// Photonics

# Beating classical computers with Borealis

The story behind the story of the world’s first public cloud-deployed computer with quantum computational advantage

*By Jonathan Lavoie and Zachary Vernon*

Xanadu recently announced the launch of Borealis, our newest quantum computer, for public access over the cloud. With 216 squeezed-state qubits — almost twenty times more than X12, our recent previous cloud-ready system — Borealis is the largest photonic quantum computer ever built, and the first of its kind to ever be made accessible to the public.

Even more remarkable is the power Borealis provides on a very specific type of mathematical problem known as *Gaussian Boson Sampling*. Abstractly, this problem refers to generating random numbers that obey certain patterns expressed through a mathematical function called the Hafnian. The details of the specific mathematical problem chosen here are not particularly important; the key is that it is a great example to demonstrate the difference in power between classical and quantum computers. It turns out that such a function is astoundingly hard to compute on a classical computer. In fact generating random samples with properties related to Hafnians is simply intractable for such machines, once the size of the inputs grows beyond a certain point. Borealis was designed to access this space of mathematical problems, allowing remote users to run their own quantum programs to encode matrices, and returning to them the output of the machine — samples from the Hafnian-based probability distribution specified by the user.

To showcase these capabilities, we put Borealis through one of the most demanding tests in the field of quantum computing: a demonstration of *quantum computational advantage*. Sometimes also referred to as achieving *quantum supremacy*, this means showing that, for a particular well-defined task, the quantum computer in question outperforms the fastest available classical supercomputers in the world running the best-known algorithms for the job. Building a quantum machine that can pass this benchmark is extremely difficult, and so quantum computational advantage has only been achieved successfully a few times. The quantum computing team at Google was the first to do so, in 2019 using their 53-qubit Sycamore superconducting circuit processor on a slightly different random sampling algorithm. Shortly after that came a demonstration of Gaussian Boson Sampling on Jiuzhang, an optical machine built by a team at the University of Science and Technology of China; the same group then executed a demonstration with their own superconducting processor, and also upgraded Jiuzhang for a more sophisticated optical demonstration. To date, no other machines – neither from academic research groups nor companies – have achieved quantum computational advantage.

Excitingly, Borealis broke through this barrier, passing the test with flying colours and becoming the first computer capable of quantum computational advantage to be deployed on the cloud. The runtime advantage over classical computers is extreme: it would take, on average, 9000 years for the most powerful supercomputer in the world to produce a single output when running this task via direct simulation. Borealis requires only 36 microseconds. This advantage gap is unprecedented for optical machines, being over 50 million times larger than that for the earlier photonic quantum advantage demonstrations. The results of this test were peer-reviewed, and are now published in the scientific journal *Nature*.

Aside from its cloud deployment, Borealis also lays claim to a number of other important firsts. Most crucially, it is the first *photonic* quantum computer with quantum computational advantage to offer users full programmability over all its gates — over 1200 parameters can be freely specified by the user encoding their program, as well as the brightness of the input squeezed-state qubits. While the superconducting Sycamore machine was programmable, such extensive control was an important feature lacking in previous photonic machines, which were largely confined to fixed, randomized gate sequences.

So how does Borealis work, what can it be used for, and what technological implications does this news have for the development of practically useful quantum computers?

### Under the hood: how Borealis works

Borealis has a unique architecture, designed to generate and process a large number of squeezed-state qubits in a hardware-efficient fashion. To generate and entangle our state, we use time multiplexing, where a source of squeezed-state qubits produces a train of 216 pulses of squeezed light. Each pulse of squeezed light is made of a quantum superposition of photon pairs, generated by passing bright laser pulses through a special nonlinear crystal inside an optical resonator. Here is a high-level diagram of the machine to help understand the role of each subsystem:

To implement a sequence of quantum gates on and generate entanglement between the squeezed-state qubits, this train of pulses enters a large interferometer which is made of three concatenated and dynamically programmable loop-based interferometers. Each of the three loops incorporates some of the most important building blocks of a photonic quantum computer: a programmable beamsplitter, a programmable phase shifter, and an optical fibre delay line playing the role of a buffer memory for light. The loops are the key components of the system allowing each incident pulse to be delayed in an optical fibre until another pulse arrives. When a pulse arrives at a beamsplitter gate, the gate can either switch the pulse into the fibre (store in memory), switch the pulse out of the loop (retrieve from memory), or perform an entangling gate between the pulse being retrieved from the loop and the next incoming pulse. An important detail about the three loops is that their delay lengths, or storage times, are distinct: the second one is six times longer than the first one, and the third six times longer than the second. This geometry allows the entanglement between squeezed-light qubits to extend beyond temporally adjacent pulses, something that would be difficult to achieve in a purely spatial architecture.

