Avoiding symmetry roadblocks and minimizing the measurement overhead of adaptive variational quantum eigensolvers

Quantum simulation of strongly correlated systems is potentially the most feasible useful application of near-term quantum computers. Minimizing quantum computational resources is crucial to achieving this goal. A promising class of algorithms for this purpose consists of variational quantum eigensolvers (VQEs). Among these, problem-tailored versions such as ADAPT-VQE that build variational ans\"atze step by step from a predefined operator pool perform particularly well in terms of circuit depths and variational parameter counts. However, this improved performance comes at the expense of an additional measurement overhead compared to standard VQEs. Here, we show that this overhead can be reduced to an amount that grows only linearly with the number $n$ of qubits, instead of quartically as in the original ADAPT-VQE. We do this by proving that operator pools of size $2n-2$ can represent any state in Hilbert space if chosen appropriately. We prove that this is the minimal size of such "complete" pools, discuss their algebraic properties, and present necessary and sufficient conditions for their completeness that allow us to find such pools efficiently. We further show that, if the simulated problem possesses symmetries, then complete pools can fail to yield convergent results, unless the pool is chosen to obey certain symmetry rules. We demonstrate the performance of such symmetry-adapted complete pools by using them in classical simulations of ADAPT-VQE for several strongly correlated molecules. Our findings are relevant for any VQE that uses an ansatz based on Pauli strings.Comment: 15+10 pages, 7 figure

Disposable electrochemical flow cells for catalytic adsorptive stripping voltammetry (CAdSV) at a bismuth film electrode (BiFE)

Catalytic adsorptive stripping voltammetry (CAdSV) has been demonstrated at a bismuth film electrode (BiFE) in an injection-moulded electrochemical micro-flow cell. The polystyrene three-electrode flow cell was fabricated with electrodes moulded from a conducting grade of polystyrene containing 40% carbon fibre, one of which was precoated with Ag to enable its use as an on-chip Ag/AgCl reference electrode. CAdSV of Co(II) and Ni(II) in the presence of dimethylglyoxime (DMG) with nitrite employed as the catalyst was performed in order to assess the performance of the flow cell with an in-line plated BiFE. The injection-moulded electrodes were found to be suitable substrates for the formation of BiFEs. Key parameters such as the plating solution matrix, plating flow rate, analysis flow rate, solution composition and square-wave parameters have been characterised and optimal conditions selected for successful and rapid analysis of Co(II) and Ni(II) at the ppb level. The analytical response was linear over the range 1 to 20 ppb and deoxygenation of the sample solution was not required. The successful coupling of a microfluidic flow cell with a BiFE, thereby forming a “mercury-free” AdSV flow analysis sensor, shows promise for industrial and in-the-field applications where inexpensive, compact, and robust instrumentation capable of low-volume analysis is required

TETRIS-ADAPT-VQE: An adaptive algorithm that yields shallower, denser circuit ans\"atze

Adaptive quantum variational algorithms are particularly promising for simulating strongly correlated systems on near-term quantum hardware, but they are not yet viable due, in large part, to the severe coherence time limitations on current devices. In this work, we introduce an algorithm called TETRIS-ADAPT-VQE, which iteratively builds up variational ans\"atze a few operators at a time in a way dictated by the problem being simulated. This algorithm is a modified version of the ADAPT-VQE algorithm in which the one-operator-at-a-time rule is lifted to allow for the addition of multiple operators with disjoint supports in each iteration. TETRIS-ADAPT-VQE results in denser but significantly shallower circuits, without increasing the number of CNOT gates or variational parameters. Its advantage over the original algorithm in terms of circuit depths increases with the system size. Moreover, the expensive step of measuring the energy gradient with respect to each candidate unitary at each iteration is performed only a fraction of the time compared to ADAPT-VQE. These improvements bring us closer to the goal of demonstrating a practical quantum advantage on quantum hardware.Comment: 10 pages, 7 figure

An adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer

The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the original QAOA ansatz is not optimal, there is no systematic approach for finding better ans\"atze. We address this problem by developing an iterative version of QAOA that is problem-tailored, and which can also be adapted to specific hardware constraints. We simulate the algorithm on a class of Max-Cut graph problems and show that it converges much faster than the original QAOA, while simultaneously reducing the required number of CNOT gates and optimization parameters. We provide evidence that this speedup is connected to the concept of shortcuts to adiabaticity.Comment: 5 pages, 3 figure

Environmental DNA reveals links between abundance and composition of airborne grass pollen and respiratory health

This is the final version. Available on open access from Elsevier via the DOI in this recordData and Code Availability Statement: Data collected using qPCR is archived and on NERC EIDC [https://doi.org/10.5285/28208be4-0163-45e6-912c-2db205126925]. Standard pollen monitoring ‘count’ data were sourced from the MEDMI database, with the exception of data from Bangor which were produced as part of the present study and are available on request. Prescribing datasets are publicly available, as are weather, air pollution, deprivation (IMD) and rural-urban category data. Hospital episode statistics (HES) datasets are sensitive, individual-level health data, which are subject to strict privacy regulations and are not publicly available. The study did not generate any unique codeGrass (Poaceae) pollen is the most important outdoor aeroallergen, exacerbating a range of respiratory conditions, including allergic asthma and rhinitis (‘hay fever’). Understanding the relationships between respiratory diseases and airborne grass pollen with view to improving forecasting has broad public health and socioeconomic relevance. It is estimated that there are over 400 million people with allergic rhinitis and over 300 million with asthma, globally, often comorbidly . In the UK, allergic asthma has an annual cost of around US$ 2.8 billion (2017). The relative contributions of the >11,000 (worldwide) grass species to respiratory health have been unresolved, as grass pollen cannot be readily discriminated using standard microscopy. Instead, here we used novel environmental DNA (eDNA) sampling and quantitative PCR (qPCR) , to measure the relative abundances of airborne pollen from common grass species, during two grass pollen seasons (2016 and 2017), across the UK. We quantitatively demonstrate discrete spatiotemporal patterns in airborne grass pollen assemblages. Using a series of generalised additive models (GAMs), we explore the relationship between the incidences of airborne pollen and severe asthma exacerbations (sub-weekly) and prescribing rates of drugs for respiratory allergies (monthly). Our results indicate that a subset of grass species may have disproportionate influence on these population-scale respiratory health responses during peak grass pollen concentrations. The work demonstrates the need for sensitive and detailed biomonitoring of harmful aeroallergens in order to investigate and mitigate their impacts on human health.Natural Environment Research Council (NERC)National Institute for Health Research (NIHR)Public Health EnglandUniversity of ExeterUniversity College LondonMet Offic