to trap them).

Despite all of these advantages, using atomic ions as qubits in a quantum computer poses some challenges which must be overcome. They are error prone due to interactions with stray photons, background gases in the vacuum system, or stray electromagnetic fields from outside interference. Furthermore, care must be taken to avoid crosstalk, an unwanted affect where light being used to perform an operation on one qubit scatters and affects a nearby qubit. It is also difficult to scale up to larger numbers of qubits.

In order to build a quantum computer with atomic ion qubits, the authors list four key needs:

1. The ability to perform an operation on a qubit without affecting other nearby qubits (aka crosstalk)
2. The ability to read qubits’ states without disturbing nearby qubits
3. The ability to entangle two different groups of qubits
4. The ability to quickly re-arrange and/or move ion-qubits within a Coulomb crystal without heating the ions

All of this needs to be accomplished in large arrays of ions while maintaining the same high fidelities that experiments with small numbers of ions have demonstrated.

One approach designed to address the problem of errors due to crosstalk is the dual-species approach. As its name implies, this approach makes use of two different species of atoms that are trapped together. Generally, at least one of the species will be easy to laser cool and can be used to sympathetically cool the other species of ion it is co-trapped with. (As one species is Doppler cooled, the other species which cannot be Doppler cooled will be “sympathetically cooled” due to Coulomb repulsion between it and the laser cooled species.) The two different species of atoms should also be close in mass to enable efficient sympathetic cooling as well as to minimize the difference in response to both applied and stray electric and magnetic fields [4].

By arranging the atomic ions in the trap such that the species of atom alternates every other ion, you can prevent crosstalk between neighboring qubits. This allows for much easier addressing of individual qubits without worrying about accidentally affecting its nearest neighbors.

However, dual-species brings its own challenges, one of which is needing twice as many laser systems to be able to address the two different atomic species. Perhaps the biggest challenge, however, is the difference in mass between the two species. Because the acceleration an ion experiences is proportional to its charge to mass ratio, a difference in mass means that the two species will experience a different acceleration from the same electromagnetic field. This is problematic since ion traps use electromagnetic fields to trap ions. It also makes it difficult to re-arrange/shuttle qubits around within the trap.

This is where the authors’ proposed omg architecture comes in. The omg architecture aims to keep the advantages of the dual species architecture while eliminating the difference in mass (and thus all of the difficulties associated with having two different masses).

omg Architecture

The omg architecture uses two different types of electronic qubits within the same species of atomic ion (nobody said we had to use the exact same two energy levels in every atom as our qubit states, did they?). The authors name this architecture omg after the three types of electronic qubits housed within a single species of atomic ion:

• o for optical-frequency qubits
• m for metastable-state qubits
• g for ground-state qubits

The optical-frequency qubit consists of a ground state and a metastable state whose energy difference corresponds to a visible wavelength of light. These qubits are addressed with lasers.

The metastable-state qubit consists of two metastable states (e.g. hyperfine levels or Zeeman levels) typically in the ²D_5/2 or ²F_7/2 state. These states must have long lifetimes compared to the length of time that information is stored in them (but don’t need to be as long as ground state qubits). These qubits are addressed with RF magnetic fields and gradients or stimulated Raman transitions.

The ground-state qubit consists of two ground states (e.g. hyperfine levels or Zeeman levels) in the ²S_1/2 state. These qubits are addressed with microwaves.

By utilizing a species of atomic ion that has all three types of qubits (hereafter referred to as omg ions), you can have dual species functionality without having a difference in mass to contend with. This really is the best of both worlds, since it means having the ability to address individual qubits without interfering with neighboring qubits while retaining the ability to easily trap, re-arrange, and shuttle ions with electromagnetic fields. Several species that the authors give as omg candidates are ⁴³Ca⁺, ⁸⁷Sr⁺, ¹³³Ba⁺, ¹³⁵Ba⁺, ¹³⁷Ba⁺, ¹⁷¹Yb⁺, ¹⁷³Yb⁺.

