Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules

Abstract

In this article, we estimate the cost of simulating electrolyte molecules in Li-ion batteries on a fault-tolerant quantum computer, focusing on the molecules that can provide practical solutions to industrially relevant problems. Our resource estimate is based on the fusion-based quantum computing scheme using photons, but can be modified easily to the more conventional gate-based model as well. We find the cost of the magic state factory to constitute no more than ∼ 2% of the total footprint of the quantum computer, which suggests that it is more advantageous to use algorithms that consume many magic states at the same time. We suggest architectural and algorithmic changes that can accommodate such a capability. On the architecture side, we propose a method to consume multiple magic states at the same time, which can potentially lead to an order of magnitude reduction in the overall computation time without incurring additional expense in the footprint. This is based on a fault-tolerant measurement of a Pauli product operator in constant time, which may be useful in other contexts as well. We also introduce a method to implement an arbitrary fermionic basis change in logarithmic depth, which may be of independent interest. * IK's contribution was carried out while he was affiliated with PsiQuantum. IK's current affiliation is the

Logical blocks for fault-tolerant topological quantum computation

“…To the best of our knowledge, some of the Clifford operations we present-in particular the phase gate and CNOT gate-are the most efficient versions in the literature in terms of volume (defined as the volume of the template cell-complex). These Clifford operations form the backbone of the quantum computer, and set for instance the cost of and rate at which magic states can be distilled and consumed (the latter of which can become quite expensive for applications with large numbers of logical qubits [89,90]). Later, in Sec.…”

Low-overhead fault-tolerant quantum computing using long-range connectivity

“…Current algorithms for minimal non-trivial quantum chemistry calculations [62] require around 100−200 logical qubits and so even at this regime it may be beneficial to use quantum LDPC codes. We expect that for larger algorithms, such as more complex quantum chemistry algorithms [4][5][6] or Shor's algorithm [8,63], where several thousand logical qubits are required the overhead gains will be substantial. These encouraging reductions in overhead motivate experimental work towards the design and realisation of quantum LDPC codes in the laboratory.…”

“…Lastly, further study into compilation of quantum algorithms will allow us to determine what level of parallelism is required to efficiently execute a quantum computation. A commonly employed elementary fault-tolerant gate set consists of non-destructive measurements of arbitrary Pauli strings [6,53,65]. If the parallelism is strictly less than the number of logical qubits, clearly not all the Pauli strings can be measured directly.…”

“…Faulttolerant architectures come with a significant overhead cost, using a large number of low-noise physical qubits to encode and process quantum information with even a small number of protected qubits. Specifically, it has been estimated that millions of qubits will be needed to solve relevant problems in quantum chemistry [2][3][4][5][6], to break cryptosystems [7,8] or to get an advantage over classical algorithms using polynomial speedups [9][10][11]. These large overheads provide a daunting challenge for scaling up from today's noisy devices to large-scale faulttolerant quantum computers.…”

Morphing quantum codes

“…The celebrated threshold theorem [1][2][3] proves that scalable faulttolerant quantum computation is possible in principle, and moreover fault-tolerance can be achieved with constant overhead for particular families of quantum errorcorrecting codes [4,5]. However this is not the end of the story, as these asymptotic results can hide large constant factors and the requirements of quantum error correction [6][7][8][9][10] are still beyond the capabilities of today's hardware [11][12][13][14][15]. Therefore, it is imperative to develop new quantum codes that are more efficient, more resilient to noise, and more tailored to hardware.…”