MPSStateSpace and MPSSimulator are not compatible with StateSpace and Simulator

[jaeyoo]

We saw that MPSSimulator doesn't work with a function due to lack of a definition:

• ApplyFusedGate() : gate_appl.h
  • fp_type is not defined in MPSSimulator

In file included from tensorflow_quantum/core/ops/math_ops/tfq_simulate_mps_1d.cc:20:
external/local_config_tf/../qsim/lib/gate_appl.h: In instantiation of 'void qsim::ApplyFusedGate(const Simulator&, const Gate&, typename Simulator::State&) [with Simulator = qsim::mps::MPSSimulator<const tfq::QsimFor&, float>; Gate = qsim::GateFused<qsim::Gate<float, qsim::Cirq::GateKind> >; typename Simulator::State = qsim::mps::MPSStateSpace<const tfq::QsimFor&, float>::MPS]':
tensorflow_quantum/core/ops/math_ops/tfq_simulate_mps_1d.cc:165:59:   required from here
external/local_config_tf/../qsim/lib/gate_appl.h:139:11: error: no type named 'fp_type' in 'class qsim::mps::MPSSimulator<const tfq::QsimFor&, float>'
  139 |     using fp_type = typename Simulator::fp_type;
      |           ^~~~~~~

Also, MPSStateSpace doesn't work with some functions due to different names:

• tfq::ComputeExpectationQsim()
  • StateSpace::Copy() vs MPSStateSpace::CopyMPS()
  • StateSpace::SetZeroState() vs MPSStateSpace::SetMPSZero()
  • StateSpace::RealInnerProduct() vs MPSStateSpace::lnnerProduct()

[jaeyoo]

StateSpace::SetZeroState() should be StateSpace::SetStateZero()