Estimating the expectation value of an operator corresponding to an observable is a fundamental task in quantum computation. It is often impossible to obtain such estimates directly, as the computer is restricted to measuring in a fixed computational basis. One common solution splits the operator into a weighted sum of Pauli operators and measures each separately, at the cost of many measurements. An improved version collects mutually commuting Pauli operators together before measuring all operators within a collection simultaneously. The effectiveness of doing this depends on two factors. Firstly, we must understand the improvement offered by a given arrangement of Paulis in collections. In our work, we propose two natural metrics for quantifying this, operating under the assumption that measurements are distributed optimally among collections so as to minimise the overall finite sampling error. Motivated by the mathematical form of these metrics, we introduce SORTED INSERTION, a collecting strategy that exploits the weighting of each Pauli operator in the overall sum. Secondly, to measure all Pauli operators within a collection simultaneously, a circuit is required to rotate them to the computational basis. In our work, we present two efficient circuit constructions that suitably rotate any collection of k independent commuting n-qubit Pauli operators using at most kn−k(k+1)/2 and O(kn/log⁡k) two-qubit gates respectively. Our methods are numerically illustrated in the context of the Variational Quantum Eigensolver, where the operators in question are molecular Hamiltonians. As measured by our metrics, SORTED INSERTION outperforms four conventional greedy colouring algorithms that seek the minimum number of collections.

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Computational chemistry is an essential tool in the pharmaceutical industry. Quantum computing is a fast evolving technology that promises to completely shift the computational capabilities in many areas of chemical research by bringing into reach currently impossible calculations. This perspective illustrates the near-future applicability of quantum computation of molecules to pharmaceutical problems. We briefly summarize and compare the scaling properties of state-of-the-art quantum algorithms and provide novel estimates of the quantum computational cost of simulating progressively larger embedding regions of a pharmaceutically relevant covalent protein–drug complex involving the drug Ibrutinib. Carrying out these calculations requires an error-corrected quantum architecture that we describe. Our estimates showcase that recent developments on quantum phase estimation algorithms have dramatically reduced the quantum resources needed to run fully quantum calculations in active spaces of around 50 orbitals and electrons, from estimated over 1000 years using the Trotterization approach to just a few days with sparse qubitization, painting a picture of fast and exciting progress in this nascent field.

Quantum computers are special purpose machines that are expected to be particularly useful in simulating strongly correlated chemical systems. The quantum computer excels at treating a moderate number of orbitals within an active space in a fully quantum mechanical manner. We present a quantum phase estimation calculation on F2 in a (2,2) active space on Rigetti's Aspen‐11 QPU. While this is a promising start, it also underlines the need for carefully selecting the orbital spaces treated by the quantum computer. In this work, a scheme for selecting such an active space automatically is described and simulated results obtained using both the quantum phase estimation (QPE) and variational quantum eigensolver (VQE) algorithms are presented and combined with a subtractive method to enable accurate description of the environment. The active occupied space is selected from orbitals localized on the chemically relevant fragment of the molecule, while the corresponding virtual space is chosen based on the magnitude of interactions with the occupied space calculated from perturbation theory. This protocol is then applied to two chemical systems of pharmaceutical relevance: the enzyme [Fe] hydrogenase and the photosenzitizer temoporfin. While the sizes of the active spaces currently amenable to a quantum computational treatment are not enough to demonstrate quantum advantage, the procedure outlined here is applicable to any active space size, including those that are outside the reach of classical computation.

Inspired by the challenge of scaling-up existing silicon quantum hardware, we propose a 2d spin-qubit architecture with low compilation overhead. The architecture is based on silicon nanowire split-gate transistors which form 1d chains of spin-qubits and allow the execution of two-qubit operations among neighbors. We introduce a silicon junction which can couple four nanowires into 2d arrangements via spin shuttling and Swap operations. We then propose a modular sparse 2d spin-qubit architecture with unit cells of diagonally-oriented squares with nanowires along the edges and junctions on the corners. Targeting noisy intermediate-scale quantum (NISQ) demonstrators, we show that the proposed architecture allows for compilation strategies which outperform methods for 1d chains, and exhibits favorable scaling properties which enable trading-off compilation overhead and colocation of control electronics within each square by adjusting the nanowire length. An appealing feature of the proposed architecture is its manufacturability using complementary-metal-oxide-semiconductor (CMOS) fabrication processes.