Assessing requirements to scale to practical quantum advantage

TL;DR

The paper presents a modular framework and the Azure Quantum Resource Estimator to quantify resources across the quantum computing stack, from high-level quantum programs to fault-tolerant hardware. By evaluating three impactful applications (quantum dynamics, quantum chemistry, and factoring), it demonstrates that achieving practical quantum advantage requires $Q$-level logical qubits and a substantial number of physical qubits due to QEC overhead, with runtimes and resource demands highly sensitive to qubit speed, error rates, and connectivity. The authors identify controllability, speed, and 2D connectivity as core scale-up requirements and argue that 2D-connected devices with parallel operation and efficient decoders are essential for fault-tolerant scaling, while T-state distillation often dominates resource cost. Overall, the work provides a actionable framework for exploring design choices across the stack to accelerate progress toward practical quantum advantage and highlights the significant engineering challenges ahead.

Abstract

While quantum computers promise to solve some scientifically and commercially valuable problems thought intractable for classical machines, delivering on this promise will require a large-scale quantum machine. Understanding the impact of architecture design choices for a scaled quantum stack for specific applications, prior to full realization of the quantum system, is an important open challenge. To this end, we develop a framework for quantum resource estimation, abstracting the layers of the stack, to estimate resources required across these layers for large-scale quantum applications. Using a tool that implements this framework, we assess three scaled quantum applications and find that hundreds of thousands to millions of physical qubits are needed to achieve practical quantum advantage. We identify three qubit parameters, namely size, speed, and controllability, that are critical at scale to rendering these applications practical. A goal of our work is to accelerate progress towards practical quantum advantage by enabling the broader community to explore design choices across the stack, from algorithms to qubits.

Figures (11)

• Figure 1: The stacks for classical (left) and quantum (center) computing. At the top of the stack the program is expressed in a natural, high-level language such as C/C++ (classical) or Q# (quantum). This program is re-expressed as different program representations (manilla scrolls) in a sequence of languages (blue boxes) which are represented here as layers, with each layer being a lower-level language than that above, down to the physical signals controlling the device. A complementary viewpoint is that the instruction set available to the language at one layer can be combined to form a more elaborate instruction set for the layer above. The scrolls are shortest at the top, symbolizing that program representations are simplest when expressed in higher-level languages, while the blue boxes are smallest at the base of the stack, symbolizing that instruction sets are simplest at the lower levels. (right) Our quantum resource modeling framework is a modular representation of the layers of the quantum computing stack, which collects together the upper layers as quantum program representations, and the lower layers as quantum machine models, with the quantum ISA connecting both.
• Figure 2: A sketch of how the tool estimates resources for the three example applications and six qubit parameter examples we consider. Note the stack is represented left-to-right rather than top-to-bottom. Applications, addressed by a high-level quantum program, are first translated explicitly to a QIR program which is input into the tool, where its compilation down to an ISA-level executable is modeled. All our examples flow to the same planar quantum ISA, which has an instruction set consisting of logical surface code operations. On the hardware side, we input physical qubit parameters to the tool including the physical qubit instruction set and the times and error rates of those instructions. The tool then models how these noisy qubits are used to build up protected logical qubits and to fault-tolerantly implement the planar quantum ISA instructions using configurable QEC models. The tool outputs resource estimates such as the number of physical qubits and time required to run the application.
• Figure 3: Estimates of the resources required to implement three applications, assuming the qubit parameter examples specified in \ref{['tab:qubit-type']}. We explore a trade-off in the quantum dynamics application by considering two implementations: one which uses sufficient T factories to supply the needs of the shortest-depth algorithm and another which slows the algorithm down, allowing for a reduced number of T factories.
• Figure 4: The examples and options included in the quantum stack for our resource estimates. We consider three application examples at the top, and a range of hardware parameter examples relevant for a variety of hardware approaches at the base of the stack. We label layers of the quantum stack on the right, and the maps between these layers on the left. To highlight our qubit parameter examples, we separate the microarchecture layer into two sub-layers. All our examples flow through the same planar quantum ISA. Applications are translated down the software stack and the resulting ISA-level executable is input to the tool. The tool also takes as input configurable architecture models that include fault-tolerance details and physical qubit models. The tool outputs resource estimates such as the number of physical qubits or time required to run the application.
• Figure 5: We consider gate-based and Majorana instruction sets for physical qubits. Both sets include state preparation in the Pauli basis (green), T state preparation (yellow), T gate application (yellow), and measurement in all Pauli basis (blue). (a) The gate-based instruction set also includes Hadamard H and S gates, and CNOT and CZ entangling gates between adjacent qubits (all orange). (b) The Majorana instruction set also allows non-destructive joint Pauli measurements of adjacent qubits (blue).