It can be difficult to represent the entire quantum circuit of Borealis, including all the connectivity, due to its size and large number of inputs and outputs. The fibre delays and accompanying beamsplitters and phase shifters implement gates between both temporally adjacent and distant modes which can be depicted as a three-dimensional lattice. Here is one way to represent how Borealis progressively synthesizes large quantum states: the first loop effects two-mode programmable gates between temporally adjacent squeezed-state qubits in one dimension, while the second and third respectively mediate gates between squeezed-state qubits separated by 6 and 36 time bins in the second and third dimensions.

The final stage in Borealis is the readout: measuring the number of photons in each of the output 216 pulses. This is what we refer to as sampling, and is the difficult task a supercomputer fails at doing efficiently for the quantum states generated by Borealis. One way to appreciate why it is difficult for any classical computer to prepare the right samples, with the right probabilities, is to recognize the enormous amount of possible outcomes in one experiment. Due to the entanglement in the system, the probabilities of these outcomes from each of the 216 squeezed-state qubits are not independent, and implementing this with a classical computer quickly becomes intractable.

In Borealis, we employ highly sensitive energy sensors to count photons. These are called photon-number-resolving detectors, or PNRs for short. Once incident light is absorbed by the detector, the increase of energy will lead to a sequence of electronic events resulting in a signal proportional in amplitude to the energy absorbed by the detector. So, the higher the signal recorded, the higher the energy was in one pulse and thus, the higher the number of photons. The signal amplitudes are discretized according to the number of photons detected, and our analysis tools can precisely extract this information from the electrical pulses. The PNR detectors are the only part of Borealis requiring cryogenic cooling.

Our detectors are fast, but the clock speed at which the beamsplitter and phase gates are operated is faster, and the squeezed-light pulses arrive at too high a rate for our current generation of PNRs to do their job accurately. To bridge the gap in clock speeds, we built a demultiplexing system, or “demux”. The role of the demux is to rearrange the train of squeezed-light pulses in space, using a network of optical switches. Instead of using a single PNR to sample all 216 incoming squeezed-light pulses, we periodically distribute the squeezed-state qubits to 16 detection channels. Scanning through our readout channels in this manner allows our clock speed to run 16x faster than any individual detector channel. As an analogy, imagine a single line of travelers in front of a single customs agent upon arrival at the airport, versus the same line with 16 agents; the same amount of people will get through the airport much more quickly.

### Use cases in the NISQ era

There is a lot of debate over what applications near-term quantum computers — those in our era of “noisy intermediate-scale quantum” (NISQ) machines — can access. For Borealis, any such application would need to fit within the paradigm of Gaussian Boson Sampling, which is restricted to a specific class of mathematical problems related to Hafnian-linked probability distributions. A number of potential use cases in this realm have been studied, most of which map to problems that can be encoded in graphs — networks of points connected by edges, with numerical weights assigned to each edge. Such problems translate very naturally to the specific set of states and gates offered by Borealis.

Small-scale demonstrations of these types of problems have been carried out on our earlier cloud-deployed quantum computers, including our X8 system that implements Gaussian Boson Sampling over 8 squeezed-state qubits. Using X8, we showed that graphs belonging to different structural classes can be effectively distinguished by encoding them in the device and analyzing the distribution of outputs, and that a toy model of a molecule could be encoded and its vibronic spectrum deduced. On Borealis, our own analysis focused on a mathematically conclusive demonstration of quantum computational advantage, for which randomized gate sequences were programmed. But more application-oriented demonstrations like those showcased for X8 can also be investigated, albeit with different restrictions associated with Borealis’ specific connectivity and available gate parameters. We leave this open as an invitation for researchers to trial their own ideas on our device over the cloud.

