Qu&Co comments on this publication:

In this arXiv submission by Qu & Co and Covestro, a well-known approximation in classical computational methods for quantum chemistry is applied to a quantum computing scheme for simulating molecular chemistry efficiently on near-term quantum devices. The restricted mapping allows for a polynomial reduction in both the quantum circuit depth and the total number of measurements required, as compared to the conventional variational approaches based on near-term quantum simulation of molecular chemistry, such as UCCSD. This enables faster runtime convergence of the variational algorithm to a potentially higher accuracy by using a larger basis set allowed by the restricted mapping. The latter is shown via an example simulation of the disassociation curve of lithium hydride. These results open up a new direction for efficient near-term quantum chemistry simulation, as well as decreasing the effective quantum resource requirements for future fault-tolerant quantum computing schemes.

Qu&Co comments on this publication:

Recently some contributors to a paper describing a quantum-supremacy experiment inadvertently posted an older version of this paper online, which was quickly picked-up by the popular press resulting in a flurry of (in many cases) unfounded claims about the progress of quantum-computing. We believe that it is important for people interested in this topic to inform themselves through reading a balanced opinion from someone who is an expert in this field. Therefore we kindly refer to Scott Aaronson's excellent blogpost on this matter. 

Qu&Co comments on this publication:

In this article by McKinsey & Co, a strategy consulting firm, Florian Budde and Daniel Volz state that the chemical companies must act now to capture the benefits of quantum computing. Of course we at Qu & Co are a bit biased on this topic, but we do agree with the authors that the chemical sector is likely to be an early beneficiary of the vastly expanded modeling and computational capabilities, which is promised to be unlocked by quantum computing.

Qu&Co comments on this publication:

In this market outlook, The Boston Consulting group assesses how and where quantum computing will create business value, the likely progression, and what steps executives should take now to put their firms in the best position to capture that value. The report is based on interviews and workshops involving more than 100 experts, a review of some 150 peer-reviewed publications, and analysis of more than 35 potential use cases. 

Qu&Co comments on this publication:

Currently, the latest state-of-the-art quantum computers are so-called NISQ (noisy intermediate-scale quantum) devices, meaning they have a number of qubits which approaches competition with classical simulation of the output of such systems, yet the systems are noisy and no fault-tolerance can be achieved yet. The question is: are there methods which can sufficiently compensate for their noisy nature, enabling the emergence of quantum advantage on these devices? In recent years, many error correction and mitigation schemes have been developed: from Richardson extrapolation techniques to extend results down to `zero noise’, to parity check measurements and more. But typically, those techniques require additional complicated circuitry, ancillary qubits, pulse modifications, or calibration/tuning steps. In this paper, an alternative strategy based on the general principle of a class of methods called Quantum Subspace Expansion (QSE) is proposed. In this strategy, one performs clever post-processing of classical data with or without additional measurements with (at most) simple additional operations in the circuit and no (scaling) ancillary qubits. This paper generalizes the application of QSE error mitigation to any quantum computation, not restricting itself necessarily to problem-specifics like chemistry. Another interesting idea presented here is to use NISQ devices to experimentally study small quantum codes for later use in larger-scale quantum computers implementing error correcting code, such as in future FTQC (fault-tolerant quantum computing).

Qu&Co comments on this publication:

Thus far, quantum chemistry quantum algorithms have been experimentally demonstrated only on gate-based quantum computers. Efforts have been made to also map the chemistry problem Fermionic Hamiltonian to an Ising Hamiltonian in order to solve it on a quantum annealer.  However, the number of qubits required still scales exponentially with the problem size (the number of orbitals considered in the electronic structure problem). As an alternative, this paper presents a different approach exploiting the efficiency at which quantum annealers can solve discrete optimization problems, and mapping a qubit coupled cluster method to this form. They simulate their method on an ideal Ising machine and on a D-Wave 2000Q system, and find promising success rates for smaller molecules. However, further investigation would be necessary to investigate the usability for larger or more complex systems, as the scaling of their folding technique with the number of local minima is unknown. In addition, it is unclear from the experimental data whether the limitations of the D-Wave system  as compared to a perfect Ising machine could hinder expected performance gains for more complex systems.

