  Quantum computers are expected to contribute more efficient and accurate ways
of modeling economic processes. Quantum hardware is currently available at a
relatively small scale, but effective algorithms are limited by the number of
logic gates that can be used, before noise from gate inaccuracies tends to
dominate results. Some theoretical algorithms that have been proposed and
studied for years do not perform well yet on quantum hardware in practice. This
encourages the development of suitable alternative algorithms that play similar
roles in limited contexts.
  This paper implements this strategy in the case of quantum counting, which is
used as a component for keeping track of position in a quantum walk, which is
used as a model for simulating asset prices over time. We introduce quantum
approximate counting circuits that use far fewer 2-qubit entangling gates than
traditional quantum counting that relies on binary positional encoding. The
robustness of these circuits to noise is demonstrated.
  We compare the results to price change distributions from stock indices, and
compare the behavior of quantum circuits with and without mid-measurement to
trends in the housing market. The housing data shows that low liquidity brings
price volatility, as expected with the quantum models.
