May 20, 2021

# Distance Scales for Interconnecting Quantum Computing Elements

We need decent terminology and scales of distance when discussing the interconnection of quantum computing elements, whether they be individual qubits, lattices of qubits, chips of qubits, modules of qubits, subsystems of quantum computers, complete quantum computers, or networked quantum computer systems, from 1 angstrom to millions of miles. This informal paper scopes out the magnitude of the distance scales for interconnecting quantum computing elements. These concepts also apply to *quantum sensing*, and *quantum storage*.

The goal here is that when someone speaks about *quantum connections*, *modular quantum computers*, *quantum networking*, and *distributed quantum processing*, we need to understand what distance scales they are working with so that we can understand what the challenges might be at those distances or what distances or range of distances they are contemplating to support.

**Topics to be discussed:**

- My main motivation.
- Main issues
- This paper is not about the technology of quantum interconnections
- Go metric!
- Rough scales rather than precise distances.
- What is a quantum computing element?
- Quantum computing architecture
- Lattice of qubits
- What is a quantum connection?
- Modular quantum computers.
- Distributed quantum processing.
- There’s no single technology for all distance scales.
- Twin constraints of distance between qubits.
- Spooky action at a distance.
- Stationary and flying qubits.
- Shuttling qubits and modular quantum computers.
- Shuttling qubits and quantum networking.
- Range of distance scales for each technology.
- Quantum communication.
- Quantum networking.
- Quantum storage.
- Quantum sensing.
- Signal carrier, medium, materials, and environment.
- Distance scales — logical and physical.
- Logical or functional distance scales.
- Physical distance scales.
- Quantum networking distance scales.
- No rack-size quantum computers at present
- When might we see the first modular or networked quantum computers?
- Security
- Summary and conclusions

# My main motivation

What really got me thinking about quantum connections and distances for quantum computing elements were the challenges creating modular quantum computers, where qubits may be in different modules, separated by some distance.

My two main interests were:

- To support much larger numbers of qubits.
- To support greater connectivity between qubits, especially those which are not physically adjacent.

As a secondary matter, I have a longer-term interest in quantum networking, where entire quantum computers may be separated by significant distances, significantly greater than the distance between modules in a single quantum computer. And the goal is to support quantum interactions across the network, not merely transfer of classical qubits across the network.

And as a tertiary matter, I am interested in exploiting *spooky action at a distance* — getting effects at a distance without movement of data or qubits to achieve those effects.

# Main issues

**Limit of qubits in a single lattice.**Desire to support multiple groups (lattices) of qubits on a single chip.**Limit of qubits on a single chip.**Desire to support multiple chips.**Difficulties of connecting or coupling qubits on a single chip.**Either simply not physically adjacent or at too great a distance.**Difficulties of connecting or coupling qubits between multiple chips.**Generally a matter of the distance.**Desire for modular quantum computers.**Desire to support multiple modules and subsystems to handle much larger numbers of qubits. And cope with connectivity issues for larger numbers of qubits — and distance between qubits to be connected.**Shuttling (moving) qubits.**To bring them closer to enable or facilitate two-qubit gates on quantum computers which support shuttling (e.g., trapped-ion devices.)**Desire for tightly-linked quantum computers.**Analogous to classical multiprocessors. Multiple quantum processors working very closely together without heavy overhead of open networking.**Desire to network quantum computers.**Desire to support distributed quantum computing. And much larger numbers of qubits. And dealing with significant distances for quantum connectivity.

# This paper is not about the technology of quantum interconnections

Although the technologies relevant to quantum connections are very interesting and very important, the actual technologies themselves are outside the scope of this informal paper which focuses only on distance itself. So when an interconnect technology is discussed, the issues discussed in this paper will be relevant solely from the perspective of distance alone.

# Go metric!

Although I am an American and prone to preferring inches, feet, and miles, and occasionally lapse into those English units, I’ve endeavored to stick strictly to the metric system for distances here in this paper.

# Rough scales rather than precise distances

The emphasis of this informal paper is on very, very rough scales of distance rather than any sense of precise distances. In fact, just about all of the numbers used here are intended to be rough, general, nonspecific ranges of distance.

