Rent’s rule and extensibility in quantum computing

Abstract

Quantum computing is on the verge of a transition from fundamental research to practical applications. Yet, to make the step to large-scale quantum computation, an extensible qubit system has to be developed. In classical semiconductor technology, this was made possible by the invention of the integrated circuit, which allowed to interconnect large numbers of components without having to solder to each and every one of them. Similarly, we expect that the scaling of interconnections and control lines with the number of qubits will be a central bottleneck in creating large-scale quantum technology. Here, we define the quantum Rent's exponent p to quantify the progress in overcoming this challenge at different levels throughout the quantum computing stack. We further discuss the concept of quantum extensibility as an indicator of a platform's potential to reach the large quantum volume needed for universal quantum computing and review extensibility limits faced by different qubit implementations on the way towards truly large-scale qubit systems. I. THE TYRANNY OF NUMBERSOne of the most significant advances in the field of quantum computation has been the invention of quantum error correction (QEC) [1][2][3]. While quantum bits (qubits) are delicate systems, these algorithms can enable fault-tolerant quantum computation with sophisticated correction codes tolerating error rates of up to 1% [2]. Similar values are already achieved or within reach for experimentally observed qubit infidelities across a range of different platforms [4][5][6][7][8][9][10][11]. However, a tradeoff between the tolerated error rates and the number of qubits has to be made. Quantum error correction can lead to an overhead between 10 3 and 10 4 physical qubits per logical qubit [2,12], such that millions or even billions of physical qubits will be required for practical applications. To host and control this daunting number of qubits, formidable requirements have to be met by different elements of the system, including interconnects, control electronics and quantum software. It is therefore essential to develop an extensible approach to the hardware and software throughout the full quantum computing stack.

Single-electron operations in a foundry-fabricated array of quantum dots

“…While the compact one-gate-per-qubit architecture in accurately dimensioned silicon devices 10 , 12 may ultimately facilitate the wiring fanout of a large-scale quantum computer 23 , an overall tunability of certain array parameters may initially be essential. Figure 3 d demonstrates phenomenologically that all transition times studied can be decreased significantly by increasing the top-gate voltage.…”

The germanium quantum information route

“…After two decades of research on quantum computation with quantum dots 3 , the ingredients for extensible qubit tiles are becoming concrete 204,223 and several appealing architectures have been proposed [224][225][226][227] . Attractive architectures for large-scale quantum computing are based on qubit modules, consisting of linear or two-dimensional arrays, interconnected using longrange links 204 .…”

Semiconductor quantum computation

“…Now that high fidelity control and readout of single-and two-qubit gates in semiconductor have been demonstrated, the next challenge lies in how to scale it to tens and hundreds of qubits. Corresponding constraints and problems were investigated thoroughly since 2015, including the geometry and operation time constraints [177,178], engineering configuration for quantum-classical interface [179][180][181][182], and even the quantifying of system extensibility [183]. In the light of these discussions, several proposals for scaling up were proposed, varying from the crossbar network [38,39] for spin-1/2 qubits in silicon MOS quantum dots, the two dimensional lattice of donor qubits in silicon [35,36], to the hybrid architecture like donor-dot structure [37] and flip-flop qubit structure [113].…”