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Infrastructure for heat provision in the built environment needs to change remarkably to support lowering carbon emissions and achieving climate mitigation targets before 2050. We propose a computational approach for finding a mix of heat options per neighbourhood that minimises cumulative carbon emissions between 2030 and 2050, referred to as committed emissions, while at the same time adhering to technological constraints at both the household and neighbourhood scales. To establish this approach, we integrated bottom-up heat demand modelling at neighbourhood scale with a mixed-integer non-linear optimisation problem. Nine scenarios with different pathways for the insulation of buildings and the decarbonisation in electricity generation were considered and applied to three neighbourhoods in the city of Amsterdam, the Netherlands. The results show that (i) the committed emissions are ten times lower between 2030 and 2050 in scenarios in which ambitious measures are taken for the insulation of buildings and the decarbonisation in electricity generation, (ii) only in these 'ambitious scenarios' low temperature heat systems, such as heat pumps and low temperature heat networks, are optimal solutions for minimising committed emissions, (iii) if less ambitious insulation and decarbonisation measures are taken, high temperature heat options can be part of the heat mix with lowest committed emissions, and (iv) the minimum heat density for low temperature heat networks is not always achieved, creating risks for carbon lock-ins when applying these heat networks. Our results clearly indicate that pathways for the retrofitting of buildings and the decarbonisation in electricity generation need to be taken into account jointly when designing renewable and low-carbon heat systems to optimally reduce carbon emissions towards 2050 and reduce future carbon lock-ins. • Bottom-up heat demand models enable testing spatial heat system requirements. • Power supply decarbonisation and building insulation characterise ambitious policies. • Hybrid or low temperature heat systems are optimal solutions for ambitious policies. • Ambitious decarbonisation policies can lower committed emissions tenfold. • Heat networks can cause a carbon lock-in due to the needed minimum heat density. [ABSTRACT FROM AUTHOR]