# What is a quantum computing element?

The focus here is on the *quantum* elements of a quantum computer. There is of course additional classical circuitry as well, but this paper is not treating classical circuitry — which focuses on classical bits — as quantum processing elements.

To be clear, the concern and focus in this paper is not all components of a quantum computer, but simply those components for which distance, great or small, is significant — from a quantum perspective.

And the concern is not for specific components (other than qubits themselves), but major components in a more abstract sense than anything specific (other than qubits themselves.)

For the purposes of this informal paper, a *quantum computing element* is any of:

**Qubit.**An individual qubit.**Lattice of qubits.**A contiguous lattice, grid, or other arrangement of qubits with direct connections. On a single chip or space in a vacuum for trapped ions and neutral atoms.**Quantum chip.**A chip containing qubits. One or more lattices of contiguous qubits. May be a single lattice or multiple lattices, analogous to a multi-core classical processor chip.**Module.**A module of qubits. One or more quantum chips (and possibly non-quantum support circuitry. May be a single chip containing some number of qubits in one or more lattices, or multiple quantum chips and multiple lattices.**Subsystem.**A subsystem of a quantum computer. Multiple modules, with quantum connections between the modules.**Quantum processing unit (QPU).**A complete quantum processing unit (QPU). One or more modules and subsystems. Especially the control circuitry for executing quantum logic gates and measurements.**Multiple QPUs.**Multiple quantum processing units in the same quantum computer system. They may be independent and isolated and simply share all of the non-quantum hardware and support software, or they may support quantum connections between qubits of the QPUs. Comparable to a multi-core classical computer chip.**Quantum computer system.**A complete quantum computer system. Might be a single QPU or multiple QPUs with quantum connections between them. Also classical network connections to external classical computer systems.**Tightly-coupled quantum computers.**Much closer and faster than even a local area network or local cluster. Comparable to a classical multiprocessor system. Possibly comparable to a classical supercomputer. This is tightly-coupled quantum state — classical bits are not relevant.**Network of quantum computer systems.**Using a quantum network to connect quantum computers, at the quantum level — connecting quantum states rather than classical bits. Four scales: local cluster of quantum computers, quantum local area networks, quantum wide area networks, and quantum Internet.**Local cluster of quantum computers.**A quantum local area network, but relatively short distances — maybe a few feet to twenty feet. Looser and further distance than tightly coupled. Greater interaction within the cluster than between computers on a local area network.**Quantum local area network.**Typically within a building. Looser and further distance than tightly-coupled or clusters.**Quantum wide area network.**Much looser and much greater distance than a quantum local area network.**Quantum Internet.**Great distances and little control over connections. Open access.

Quantum computers can also be connected to traditional local area and wide area networks and the Internet, but those connections are not quantum connections — classical bits can be transferred, not quantum state.

# Quantum computing architecture

Although quantum computing architectures are quite relevant to this paper, the finer details of architecting a quantum computer are far beyond the scope of this informal paper. A number of concepts from quantum computing architecture are in fact relevant, such as the quantum computing elements just elaborated, but any further detail is beyond the scope of this paper since the primary focus is distance scales for interconnections between these quantum computing elements.

# Lattice of qubits

The fundamental quantum computing element for interconnection of qubits is the *lattice* or *grid* of qubits. The precise arrangement of qubits won’t necessarily be a simple, clean square or rectangle, but is nonetheless still referred to as a *lattice of qubits* (or a *grid of qubits*.)

All of the qubits in a lattice of qubits are spaced far enough apart to maintain isolation between the quantum states of adjacent qubits, but close enough to enable qubits to be entangled under control of the execution of a quantum logic gate.

The focus of this paper is less about interactions within a lattice of qubits, and more about interconnections between qubits of different lattices.

Lattice and grid are approximate synonyms in this paper.

# What is a quantum connection?

In contrast to a classical connection such as a wire, fiber optic cable, or radio link which transfers classical bits, a *quantum connection* permits *interaction* between the quantum states of two or more qubits. Interactions include:

- Execution of a quantum logic gate — on a single qubit.
- Execution of a quantum logic gate — between two or more qubits.
- Entanglement between two or more qubits.
- Measurement of a qubit.

