Abstract
The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman–Vernon double path integral over the histories of the qubits and of an environment, and afterward tracing out the environment. The qubit histories are taken to be paths on the two-sphere S^2 as in Klauder’s coherent-state path integral of spin, and the environment is assumed to consist of harmonic oscillators initially in thermal equilibrium, and linearly coupled to to qubit operators hat{S}_z. The environment can then be integrated out to give a Feynman–Vernon influence action coupling the forward and backward histories of the qubits. This representation allows to derive in a simple way estimates that the total error of operation of a quantum computer without error correction scales linearly with the number of qubits and the time of operation. It also allows to discuss Kitaev’s toric code interacting with an environment in the same manner.
Highlights
Quantum computers are physical devices that manipulate quantum states to execute information-processing tasks [46,49]
Aurell qubits have been widely reported on recently [18,56], the current public state-of-the-art is that around ten qubits can be manipulated in the lab in a manner approaching to what would be required for a general-purpose quantum computer [37]
The goal of this paper is to consider this problem from a global point of view by investigating the errors caused by coupling a system of spins to a thermal bath of bosonic degrees of freedom. Such errors can be correlated over arbitrary distances at low enough temperature, but in a specific way determined by the physical interaction
Summary
Quantum computers are physical devices that manipulate quantum states to execute information-processing tasks [46,49]. The goal of this paper is to consider this problem from a global point of view by investigating the errors caused by coupling a system of spins to a thermal bath of bosonic degrees of freedom. Such errors can be correlated over arbitrary distances at low enough temperature, but in a specific way determined by the physical interaction. For the paradigmatic example of the Kitaev toric code it is further showed that coupling to a bath has effects exponentially small in the size of the lattice For such a system only the errors normally considered need to be corrected.
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