Enhancing Quantum Communications with Optimal One-Shot Entanglement Sharing
By Robert Davis with contributions from Vikesh Siddhu and John Smolin
The first working quantum computer was built in 1997 with just two qubits. A year later, the first quantum computer to run a version of Shor’s algorithm did so with just seven qubits. Quantum hardware development has come a long way in the decades since, but we’ll likely need thousands of qubits to perform truly useful computations. So, how are we going to reach that scale?
Today, the largest and most powerful quantum processors in the world boast just a few hundred qubits at most. They’re a long way off from reaching a thousand qubits, let alone thousands of qubits. It could take many years for us to achieve those numbers on a single quantum processor. However, researchers believe we can make our way to high-qubit count operations much sooner by linking multiple quantum processors together in a quantum intranet. This is a field of study known as quantum communications.
How do these linkages work? Right now the short answer to that question is: not very well. This model of modular quantum computing is fairly new. Engineers are just getting started developing the physical cables and other interconnects needed to share quantum information across multiple quantum processors, and we’ve still got a lot of questions to answer about how best to use those interconnects.
In a forthcoming paper, IBM researchers Vikesh Siddhu and John Smolin decided to try their hand at tackling one of those questions. Specifically, they asked: How can we share quantum entanglement across two quantum computing nodes while maintaining the highest possible fidelity and using the fewest resources?
We’ll explain their solution in the article below. But first, let’s review some quantum communications basics.
Entanglement sharing in quantum communications
Quantum entanglement is a phenomenon in which two or more particles become correlated more strongly than classical probability would otherwise allow. Once particles enter into a quantum correlation like entanglement, you can separate them by as much distance as you like and the correlation between them will remain the same — as long as you don’t disturb the particles themselves.
In quantum computing, we can create entanglement between quantum bits that is equivalent to the entanglement that occurs between particles. This qubit entanglement plays an essential role in quantum information processing, enabling foundational techniques like building quantum algorithms, quantum cryptography, quantum teleportation and more.
Entanglement forms the backbone of quantum communication. Anytime we send quantum information through an interconnect from one quantum computing node to another, we are essentially “sharing entanglement” between two quantum systems. This means that if we want to perform high-qubit count computations using multiple quantum systems linked together, we’ll need to continuously refine the methods, metrics and protocols we use to share entanglement across quantum channels. In other words, the better we get at entangling qubits in separate quantum nodes, the more useful these modular quantum systems will be.
Why entanglement sharing is a lot harder than it looks
One might assume that linking a few quantum processors together shouldn’t be too difficult. We’ve been linking classical computers together in vast, complex networks for decades. Quantum systems should be easy enough, right?
Not quite. Today, communication between classical processors is about as challenging as writing a letter, putting it in an envelope, and handing it to someone else. Communication between two quantum processors is more like balancing two perfectly synchronized spinning plates on your index fingers, and passing one of those plates to another person, all without letting either plate fall out of sync. Also — small detail — you have to do this in the middle of a crowded outdoor rock concert, while a hurricane passes overhead.
That’s a bit more complicated than classical communications. The difference is that in classical communication, we only have to worry about sending classical information from one system to another — e.g., a tidy list of 0s and 1s. In quantum communication, we are sending quantum states from one system to another. Quantum states are extremely delicate and it only takes a small disturbance to make them collapse into classical information.
The other issue is that the links between quantum systems are usually quite noisy — and that noise can be even more destructive than our metaphorical mid-concert hurricane. Figuring out a strategy for dealing with noise in between separate quantum nodes is probably one of the biggest challenges in quantum communications, and one of the most important elements of the technique developed.
Working backwards toward high-fidelity entanglement sharing
In their upcoming paper, IBM researchers Vikesh Siddhu and John Smolin detail a mathematical apparatus that makes it possible to figure out the input you should prepare to share entanglement of the highest possible fidelity between groups of qubits.