# Modular quantum computers

A lattice of qubits is the most efficient approach to enabling interactions between a modest to moderate number of qubits, but beyond a few dozen qubits, practical issues begin to intrude. Multiple lattices are possible on a single *chip*, but even that runs into some of the same practical limitations. *Modular quantum computers* address such practical issues, enabling quantum connections between lattices on an arbitrary number of modules.

Modular quantum computers could support hundreds or even thousands of qubits.

Distance scales within a modular quantum computer could range from a few centimeters to a meter or so.

# Distributed quantum processing

As capable as even modular quantum computers might be, even they quickly run into practical limitations. As with classical computing, distributed computing — *distributed quantum computing* — can transcend the limitations of lattices, chips, and modules of qubits, networking an arbitrary number of quantum computers using quantum connections.

This is not merely placing quantum computers on a LAN, WAN, or the Internet, transferring classical bits, but *quantum networking* with *quantum connections* which enable transfer and interaction of the *quantum states* of qubits.

Distance scales for distributed quantum processing can vary greatly, from under a meter to a few meters to tens or hundreds of meters to kilometers, tens of kilometers, hundreds of kilometers, to even millions of kilometers for deep space. Clearly a range of technologies will likely be needed to cope with the wide-ranging demands of such disparate distances.

# There’s no single technology for all distance scales

It would be nice if there was one quantum interconnection technology that allowed quantum computing elements to be connected at all possible distance scales, but there just isn’t any such technology, not now and not likely any time in the future.

# Twin constraints of distance between qubits

Qubits cannot be placed at arbitrary distances. The distance between two qubits must satisfy two constraints:

**Isolation.**The two qubits must be far enough apart that unless explicitly entangled, they constitute*isolated quantum systems*. Changes to the quantum state of one qubit cannot affect the quantum state of the other qubit.**Interaction.**The two qubits must be placed close enough that they can*interact*when a quantum logic gate is executed that refers to those two qubits. Or when a qubit is to be measured. There must be a viable*quantum connection*between the two qubits, such as a*cavity*or*coupler*through which a laser or microwave signal can reliably travel to perform the interaction.

*Measurement* is simply a special or simplified form of interaction.

# Spooky action at a distance

Once two qubits have become entangled, they no longer rely on an explicit connection since they directly share the same quantum state. But they do have to become entangled first before spooky action at a distance can kick in.

Two qubits must be initially entangled using some *quantum connection* at some viable distance for that quantum connection to function. Once entangled, those qubits can be moved to any other distance, with spooky action at a distance maintaining the entanglement despite being more distant than was required to establish the initial entanglement.

Technically, distance shouldn’t matter for entangled qubits, and it doesn’t once the qubits are entangled, but the initial separation of entangled quantum systems can be problematic, including taking macroscopic time, especially for relativistic distances. Entangled qubits have a coherence time that may be too brief to move the entangled qubits more than a relatively small distance. That coherence time and equivalent distance should be clearly documented for each qubit technology.

# Stationary and flying qubits

Some qubits are *stationary qubits*, hardwired into a semiconductor substrate, for example. They cannot be moved. They must be at a far enough distance apart to maintain isolation, but close enough for some mechanism such as a resonator or coupler to allow them to interact under control of execution of a quantum logic gate.

Other qubits are *flying qubits* such as photons or trapped ions or neutral atoms, commonly held in place such as using lasers or magnetic fields. They can be moved, such as *shuttling* of ions in a trapped-ion quantum computer.

# Shuttling qubits and modular quantum computers

Some trapped-ion quantum computers have the ability to move qubits, trapped ions, around dynamically.

The main goal of shuttling is to support a much larger number of qubits than can be directly operated on, and then using shuttling to dynamically bring qubits closer together so that two-qubit operations can be performed at a shorter distance.

Put simply, shuttling enables modular quantum computing — for a trapped-ion or neutral-atom quantum computer.

Shuttled qubits must be kept far enough apart to maintain isolation of their quantum states.

But they must be able to be moved close enough to perform interactions under control of execution of a quantum logic gate.

Those two distances must be known and maintained for a trapped-ion quantum computer to function properly.

