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CONTROL OF NON-RESONANT EFFECTS IN A NUCLERA SPIN QUANTUM COMPUTER WITH A LARGE NUMBER OF QUBITS

G. P. Berman

Published Feb 1, 2001• 0 citations
OpenAlex

Abstract

The authors discuss how to simulate simple quantum logic operations with a large number of qubits. These simulations are needed for experimental testing of scalable solid-state quantum computers. Quantum logic for remote qubits is simulated in a spin chain. Analytical estimates are presented for possible correlated errors caused by non-resonant transitions. A range of parameters is given in which non-resonant effects can be minimized.

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arXiv:quant-ph/0609104•Physical Review A•Oct 27, 2006•1 citation
The authors discuss how to simulate simple quantum logic operations with a large number of qubits. These simulations are needed for experimental testing of scalable solid-state quantum computers. Quantum logic for remote qubits is simulated in a spin chain. Analytical estimates are presented for possible correlated errors caused by non-resonant transitions. A range of parameters is given in which non-resonant effects can be minimized.
The perturbation theory is developed based on small parameters which naturally appear in solid state quantum computation. We report the simulations of the dynamics of quantum logic operations with a large number of qubits (up to 1000). A nuclear spin chain is considered in which selective excitations of spins are provided by having a uniform gradient of the external magnetic field. Quantum logic operations are utilized by applying resonant electromagnetic pulses. The spins interact with their nearest neighbors. We simulate the creation of the long-distance entanglement between remote qubits in the spin chain. Our method enables us to minimize unwanted non-resonant effects in a controlled way. The method we use cannot simulate complicated quantum logic (a quantum computer is required to do this), but it can be useful to test the experimental performance of simple quantum logic operations. We show that: (a) the probability distribution of unwanted states has a ``band'' structure, (b) the directions of spins in typical unwanted states are highly correlated, and (c) many of the unwanted states are high-energy states of a quantum computer (a spin chain). Our approach can be applied to simple quantum logic gates and fragments of quantum algorithms involving a large number of qubits.
We develop a dynamical perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by nonresonant transitions are estimated. We verify our perturbation approach using exact numerical solution for relatively small (N=10)(N=10)(N=10) number of qubits. A preferred range of parameters is found in which the errors in processing quantum information are reasonably small. Our results can be useful for understanding the mechanisms of errors and for experimental testing of scalable solid-state quantum computers.
The errors caused by the transitions with large frequency offsets (nonresonant transitions) are calculated analytically for a scalable solid-state quantum computer based on a one-dimensional spin chain with Ising interactions between neighboring spins. Selective excitations of the spins are enabled by a uniform gradient of the external magnetic field. We calculate the probabilities of all unwanted nonresonant transitions associated with the flip of each spin with nonresonant frequency and with flips of two spins: one with resonant and one with nonresonant frequencies. It is shown that these errors oscillate with changing gradient of the external magnetic field. Choosing the optimal values of this gradient allows us to decrease these errors by 50%.
We report the simulations of the dynamics of quantum-logic operations with large number of qubits (up to 1000). A nuclear-spin chain in which selective excitations of spins are provided by the gradient of the external magnetic field is considered. The spins interact with their nearest neighbors. We simulate the quantum controlled-NOT (CN) gate implementation for remote qubits, which provides the long-distance entanglement. Our approach can be applied to any implementation of quantum-logic gates involving a large number of qubits.
The errors caused by qubit displacements from their prescribed locations in an ensemble of spin chains are estimated analytically and calculated numerically for a quantum computer based on phosphorus donors in silicon. We show that it is possible to polarize (initialize) the nuclear spins even with displaced qubits by using controlled-NOT gates between the electron and nuclear spins of the same phosphorus atom. However, a controlled-NOT gate between the displaced electron spins is implemented with large error because of the exponential dependence of exchange interaction constant on the distance between the qubits. If quantum computation is implemented on an ensemble of many spin chains, the errors can be small if the number of chains with displaced qubits is small.