1. 1 Modeling Quantum Information Systems Paul E. Black National Institute of Standards and Technology Andrew W. Lane University of Kentucky

2. 2 Quantum Computation Simulator Model QCSim: simulator “engine” results Inputs 0 0 0 0 0 1 0 1 0... Gate behavior analysis Physical system

3. 3 Simulator vs. Custom Program SimulatorCustom Fixed, general code Many inputs Specific code Few inputs

4. 4 Simulation Taxonomy Detail –Classical –Dirac ket (pure states) –Density matrix (mixed states) Time –Discrete –Continuous State –Discrete (n-level) –Continuous (finite) –Infinite Time DiscreteContinuous Mixed State Pure State Classical QCSim Detail

5. 5 Simulation Taxonomy (cont.) Values –Concrete (e.g., ) –Symbolic (e.g., ) Simulation –Randomized (Monte Carlo or quantum trajectories) –Branching (one run; explore all choices) –Complete state (one run)

6. 6 Trick 1: Carry Extra Information Extra information –qubit (rep1) so original is unchanged by noise –ancilla to correct replicas Extra gates to compute net error rate Figure 2. [3,1] Hamming code XX original rep2 rep3 noise XX original rep1 rep2 rep3 noise current state: original 0.99995 0 0 5e-05

7. 7 Reliability with & w/o Inversion Inverting one qubit increases reliability in the presence of generalized amplitude damping With Inversion no inversion

8. 8 Trick 2: Use Existing Primitives H H H H H H H H Figure 3. BB84 Shared Secret Key Alice’s info photon Eve’s basis Alice’s basis Bob’s basis Classical choice: Hadamard & measurement ● Measurement in other bases: Hadamard

9. 9 Trick 3: Trade-off Complexity Complex input, simple model = 2|000> + 2|011> + i|100> + i|111>; or Figure 4. Quantum teleportation |>|> EPR pair Z H { H ● Simple input, complex model = 2|000> + i|100>;

10. 10Conclusions Tune physical implementations to actual noise. Add extra stuff to the model to process results. Use Hadamard and measurement for classical random choice. Model physical effects with existing. Trade-off complexity between model and inputs. Simulator code available at http://hissa.nist.gov/~black/Quantum/