For a discussion of a quantum computer architecture based on shuttling of trapped ions, read:

- “
*To build up a large-scale quantum computer, we have proposed a ‘quantum charge-coupled device’ (QCCD) architecture consisting of a large number of interconnected ion traps. By changing the operating voltages of these traps, we can confine a few ions in each trap or shuttle ions from trap to trap. In any particular trap, we can manipulate a few ions using the methods already demonstrated, while the connections between traps allow communication between sets of ions.*” **Architecture for a large-scale ion-trap quantum computer**- D. Kielpinski, C. Monroe & D. J. Wineland
- https://www.nature.com/articles/nature00784
- http://iontrap.umd.edu/wp-content/uploads/2012/12/Architecture-for-a-large-scale-ion-trap-quantum-computer.pdf

For the purpose of this paper, the open question is what distance scales are relevant between ion traps, both minimum and maximum, as well as the optimum range.

# Shuttling qubits and quantum networking

Although modular quantum computers may be the primary interest in shuttling of qubits, quantum networking, at least over short distances, such as for tightly-coupled quantum computers, or local clusters of quantum computers, might also utilize shuttled qubits.

# Range of distance scales for each technology

Any particular interconnection technology will have a range of distance scales over which it can operate. So both a *minimum distance* and a *maximum distance* should be specified for each particular technology.

There may be a variety of options for a given technology as well, each potentially affecting the minimum and maximum distance scales.

Technologies frequently come as families as well, each member of the family having its own quirks and minimum and maximum distance scales as well, but some distances may be shared across all members of the family.

# Quantum communication

Although the focus of this paper is quantum computing, many of the concepts and distance scales are likely to apply to quantum communication as well.

# Quantum networking

Quantum networking is considered part of or at least integrated with quantum computing in this paper. If nothing else, quantum networking enables distributed quantum computing.

# Quantum storage

The concepts of distance scales also apply to quantum storage. In particular, issues related to connecting a quantum computer and quantum storage separated by some distance.

# Quantum sensing

The concepts of distance scales also apply to quantum sensing. In particular, issues related to connecting a quantum sensor and a quantum computer at some distance.

# Signal carrier, medium, materials, and environment

Although this paper is focused on distance alone, it might be helpful for distance to be qualified by factors related to how quantum state is propagated from point A to point B.

There are four factors:

**Signal carrier.**Electron, photon, ion, neutral atom. Frequency or energy.**Medium.**Wire, optical fiber, vacuum, air. The normal path of the signal.**Materials.**What type of wire, cable, or optical fiber. What other materials the signal might need to traverse or propagate through.**Environment.**Including temperature — cryogenic, room temperature, humidity, air pressure, etc. Noisiness — extraneous electromagnetic radiation.

# Distance scales — logical and physical

This paper presents distance scales from two perspectives:

**Logical or functional distance scales.**What capabilities are being attempted or enabled. What is the functional effect. Why do it. What is trying to be accomplished.**Physical distance scales.**The actual distances. What physical entities are being traversed.

# Logical or functional distance scales

The whole point of a *logical or functional distance* is to focus on what functional purpose is being accomplished at that distance scale. What capabilities are being attempted or enabled. What is the functional effect at that distance scale. Why do it. What is trying to be accomplished. This is distinct from the actual physical distance scales, which are detailed in the next section, *Physical distance scales*.

