Precision characterisation of two-qubit Hamiltonians via entanglement mapping

Abstract

We show that the general Heisenberg Hamiltonian with non-uniform couplings can be characterised by mapping the entanglement it generates as a function of time. Identification of the Hamiltonian in this way is possible as the coefficients of each operator control the oscillation frequencies of the entanglement function. The number of measurements required to achieve a given precision in the Hamiltonian parameters is determined and an efficient measurement strategy designed. We derive the relationship between the number of measurements, the resulting precision and the ultimate discrete error probability generated by a systematic mis-characterisation, when implementing two-qubit gates for quantum computing.

6 Pages, 3 figures

References in corpus (36)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Quantum Computation with Quantum Dots
• Mixed State Entanglement and Quantum Error Correction
• Quantum state engineering with Josephson-junction devices
• The Physical Implementation of Quantum Computation
• On the Measurement of Qubits
• The logarithmic negativity: A full entanglement monotone that is not convex
• Quantum Computing with Very Noisy Devices
• On the Improvement of Frequency Stardards with Quantum Entanglement
• A Theory of Fault-Tolerant Quantum Computation
• Universal Quantum Computation with the Exchange Interaction
• Electron Spin Resonance Transistors for Quantum Computing in Silicon-Germanium Heterostructures
• Complete Characterization of a Quantum Process: the Two-Bit Quantum Gate
• A geometric theory of non-local two-qubit operations
• Overhead and noise threshold of fault-tolerant quantum error correction
• Fault-Tolerant Error Correction with Efficient Quantum Codes
• Charge-based quantum computing using single donors in semiconductors
• Exchange in silicon-based quantum computer architecture
• Design and proof of concept for silicon-based quantum dot quantum bits
• Practical design and simulation of silicon-based quantum dot qubits
• Quantum Computing with an 'Always On' Heisenberg Interaction
• Inflationary models inducing non-Gaussian metric fluctuations
• Internal Consistency of Fault-Tolerant Quantum Error Correction in Light of Rigorous Derivations of the Quantum Markovian Limit
• Optimal Control of Coupled Josephson Qubits
• Silicon quantum computation based on magnetic dipolar coupling
• Identifying an Experimental Two-State Hamiltonian to Arbitrary Accuracy
• Experimental Hamiltonian identification for controlled two-level systems
• Measuring the entanglement of bipartite pure states
• Scheme for direct measurement of a general two-qubit Hamiltonian
• Universal Quantum Logic from Zeeman and Anisotropic Exchange Interactions
• Identifying a Two-State Hamiltonian in the Presence of Decoherence
• Improved ancilla preparation scheme increases fault-tolerant threshold
• Quantum-Dot Cellular Automata using Buried Dopants
• Generation of quantum logic operations from physical Hamiltonians
• Fault-Tolerant Quantum Computation via Exchange interactions
• A Non-Adiabatic Controlled Not Gate for the Kane Solid State Quantum Computer

Cited by in corpus (14)

• Silicon Quantum Electronics
• Scanning Quantum Decoherence Microscopy
• Indirect Hamiltonian Identification through a small gateway
• Hamiltonian Tomography via Quantum Quench
• Two-Qubit Hamiltonian Tomography by Bayesian Analysis of Noisy Data
• Hamiltonian tomography for quantum many-body systems with arbitrary couplings
• Scalable Hamiltonian learning for large-scale out-of-equilibrium quantum dynamics
• A precise CNOT gate in the presence of large fabrication induced variations of the exchange interaction strength
• Subspace Confinement: How good is your qubit?
• Direct Estimation of Single- and Two-Qubit Hamiltonians and Relaxation Rates
• Robustly learning the Hamiltonian dynamics of a superconducting quantum processor
• Physics-based mathematical models for quantum devices via experimental system identification
• One qubit almost completely reveals the dynamics of two
• Modelling the effect of charge noise on the exchange interaction between spins