Still, as with all NISQ-era machines, there is a limited scope of addressable applications, and with it the question of whether a *practical* advantage over classical techniques can be accessed. This question is still open, and there is a widespread and growing view among researchers working on both quantum computer hardware and applications that a longer-term view of technology development is needed in order to unlock the true potential of quantum computing. In particular, the ability to scale up to millions of qubits, and correct for errors as they occur in the storage and processing of quantum information, remain the central goals for hardware development in our field. Alongside many experts in both hardware and algorithm development, it is our view that large-scale, *fault-tolerant* machines are required in order to deliver the full utility of quantum computing.

### Toward practical quantum computing: error correction and fault-tolerance

So what does Borealis have to do with fault-tolerant quantum computing? While Borealis is firmly within the territory of NISQ-era devices, a number of the technologies developed for and employed within it are critical components of our architecture for a universal, fault-tolerant quantum computer. Viewed through this lens, building Borealis is a way to showcase and benchmark some of these underlying technologies in an extremely demanding context, namely a conclusive demonstration of quantum computational advantage.

The most significant example of such a technology embedded within Borealis and needed for fault-tolerance is the use of stabilized fibre optic delay lines to store photonic squeezed-state qubits in buffer memory. In our fault-tolerant architecture, this technique is required in order to knit together a large quantum state in which some of the entanglement exists between qubits generated at different times. Generating entanglement between qubits born at different times allows us to implement quantum circuits having large gate depth *without* propagating each qubit through a similarly large number of physical components. Avoiding deep gate networks at the hardware level gives our architecture the opportunity, after each gate and at every clock cycle, to diagnose and correct errors.

Entangling qubits from different clock cycles is very difficult, as it depends on the ability to store a qubit circulating in a fiber optic cable for one full clock cycle of the machine. Because the properties of these qubits are sensitive to small fluctuations at the scale of a few nanometres in the optical propagation length of their path, sophisticated techniques to actively stabilize the fiber optic loops are needed. The longest such buffer loop in Borealis is over 1 km, representing 6 microseconds of storage time. This length is actively stabilized to an effective precision of a few tens of nanometres — within about one part in 200 billion. That’s like stabilizing the length of a cable running between Vancouver and Toronto to within the width of a human hair! For our fault-tolerant architecture, we actually only need about 1 microsecond of storage time — a couple hundred metres of fiber — so it is very encouraging to be ahead of our target in this technical capability.

That’s like stabilizing the length of a cable running between Vancouver and Toronto to within the width of a human hair!

Another aspect of our fault-tolerant architecture employed in Borealis is the direct synthesis of three-dimensional entanglement itself. This highlights the ease with which photonics – again, owing to its ability to leverage fiber optics – lends itself to long-range connectivity between qubits created at physically distant locations. Long-range connectivity implemented in this way, which is unique to photonic architectures, allows us to use more sophisticated error-correcting codes that require entanglement over more distant qubits than that afforded by nearest-neighbour connectivity. In contrast, conventional codes like the surface code, for which superconducting processors are designed, are confined to nearest-neighbour connectivity. Long-range connectivity has the potential to require more modest overheads when encoding error-corrected logical qubits into arrays of *raw* physical qubits.

A number of other advances incorporated into Borealis’ hardware can be applied to the benefit of a fault-tolerant machine, including sophisticated photon detector pulse recognition algorithms to enable faster operation of our detectors, the demultiplexing system that serves as a bulk prototype for the subsystem that boosts the success rate of our fault-tolerant qubit sources, and a software control system for automating the execution of large and complex quantum circuits.

All of these advances, combined with the outcomes of our ongoing iterations on the performance of the chip-integrated components needed for fault-tolerant qubit synthesis and processing, must converge at scale to deliver a truly useful quantum computer. A lot of progress has been made toward this goal, but there is still a lot more work ahead of us. Machines like Borealis are significant milestones on this path, and demanding demonstrations like quantum computational advantage — not to mention the quantum computing research community at large having the ability to put our machine through its paces — helps build confidence that our hardware development is on the right track.

Published on **June 1, 2022**

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