**Within a single qubit.**The shortest distance.**Physically adjacent to another qubit.**Distant enough to maintain isolation, but close enough to enable interaction under control of execution of a quantum logic gate.**Within the same lattice of qubits.**Under a millimeter to a couple of millimeters.**Within the same chip.**Same quantum processing unit (QPU.) May have multiple lattices of qubits, analogous to a multi-core classical CPU chip. Maybe multiple modules within a single chip. Fraction of a centimeter to maybe a full centimeter.**Within the same module.**Maybe multiple chips for a single module. Up to a few centimeters.**Within the same subsystem.**Maybe multiple modules. Up to a few tens or dozens of centimeters. Maybe the same quantum processing unit.**Between subsystems, within the same system.**Possibly multiple subsystems. A few dozen centimeters to a meter or so. Possibly multiple processing units, but they may be integrated into a single processing unit.**Between QPUs of a multi-QPU system.**Similar to connections between subsystems — a few dozen centimeters to a meter.**Tightly-coupled systems.**Multiple systems but with a tight interconnect. Under a meter to maybe a couple of meters.**Within the same rack.**Multiple, independent but networked systems. Under a meter to maybe a couple of meters.**Adjacent racks.**Up to a couple of meters, but maybe less than a single meter.**Multiple adjacent non-rack systems.**A few to ten meters.**Within the same room.**No more than a few dozens of meters.**Within the same facility.**Such as a data center or building of a campus. Dozens to hundreds of meters.**Within the same cluster.**May be within the same rack, the same room, or the same facility.**Within the same campus.**A few hundred yards, maybe a mile.**Nearby.**Within one mile or two.**Locally.**Within 5–10 miles.**Sub-regional.**Within 50–100 miles.**Regional.**Within a few hundred miles.**Super-regional.**E.g., east or west coast or midwest. Possibly 1,000 to 1,500 miles.**Continental.**Up to a few thousand miles.**Intercontinental.**Three to ten thousand miles.**Global, planetary.**Up to 12,500 miles.**Aviation.**A few thousand to 100,000 feet.**Karman line.**The edge of space, the upper limit of the Earth’s atmosphere. 100 kilometers. 62.5 miles.**Near-planet, orbital.**Low-earth orbit (LEO). Up to a few hundred miles.**Medium earth orbit.**A thousand to a few thousand miles. Well above LEO, well under GEO**High orbital.**More than 1,000 miles above surface. Includes geostationary, geosynchronous, and polar orbital — GEO.**Space.**Beyond earth orbit.**Moon.****Mars.****Asteroids.**Beyond Mars.**Deep space.**Beyond even Mars and the asteroid belt, possibly even beyond the edge of the solar system.

# Physical distance scales

*Physical distance scales* are the actual physical distances, regardless of the functional purpose being accomplished at that distance, as opposed to *logical or functional distance scales*, detailed in the preceding section.

**Planck length.**1.616255 times 10 to the minus 35 meters or 1.616255 times 10 to the minus 25 angstroms. The absolute smallest distance possible. Not particularly relevant for building real devices, but it is the ultimate, theoretical baseline.**1 angstrom.**One tenth of a nanometer. Lower limit for most practical distances. Anything smaller practical?**Sub-nanometer.**Under 10 angstroms.**1 nanometer.**The fundamental unit for measurement at small scales. Angstrom may be preferred for even smaller scales.**5 nanometers.****10 nanometers.****100 nanometers.****1 micrometer.**AKA micron.**10 micrometers.****100 micrometers.**One tenth of a millimeter. Width of a human hair.**1 millimeter.**Rough limit for visually recognizable features. Limit between multiple lattices on a single chip — no more than a few millimeters.**10 millimeters.**One centimeter. Limit for connections within a quantum module — 2 to 10 centimeters.**100 millimeters.**Ten centimeters. One tenth of a meter. Limit for many tight quantum connections. Limit for connections between subsystems — 10 to 75 centimeters.**1 meter.**General unit for size or distance between human-scale objects. Limit for many quantum connections within a quantum computer system or tightly-linked systems.**10 meters.**Limit for quantum connections to nearby quantum computer systems.**100 meters.**One tenth of a kilometer. Limit for a quantum local area network — 10 to 250 meters, or so.**1 kilometer.**A little over half a mile (5/8 mile, 0.625 miles.) Low end for quantum wide area networks.**10 kilometers.**6.25 miles.**100 kilometers.**62.5 miles. Also the Karman line, the edge of space, the upper limit of the Earth’s atmosphere.**1,000 kilometers.**625 miles.**10,000 kilometers.**6,250 miles.**100,000 kilometers.**62,500 miles. Sufficient for even two devices in geosynchronous Earth orbit.**Moon.**Moon orbiting Earth — 363,000 kilometers to 406,000 kilometers + 12,750 kilometer diameter of Earth.**Mars.**Both Mars and Earth orbiting the sun — 56 million to 401 million kilometers.**500 million kilometers.**Deep space.

# Quantum networking distance scales

Quantum networking would occur at the level of quantum computer systems, although individual qubits can be connected. There can be a variety of distance scales for networked quantum computers.

