A Stochastic Liouville Equation Approach for the Effect of Noise in Quantum Computations

Abstract

We propose a model based on a generalized effective Hamiltonian for studying the effect of noise in quantum computations. The system-environment interactions are taken into account by including stochastic fluctuating terms in the system Hamiltonian. Treating these fluctuations as Gaussian Markov processes with zero mean and delta function correlation times, we derive an exact equation of motion describing the dissipative dynamics for a system of n qubits. We then apply this model to study the effect of noise on the quantum teleportation and a generic quantum controlled-NOT (CNOT) gate. For the quantum CNOT gate, we study the effect of noise on a set of one- and two-qubit quantum gates, and show that the results can be assembled together to investigate the quality of a quantum CNOT gate operation. We compute the averaged gate fidelity and gate purity for the quantum CNOT gate, and investigate phase, bit-flip, and flip-flop errors during the CNOT gate operation. The effects of direct inter-qubit coupling and fluctuations on the control fields are also studied. We discuss the limitations and possible extensions of this model. In sum, we demonstrate a simple model that enables us to investigate the effect of noise in arbitrary quantum circuits under realistic device conditions.

arXiv comment36 pages, 6 figures; to be submitted to Phys. Rev. A

References in corpus (22)

• Quantum Computation with Quantum Dots
• Elementary gates for quantum computation
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Quantum state engineering with Josephson-junction devices
• Decoherence Free Subspaces for Quantum Computation
• Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance
• Noiseless Quantum Codes
• Two-Bit Gates are Universal for Quantum Computation
• Reliable Quantum Computers
• Quantum Computers and Dissipation
• Experimental realization of a quantum algorithm
• Maintaining coherence in Quantum Computers
• Preserving coherence in quantum computation by pairing quantum bits
• Resilient Quantum Computation: Error Models and Thresholds
• Reducing decoherence in quantum computer memory with all quantum bits coupling to the same environment
• Experimental Realization of an Order-Finding Algorithm with an NMR Quantum Computer
• Robustness of Decoherence-Free Subspaces for Quantum Computation
• Decoherence and dissipation during a quantum XOR gate operation
• Decoherence and gate performance of coupled solid state qubits
• Decoherence and dephasing in coupled Josephson-junction qubits
• Dynamics of Dissipative Two-Level Systems in the Stochastic Approximation
• Error Rate of the Kane Quantum Computer CNOT Gate in the Presence of Dephasing

Cited by in corpus (12)

• Quantum correlation in disordered spin systems: entanglement and applications to magnetic sensing
• Spatial noise filtering through error correction for quantum sensing
• Principles of Control for Decoherence-Free Subsystems
• Elastic Spin Relaxation Processes in Semiconductor Quantum Dots
• Analyzing the impact of time-correlated noise on zero-noise extrapolation
• Impact of correlations and heavy-tails on quantum error correction
• A Study on the Noise Threshold of Fault-tolerant Quantum Error Correction
• Exponential Families for Bayesian Quantum Process Tomography
• Environment-Protected Solid State Based Distributed Charge Qubit
• Engineering Precise and Robust Effective Hamiltonians
• Entanglement dynamics and performance of two-qubit gates for superconducting qubits under non-Markovian effects
• Fidelity, quantum computations and Wilson loop