The three key ingredients for quantum computation are state preparation, gate operations, and storage. State preparation depends on the laser cooling mechanisms that are available in that particular species of atomic ion. Gate operations depend on having wavelengths that are “technologically convenient.” By technologically convenient, I mean wavelengths for which it is easy to interface to existing computer hardware (think telecom wavelengths). m-type qubits could be ideal candidates for gate operations given their longer wavelength transitions (in the MHz and Low GHz frequencies). Storage requires qubits with long lifetimes (g-type qubits have the longest lifetimes, but m-type qubits are also sufficiently long-lived for this job). o-type qubits are ideal for state readout because of their visible fluorescence.

Thus, an omg ion houses within a single atomic species everything you need to meet the three architectural requirements of a quantum computer. The authors go on to outline three possible schemes for building a quantum computer using the omg architecture. These three modes are denoted by the notation {state preparation, gate, storage} with the corresponding symbol (o, m, g) for each purpose. In all three modes, o-type qubits are used for the readout of states and g-type qubits are used for sympathetically cooling the ion array. I have summarized the three different modes below:

{m, m, m} Mode

• Uses metastable-state qubits for all operations
• Uses g-type ions for laser cooling and o-type ions for state readout of info
• Main Advantages:
  • Since all operations are performed with m-type qubits, there is no need to convert a qubit from one type to another
  • Laser cooling and g-qubit state preparation can be performed during gate operations on other ions within the crystal
• Main Disadvantages:
  • Storage is limited by the lifetime of the metastable state
  • Because m-type qubits are used for both storage and gate operations, this mode requires focused laser beams (or physically shuttling the ions away from neighbors) to avoid disturbing the storage qubits while performing gate operations

{g, m, g} Mode

• Uses m-type qubits for gate operations and g-type qubits for state preparation and storage
• Uses g-type ions for laser cooling and o-type ions for state readout of info
• Main Advantages:
  • The long lifetimes of ground-state qubits enable excellent storage of information
  • The storage qubits are protected from laser light used to perform gate operations
• Main Disadvantages:
  • Requires the ability to convert between m-type and g-type qubits without loss of information
  • This mode is likely the most difficult for readout of information as well as sympathetic cooling while an algorithm is being run (since doing so requires all g-qubits involved in the algorithm to be converted to m-qubits to protect them during these operations)

{m, g, m} Mode

• Uses m-type qubits for state preparation and storage and g-type qubits for gate operations
• Uses g-type ions for laser cooling and o-type ions for state readout of info
• Main Advantages:
  • Protects the storage qubits from laser light used to perform gate operations
  • Only the qubits involved in an active process (gate operations, cooling, or state readout) need to be converted (storage qubits are protected from such operations)
• Main Disadvantages:
  • Storage is limited by the lifetime of the metastable state
  • Requires the ability to convert between m-type and g-type qubits without loss of information

Tl;dr

The omg architecture is an architecture proposed by the authors that would utilize multiple types of qubits within the same type of atomic ion. Doing so enables various tasks to be performed on qubits more easily without scattered light or cross talk between neighboring qubits causing decoherence during the process. It also avoids the issues arising from mass-mismatch that the dual-species architecture must grapple with.

References

[1] Allcock, D. T., et al. “Omg Blueprint for Trapped Ion Quantum Computing with Metastable States.” Applied Physics Letters, vol. 119, no. 21, 2021, p. 214002., https://doi.org/10.1063/5.0069544.

[2] Heinrich, Johannes, et al. “A Be+ Ion Trap for H2+ Spectroscopy.” Thèse de doctorat: Physique: Sorbonne université.

[3] Thompson, Richard C. “Ion Coulomb Crystals.” Contemporary Physics, 2015, pp. 1–17., https://doi.org/10.1080/00107514.2014.989715.

[4] Home, Jonathon P. “Quantum Science and Metrology with Mixed-Species Ion Chains.” Advances In Atomic, Molecular, and Optical Physics, 2013, pp. 231–277., https://doi.org/10.1016/b978-0-12-408090-4.00004-9.