**Local.**Single quantum computer. No quantum networking. All current quantum computers. Any networking is strictly classical computer networking.**Tightly-coupled quantum computers.**Multiple quantum computer systems. Very, very short and very, very fast quantum connections between systems. Not clear whether this should actually be classified as quantum networking per se, but it’s borderline and different from connections within a single quantum computer. A hybrid, for sure.**Rack.**Multiple quantum computer systems within a single rack mounting. Very short distances, no more than a couple of meters, or only a fraction of a meter.**Local area.**Relatively near, multiple quantum computers. Including within a data center or single building.**Campus.**Still a local area network, but spanning multiple buildings.**Wide area.**Relatively distant, potentially large number of quantum computers.**Global.**Everywhere on the planet and possibly in earth orbit as well.**Orbital.**100 to 1,000 miles above the surface of the Earth, or even 22,000 miles for geostationary and geosynchronous orbit.**Deep space.**Beyond Earth orbit. Moon, Mars, asteroids, and beyond.

# No rack-size quantum computers at present

The concept of a *rack* as used in this paper is not relevant to most current quantum computing technology as all existing quantum computing systems are physically much larger than a standard rack as used in a typical classic computing data center. A complete quantum computer cannot fit within a single standard rack, let alone multiple quantum computers.

Actually, most current quantum computer systems *use* racks internally for their classical electronics hardware. But that’s not the use of the term rack intended in this paper.

This paper anticipates that much as happened with early classical computer systems, quantum computer systems will gradually evolve into ever-smaller form factors, eventually fitting within a fraction of a standard hardware rack.

But that’s not the reality today, nor is it likely in the near future.

Whether it takes five, seven, or ten years to get to the stage where multiple quantum computers can fit in a single standard rack is of course unknown.

# When might we see the first modular or networked quantum computers?

None of the current crop of quantum computers is modular or networked — in a quantum sense, where quantum state rather than classic bits interact beyond a single lattice of tightly connected qubits.

When might a quantum computer be built with multiple lattices, or qubits from the respective lattices of two quantum computers interact? Great question, but the answer is unknown.

IonQ has at least made some minimal public statement, and stated 2023 as a target year for introducing a modular quantum computer:

- “
*By 2023, IonQ will deploy modular quantum computers small enough to be networked together in a datacenter, and by 2025, we expect to achieve broad quantum advantage.*” **Scaling IonQ’s Quantum Computers: The Roadmap**- December 9, 2020
- https://ionq.com/posts/december-09-2020-scaling-quantum-computer-roadmap

Other than that, modular quantum computing is an open, unexplored frontier — seeking bold adventurers.

# Security

Technically it’s not strictly on-topic in this paper, but as quantum computers begin to become networked and distributed, potentially with open access, *security* begins to become an issue.

The only aspects of security that I will mention here are:

- Levels of control.
- Forms of access.

**Levels of control**

- Organizations
- Groups within organizations
- Teams
- Individuals
- Applications
- Processes
- Software modules
- Algorithms or individual functions

**Forms of access**

- Access to read
- Access to modify
- Access to add
- Access to remove
- Access to execute
- Control access to data and functions
- Monitor access to data and functions
- Access to systems
- Control access to systems
- Monitor access to systems
- Throttle access to systems
- Access to transport
- Control access to transport
- Monitor access to transport
- Throttle use of transport
- Deny access to transport

# Summary and conclusions

- When discussing a new quantum computing technology, be explicit about what distances are supported for the various elements of the quantum computing system.
- Distances need to be considered between individual qubits, lattices of qubits, chips, modules, subsystems, systems, tightly-connected systems, clusters, local area networks, wide area networks, and global networks, as well orbital, lunar, planetary, and deep space systems. And these are quantum connections, not classical connections with classical bits.
- When contemplating quantum computing over some distance, explicitly consider what different technologies might be needed to accommodate that particular distance. Different technologies may be needed for different distances.
- Current quantum computers are limited to very short distances.
- Much research is needed in quantum networking.
- Much research is needed in modular quantum computing.
- Much research is needed in tightly-coupled quantum computers.
- Much research is needed in supporting dramatically greater numbers of qubits.
- Much research is needed in supporting dramatically greater connectivity between quantum computing elements.
- Much research is needed in quantum connections in general.
- Much research is needed to facilitate operation of quantum processing elements at much greater distances (greater coherence, fewer errors), and simultaneously more research to enable many more qubits to be packed much closer (better isolation.)
- As quantum computing systems become more open, more modular, and more distributed, security becomes much more urgent.

For more of my writing: ** List of My Papers on Quantum Computing**.