I was at a Q2B conference presentation by PsiQuantum on their work to develop fault-tolerant over one million qubit quantum computers. They are developing new optical and photonic components to achieve truly breakthrough capabilities. They have a staff of over 250 people and have dedicated fabs to create their systems.

This seems like a viable path to achieving millions of fault-tolerant qubits for quantum computing. If they are successful then it would 2048 qubit RSA encryption would be broken.

They have made a lot of progress to surpass the minimum physical capabilities for their critical components. The science and the work is well developed and it seems that when they surpass the critical levels that they will be highly scalable systems. They have chosen a path to a highly scalable technology but one that has needed years of development and novel systems. The photonic approach will be great at scaling.

In 2013, the academic work was done to physically create single and low number photonic qubits. The commercial work is leveraging the capabilities of the semiconductor and photonic fiber optic communications industry. However, they are using some new materials and developing some components that are similar to but different from existing components and systems.

It is not just the potential for millions of qubits but photonic qubits would have nanosecond operations versus microsecond for superconducting qubits and millisecond for trapped ion. There are many different kinds of physical structures being leveraged by dozens of quantum computing companies. There are various kinds of superconducting qubits, trapped ion, neutral atom and photonic.

December 1, 2022, PsiQuantum announced a breakthrough technique for more efficiently implementing fault-tolerant quantum computations. This technique delivers around a 50X improvement in the run-time efficiency of compiled applications.

This technique specifically targets algorithms for error-corrected quantum computers, as opposed to non-error-corrected NISQ systems. ‘Active volume compilation’ reduces the time taken to run a given application, through more efficient use of the available hardware. This is achieved by utilizing long-range connections between different regions in the quantum computer. This technique particularly favors photonic quantum computing, where long-range connections can be achieved using conventional optical fiber.

Under assumptions given in the preprint paper by PsiQuantum, it is estimated that by using this technique, the time taken to break the very strong (2048-bit) encryption RSA key is reduced to around nine hours on a future photonic quantum computer running with a 1ns operation cycle. While the company continues its development of the large-scale fault tolerant quantum computer required to execute this application, this result dramatically reduces the demands on that future system.

The 2048-bit factoring algorithm described in the paper consists of ≈ 6.1 billion T gates on 6200 logical qubits, so the circuit volume is 38 trillion. This implies that, in the aforementioned baseline architecture, it would take 6.1 billion logical cycles on a devicewith 2 · 6200 logical qubits to finish the computation.

In a grid of superconducting qubits with a 1 microsecond code cycle, the computation would finish after 48 hours. In an array of trapped-ion qubits with a slower 1 millisecond code cycle, the computation would finish after 5.4 years.

In a photonic fusion-based implementation, the quantum computer is not an array of physical qubits, but instead a network of so-called interleaving modules, each module consisting of a resource-state generator (RSG) producing one photonic resource state every τRSG, and a number of additional switches, delay lines and single-photon detectors. Out of these components, the RSG is the most complex one, so the total number of RSGs is the relevant metric for the physical cost of the device. With τRSG = 1 ns and a maximum fiber delay length of 200 m, 9700 RSGs can be used to finish the computation in 48 hours. Interleaving modules also allow for the opposite space-time trade-off, i.e., the use of fewer hardware modules with longer delay lines, but a slower computation. 970 RSGs with a maximum fiber delay length of 2 km can finish the computation in 20 days.

They designed construct a general-purpose architecture that can execute quantum computations with a spacetime volume cost of roughly twice the active volume instead of the circuit volume. This can significantly reduce the cost of quantum computations, as, e.g., the active volume of the aforementioned 2048-bit factoring algorithm is 44 times lower than the circuit volume. This enables a much faster execution of this computation, such that 19 million physical ion-trap qubits now finish the computation in 37 days instead of 5.4 years. 970 RSGs with 2-kmlong fiber delays finish the computation in 8.9 hours instead of 20 days. And even a small network of only 10 RSGs with long 300 km free-space delays can finish the computation in 35 days instead of 5.4 years. However, the architecture relies on non-local connections between physical components. It can be thought of as a collection of surface-code patches with transversal physical two-qubit operations between a limited set of patch pairs. While the architecture can be implemented in any hardware platform with the required connectivity, it is primarily motivated by photonic qubits, where these connections are readily available, rather than matterbased ones.

Active-volume quantum computers have simple performance metrics. In the active-volume architecture, the performance of a quantum computer is characterized by the size of the memory, its speed in blocks per second, the per-block error rate, and the reaction time. The cost of a quantum computation is quantified by its memory requirement and its active volume, which is counted in units of blocks. The memory requirement determines whether a quantum computation can be executed on a specific device, while the runtime of a quantum computation is determined by its active volume in blocks and the speed of the device in blocks per second.

Photonic qubits are a natural fit for active-volume quantum computing. Psiquantum showed how an active-volume architecture can be implemented using photonic fusionbased interleaving modules. However, it is also be possible to construct active-volume architectures with other types of photonic qubits, such as architecture based on GKP encoding, or even with matter-based qubits. For example, interleaving-type schemes for superconducting qubits based on resonant cavities have been proposed and possible non-2D-local connectivity between surface-code patches has been discussed in for networks of ion traps as well as superconducting qubits. Still, the ease with which nonlocal connections can be implemented in a fusion-based architecture, and the synergy between active-volume architectures and long interleaving delays, are important advantages of photonic qubits.

**Active volume: An architecture for efficient fault-tolerant quantum computers with limited non-local connections**

*In existing general-purpose architectures for surface-code-based fault-tolerant quantum computers, the cost of a quantum computation is determined by the circuit volume, i.e., the number of qubits multiplied by the number of non-Clifford gates. We introduce an architecture using non-2D-local connections in which the cost does not scale with the number of qubits, and instead only with the number of logical operations. Each logical operation has an associated active volume, such that the cost of a quantum computation can be quantified as a sum of active volumes of all operations. For quantum computations with thousands of logical qubits, the active volume can be orders of magnitude lower than the circuit volume. Importantly, the architecture does not require all-to-all connectivity between N logical qubits. Instead, each logical qubit is connected to O(log N) other sites. As an example, we show that, using the same number of logical qubits, a 2048-bit factoring algorithm can be executed 44 times faster than on a general-purpose architecture without non-local connections. With photonic qubits, long-range connections are available and we show how photonic components can be used to construct a fusion-based active-volume quantum computer.*

Brian Wang is a Futurist Thought Leader and a popular Science blogger with 1 million readers per month. His blog Nextbigfuture.com is ranked #1 Science News Blog. It covers many disruptive technology and trends including Space, Robotics, Artificial Intelligence, Medicine, Anti-aging Biotechnology, and Nanotechnology.

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