  Quantum computers provide a fundamentally new computing paradigm that
promises to revolutionize our ability to solve broad classes of problems.
Surprisingly, the basic mathematical structures of gate-based quantum
computing, such as unitary operations on a finite-dimensional Hilbert space,
are not unique to quantum systems but may be found in certain classical systems
as well.
  Previously, it has been shown that one can represent an arbitrary multi-qubit
quantum state in terms of classical analog signals using nested quadrature
amplitude modulated signals. Furthermore, using digitally controlled analog
electronics one may manipulate these signals to perform quantum gate operations
and thereby execute quantum algorithms. The computational capacity of a single
signal is, however, limited by the required bandwidth, which scales
exponentially with the number of qubits when represented using frequency-based
encoding.
  To overcome this limitation, we introduce a method to extend this approach to
multiple parallel signals. Doing so allows a larger quantum state to be
emulated with the same gate time required for processing frequency-encoded
signals. In the proposed representation, each doubling of the number of signals
corresponds to an additional qubit in the spatial domain. Single quit gate
operations are similarly extended so as to operate on qubits represented using
either frequency-based or spatial encoding schemes. Furthermore, we describe a
method to perform gate operations between pairs of qubits represented using
frequency or spatial encoding or between frequency-based and spatially encoded
qubits. Finally, we describe how this approach may be extended to represent
qubits in the time domain as well.