To understand how this works, let’s imagine you have two quantum processors linked together by a quantum interconnect. We’ll call these processors “nodes.” It’s a simple scenario: Alice is in charge of Node 1. Bob is in charge of Node 2. Alice wants to create entanglement between a qubit in her node (qubit R) and a qubit in Bob’s node (qubit B).
To accomplish this, Alice will need to create an entangled state between two qubits in her quantum node — qubit R and a second qubit we’ll label as A. Then, she’ll send qubit A’s portion of that entangled state through the quantum interconnect to qubit B, in Bob’s node.
The problem is that quantum interconnects are noisy, and that noise will inevitably change the quantum state as it travels to Bob’s node. In other words, if Alice uses her two qubits to create something that resembles the ideal entangled state she wants to achieve with a qubit in Bob’s node, that state will likely be far from ideal by the time it makes its way through the quantum interconnect.
Previous research might say that Alice should solve this problem by asking herself a question: “What can I send through this noisy channel that will ‘land’ the best (i.e., arrive most accurately) in Bob’s node?”
Siddhu and Smolin decided to have Alice ask a different question: “If Bob had the best possible entanglement with a qubit in my node, what would that look like? And given what I know about the system and the noise, what should I send to make our setup look like that optimally-entangled state?” It’s a more complicated question, but it turns out it’s a lot easier to answer.
To figure it out, Alice and Bob must first work together to create a thorough description of the noise they see on either side of the interconnect that links their nodes together. They will create that description using quantum state tomography, a technique for creating detailed mathematical descriptions of quantum states and the noise associated with them. Bob will then send his portion of the description to Alice through a classical communications channel.
This process takes a tremendous amount of work, and poses many thorny theoretical questions of its own. Fortunately, it’s also beyond the scope of the paper, which focuses more on what to do with these descriptions, rather than how to generate them. So, we’ll set it aside for now.
Once Alice has a description of the noise, she’ll plug that into the mathematical apparatus developed by Siddhu and Smolin, and use that to generate a hypothetical description of what the best possible entanglement sharing between a qubit in her node and a qubit in Bob’s node would look like.
Then, in much the same way you might invert a function to find its input, she’ll use the same mathematical apparatus to reverse engineer what kind of quantum state she should prepare in her node, such that when it travels through the noisy interconnect, the noise itself helps it evolve into the optimal entangled state.
Of course, the math here is a little more complicated than inverting an algebraic function. For example, many (if not most) of the solutions that the mathematical apparatus arrives at will be non-physical quantum states — i.e., a quantum state that cannot be prepared by a quantum process.
If that’s the case, Alice can use the mathematical apparatus again to find the physical state that matches most closely. However, there may be multiple physical states that are essentially equal in terms of how much they resemble the original non-physical state, which can be a good thing. With some additional math, Alice can choose among the available options to find the physical state that best suits her particular needs.
Once that’s all done, Alice prepares the entangled state she wants to send through the interconnect, and “passes” half of that entanglement to Bob’s node. When that information arrives in Bob’s node, it is captured by his qubit B, and we can now say they’ve shared entanglement between two quantum nodes.
From processor interconnects to quantum telescopes
One of the exciting things about the tools Siddhu and Smolin introduce with this paper is that they have the potential to give hardware engineers some important information about the interconnects we’ll need to build a true quantum intranet. By calculating the highest-fidelity quantum state that can possibly make it through a given noisy channel, hardware developers can set a lower bound for how good their interconnects need to be to achieve adequate levels of entanglement fidelity for effective entanglement sharing across quantum nodes.
The ability to create high-fidelity entanglement between multiple quantum processors could open up a whole world of possibilities in terms of quantum communications. Solving more complex computations via multiple interconnected quantum systems is just the beginning. These advances could also lead to a larger scale “quantum internet,” in which quantum information is shared across greater distances. A quantum internet could enable the development of powerful new cryptographic protocols, and colossal “quantum telescopes” that gaze at stars with an aperture as wide as the Earth.
Of course, we’ve got a lot of progress to make before our quantum communications capabilities reach that level of sophistication. But who knows? With the right breakthroughs, entanglement sharing could one day be just as easy as sharing an email or a funny video with your friends.
