Rapid solution of problems by nuclear-magnetic-resonance quantum computation

Abstract

We offer an improved method for using a nuclear-magnetic-resonance quantum computer (NMRQC) to solve the Deutsch-Jozsa problem. Two known obstacles to the application of the NMRQC are exponential diminishment of density-matrix elements with the number of bits, threatening weak signal levels, and the high cost of preparing a suitable starting state. A third obstacle is a heretofore unnoticed restriction on measurement operators available for use by an NMRQC. Variations on the function classes of the Deutsch-Jozsa problem are introduced, both to extend the range of problems advantageous for quantum computation and to escape all three obstacles to use of an NMRQC. By adapting it to one such function class, the Deutsch-Jozsa problem is made solvable without exponential loss of signal. The method involves an extra work bit and a polynomially more involved Oracle; it uses the thermal-equilibrium density matrix systematically for an arbitrary number of spins, thereby avoiding both the preparation of a pseudopure state and temporal averaging.

19 pages

References in corpus (7)

• Quantum Algorithms Revisited
• Experimental realization of a quantum algorithm
• Effective Pure States for Bulk Quantum Computation
• Deutsch-Jozsa algorithm as a test of quantum computation
• Scalable NMR Quantum Computation
• Quantum algorithms which accept hot qubit inputs
• Solution of the Deutsch-Josza Problem by NMR Ensemble Computing without Sensitivity Scaling

Cited by in corpus (7)

• Wigner process tomography: Visualization of spin propagators and their spinor properties
• NMR Quantum Calculations of the Jones Polynomial
• Thermal Equilibrium as an Initial State for Quantum Computation by NMR
• Efficient implementations of the Quantum Fourier Transform: an experimental perspective
• Scaling issues in ensemble implementations of the Deutsch-Jozsa algorithm
• Nuclear magnetic resonance implementation of the Deutsch-Jozsa algorithm using different initial states
• Wigner State and Process Tomography on Near-Term Quantum Devices