Qu&Co comments on this publication:

This report by The Boston Consulting Group, a strategy consulting firm, targets business executives and other people looking for a broader market overview on quantum computing. The authors (Philipp Gerbert et al.) provide some insight in where the technology currently stands, who is who in the emerging ecosystem, and the potentially interesting applications. The report also analyzes some of the leading indicators of investments, patents, and publications, which countries and entities are most active and the status and prospects for the main categories of quantum hardware technologies. Additionally, the report aims to provide a simple framework for understanding quantum algorithms and assessing their applicability and potential. Finally, the authors provide their view of what can be expected in the next five to ten years, and what corporates should be doing, or getting ready for, in response. 

Qu&Co comments on this publication:

Ever since the publication of Shor’s algorithm in 1994, efficient integer factorization has been a key application area envisioned for quantum-computers, with important implications for the security of some of the most used cryptosystems. Because Shor’s algorithm requires a large-scale fault-tolerant quantum-processor, RSA-3072 encryption was so-far believed to remain safe until 2030. However, in recent years hybrid (classical-quantum) alternatives have been developed for many important quantum-algorithms. Such hybrid algorithms can be run on current-day noisy and small-scale quantum-processors. In this paper Eric Anschuetz et al. describe such a hybrid alternative for Shor’s algorithm, which they call variational quantum factoring (VQF). If some pre-processing is applied VQF scales with O(n), n being the number of bits of the integer being factored. If VQF can be optimized to scale well up to 3000+ qubits, which is very challenging, but not completely unthinkable, and if we assume the number of physical qubits in quantum-processors doubles every year, quantum-processors could have sufficiently high qubit count to break RSA-3072 as early as 2025. However, as VQF relies on a quantum-optimization algorithm (QAOA) it seems unlikely that the speed-up of VQF could be more than quadratic, which means that the runtime for breaking RSA-3072 could very well be prohibitively long and that doubling the RSA-6144 (double the key-length) would again be just  as safe as RSA-3072 is currently.

Qu&Co comments on this publication:

Many financial services players are experimenting with quantum-computing so that they can be the first to start exploiting its benefits in speed-up and tractability. Algorithms have been developed for a wide range of finance related topics e.g. Monte Carlo simulation, portfolio optimization, anomaly (fraud) detection, market forecasting and reduction of slippage. In this paper Orus et al. provide a nice overview of most of these applications. Although the paper puts much emphasis on what has been done with quantum-annealers, applying the Quantum Approximate Optimization Algorithm (QAOA) lets us map all of them to universal-gate devices, which ensures that these applications stay relevant even when annealers become obsolete.

Qu&Co comments on this publication:

This report by The Boston Consulting Group, a strategy consulting firm, provides both an introductory status overview of current and near-term qubit technologies and of practical quantum-computing applications as well as a longer-term outlook of the quantum-computing market, which the authors (Massimo Russo et al.) estimate could be as large as $50bln by 2030. The report also provides some advice to corporates on how to prepare for the arrival of practical quantum-computing applications

Qu&Co comments on this publication:

Recently, promising experimental results have been shown for quantum-chemistry calculations using small, noisy quantum processors. As full scale fault-tolerant error correction is still many years away, near-term quantum computers will have a limited number of qubits, and each qubit will be noisy. Methods that reduce noise and correct errors without doing full error correction on every qubit will help extend the range of interesting problems that can be solved in the near-term. In this paper Otten et al. present a scheme for accounting (and removal) of errors in observables determined from quantum algorithms and apply this scheme to the variational quantum eigensolver algorithm, simulating the calculation of the ground state energy of equilibrium H2 and LiH in the presence of several noise sources, including amplitude damping, dephasing, thermal noise, and correlated noise. They show that their scheme provides a decrease in the needed quality of the qubits by up to two orders of magnitude.

Qu&Co comments on this publication:

In this paper Bian et al. compare four different quantum simulation methods to simulate the ground state energy of the Hamiltonian for the water molecule on a quantum computer, being 1) the phase estimation algorithm based on Trotter decomposition, 2) phase estimation based on the direct implementation of the Hamiltonian, 3) direct measurement based on the implementation of the Hamiltonian and 4) the variational quantum eigensolver (classical-quantum hybrid) algorithm. They compare a.o. the required number of qubits, gate-complexity, accuracy/error. 

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