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Measurement-based quantum computation in a dynamical thermal state with cooling

David Jennings, Andrzej Dragan, S. D. Barrett, Stephen D. Bartlett, Terry Rudolph

Published Jun 19, 2009• 0 citations
OpenAlex

Abstract

We consider measurement-based quantum computation using the state of a spin-lattice system in equilibrium with a thermal bath and free to evolve under its own Hamiltonian. Any single qubit measurements disturb the system from equilibrium and, with adaptive measurements performed at a finite rate, the resulting dynamics reduces the fidelity of the computation. We show that, for measurements performed at a natural rate, the loss in fidelity is described by a single quantum operation on the encoded quantum state that is independent of the measurement history, and for a sufficiently low temperature we obtain a fault-tolerant threshold for the couplings to the environment.

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We consider measurement-based quantum computation using the state of a spin-lattice system in equilibrium with a thermal bath and free to evolve under its own Hamiltonian. Any single qubit measurements disturb the system from equilibrium and, with adaptive measurements performed at a finite rate, the resulting dynamics reduces the fidelity of the computation. We show that, for measurements performed at a natural rate, the loss in fidelity is described by a single quantum operation on the encoded quantum state that is independent of the measurement history, and for a sufficiently low temperature we obtain a fault-tolerant threshold for the couplings to the environment.
We consider measurement-based quantum computation using the state of a spin-lattice system in equilibrium with a thermal bath and free to evolve under its own Hamiltonian. Any single qubit measurements disturb the system from equilibrium and, with adaptive measurements performed at a finite rate, the resulting dynamics reduces the fidelity of the computation. We show that it is possible to describe the loss in fidelity by a single quantum operation on the encoded quantum state that is independent of the measurement history. To achieve this simple description, we choose a particular form of spin-boson coupling to describe the interaction with the environment, and perform measurements periodically at a natural rate determined by the energy gap of the system. We found that an optimal cooling exists, which is a trade-off between keeping the system cool enough that the resource state remains close to the ground state, but also isolated enough that the cooling does not strongly interfere with the dynamics of the computation. For a sufficiently low temperature we obtain a fault-tolerant threshold for the couplings to the environment.
Measurement-based quantum computation utilizes an initial entangled resource state and proceeds with subsequent single-qubit measurements. It is implicitly assumed that the interactions between qubits can be switched off so that the dynamics of the measured qubits do not affect the computation. By proposing a model spin Hamiltonian, we demonstrate that measurement-based quantum computation can be achieved on a thermal state with always-on interactions. Moreover, computational errors induced by thermal fluctuations can be corrected and thus the computation can be executed fault tolerantly if the temperature is below a threshold value.
We investigate the fidelity of measurement-based quantum computation (MBQC) when it is coupled with a boson environment, by measuring the cluster-state fidelity and gate fidelity. Two schemes of cluster-state preparation are studied. In the controlled-Z (CZ) creation scheme, cluster states are prepared by entangling all qubits in $|+\ensuremath{\rangle}$ state with CZ gates at all neighboring sites. The fidelity shows an oscillation pattern over time. The influence of the environmental temperature is evaluated, and suggestions are given to enhance the performance of MBQCs realized in this way. In the Hamiltonian creation scheme, cluster states are made by cooling a system with cluster Hamiltonians, of which the ground states are cluster states. A fidelity sudden-drop phenomenon is discovered. When the coupling is below a threshold, MBQC systems are highly robust against the noise. Our main environmental model is one with a single collective bosonic mode.
Quantum error correction is essential for reliable quantum computation, where surface codes demonstrate high fault-tolerant thresholds and hardware efficiency. However, noise in single-shot measurements limits logical readout fidelity, forming a critical bottleneck for fault-tolerant quantum computation. We propose a dynamic measurement scheduling protocol that suppresses logical readout errors by adaptively redistributing measurement tasks from error-prone qubits to stable nodes. Using shallow entangled circuits, the protocol balances gate errors and measurement noise. This is achieved by dynamically prioritizing resource allocation based on topological criticality and error metrics. When addressing realistic scenarios where temporal constraints are governed by decoherence limits and error-correction requirements, we implement reinforcement learning (RL) to achieve adaptive measurement scheduling. Numerical simulations show that logical error rates can be reduced by up to 34% across code distances for 3 to 11, with enhanced robustness in measurement-noise-dominated systems. Our protocol offers a versatile, hardware-efficient solution for high-fidelity quantum error correction, advancing large-scale quantum computing.
We study the non-Markovian dynamics of a qubit made up of a two-level atom interacting with an electromagnetic field (EMF) initially at finite temperature. Unlike most earlier studies where the bath is assumed to be fixed, we study the complete evolution of the combined qubit-EMF system, thus allowing for the coherent backaction from the bath on the qubit and the qubit on the bath in a self-consistent manner. In this way we can see the development of quantum correlations and entanglement between the system and its environment, and how that affects the decoherence and relaxation of the system. We find nonexponential decay for both the diagonal and nondiagonal matrix elements of the qubit's reduced density matrix in the pointer basis. The former shows the qubit relaxing to thermal equilibrium with the bath, while the latter shows the decoherence rate beginning at the usually predicted thermal rate, but changing to the zero-temperature value as the qubit and bath become entangled. The decoherence and relaxation rates are comparable, as in the zero-temperature case. On the entanglement of a qubit with the EMF we calculated the fidelity and the von Neumann entropy, which is a measure of the purity of the density matrix. The present more accurate non-Markovian calculations predict lower loss of fidelity and purity as compared with the Markovian results. Generally speaking, with the inclusion of quantum correlations between the qubit and its environment, the non-Markovian processes tend to slow down the drive of the system to equilibrium, prolonging the decoherence and better preserving the fidelity and purity of the system.
We show that the usefulness of the thermal state of a specific spin-lattice model for measurement-based quantum computing exhibits a transition between two distinct ``phases''---one in which every state is a universal resource for quantum computation, and another in which any local measurement sequence can be simulated efficiently on a classical computer. Remarkably, this transition in computational power does not coincide with any phase transition, classical, or quantum in the underlying spin-lattice model.