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This is an investigation of the limits of quantum circuit simulation withSchrodinger's formulation and low precision arithmetic. The goal is to estimatehow much memory can be saved in simulations that involve random, maximallyentangled quantum states. An arithmetic polar representation of $B$ bits isdefined for each quantum amplitude and a normalization procedure is developedto minimize rounding errors. Then a model is developed to quantify thecumulative errors on a circuit of $Q$ qubits and $G$ gates. Depending on whichregime the circuit operates, the model yields explicit expressions for themaximum number of effective gates that can be simulated before rounding errorsdominate the computation. The results are illustrated with random circuits andthe quantum Fourier transform.

The limits of quantum circuit simulation with low precision arithmetic