Interesting problems in quantum computation take the form of finding low-energy states of (pseudo)spin systems with engineered Hamiltonians that encode the problem data. Motivated by the practical possibility of producing very low-temperature spin systems, we propose and exemplify the possibility to compute by coupling the computational spins to a quantum coherent bath that serves as a heat sink. The quantum tunneling effect provides additional cooling channels to accelerate the cooling process. We demonstrate both analytically and numerically that this strategy can achieve a quantum advantage in the unstructured search problem.
Interesting problems in quantum computation take the form of finding low-energy states of (pseudo)spin systems with engineered Hamiltonians that encode the problem data. Motivated by the practical possibility of producing very low-temperature spin systems, we propose and exemplify the possibility to compute by coupling the computational spins to a quantum coherent bath that serves as a heat sink. The quantum tunneling effect provides additional cooling channels to accelerate the cooling process. We demonstrate both analytically and numerically that this strategy can achieve a quantum advantage in the unstructured search problem.
The field of quantum information has inspired new methods for cooling physical systems at the quantum scale by manipulating entropy in an algorithmic way, such as heat-bath algorithmic cooling (HBAC). These methods not only provide fundamental insight into quantum thermodynamics, but they are also at the core of practical applications in quantum science and quantum technologies. Arguably, the most promising practical applications are in quantum computing, for the preparation of pure states. The ability to prepare highly pure states is required both for initializing qubits in most quantum algorithms and for supplying reliable low-noise ancilla qubits that satisfy the fault-tolerance threshold for quantum error correction (achieving the high levels of purity required represents one of the major challenges not only for ensemble implementations but also for technologies with strong but not perfect projective measurements). \n \n \nThe heat bath algorithmic cooling protocols have inspired the work within this thesis, which examines and proposes powerful new techniques that significantly enhance cooling by taking advantage of classical and quantum correlations. These new methods go beyond the limits of conventional cooling techniques, providing a novel way to cool that allows a generalized interaction of the system with the environment, which has not been taken into account in previous work. Concretely, I have contributed to elucidating our understanding of these algorithmic cooling mechanisms by using techniques from quantum information theory and quantum thermodynamics. First, I found the analytical solution of the maximum achievable cooling of these algorithmic cooling methods, which had been a longstanding problem that remained open for almost 15 years. Then, I showed how to circumvent the cooling limits of the conventional algorithmic cooling – which were widely believed to be optimal –, creating novel methods that show how correlations can be used to significantly improve cooling. On the one hand, we fundamentally changed the way previous methods considered the interactions between the system and environment and showed how correlated relaxation processes can be essential for enhancing cooling. On the other hand, we demonstrated that correlations present in the initial state due to internal interactions can be exploited to improve cooling. Finally, we showed how, by using ideas and concepts from resource theory, it is possible to find the optimal entropy compression required for HBAC by studying the n-to-1 distillation of athermality of two level systems.
Preparation of low-energy quantum many-body states has a wide range of applications in quantum information processing and condensed-matter physics. Quantum cooling algorithms offer a promising alternative to other methods based, for instance, on variational and adiabatic principles, or on dissipative state preparation. In this work, we investigate a set of cooling algorithms in a simple, solvable fermionic model that allows us to identify the mechanisms that underlie the cooling process and, also, those that prevent it. We derive analytical expressions for the cooling dynamics, steady states, and cooling rates in the weak-coupling limit. We find that multifrequency and randomized cycle strategies can significantly enhance the performance of the quantum algorithm and circumvent some of the obstacles. We also analyze the effects of noise and evaluate the conditions under which cooling remains feasible. Furthermore, we present optimized cooling protocols that can significantly enhance cooling performance in the presence of noise. Additionally, we compare cooling and dissipative state preparation and show that, in the model analyzed here, cooling generally achieves lower energies and is more resilient to noise.
Quantum cooling has demonstrated its potential in quantum computing, which can reduce the number of control channels needed for external signals. Recent progress also supports the possibility of maintaining quantum coherence in large-scale systems. The limitations of classical algorithms trapped in the local minima of cost functions could be overcome using this scheme. According to this, we propose a hybrid quantum-classical algorithm for finding the global minima. Our approach utilizes quantum coherent cooling to facilitate coordinative tunneling through energy barriers if the classical algorithm gets stuck. The encoded Hamiltonian system represents the cost function, and a quantum coherent bath in the ground state serves as a heat sink to absorb energy from the system. Our proposed scheme can be implemented in the circuit quantum electrodynamics system using a quantum cavity. The provided numerical evidence demonstrates the quantum advantage in solving spin-glass problems.
We analyze a new computational role of coherent multi-qubit quantum tunneling that gives rise to bands of non-ergodic extended (NEE) quantum states each formed by a superposition of a large number of computational states (deep local minima of the energy landscape) with similar energies. NEE provide a mechanism for population transfer (PT) between computational states and therefore can serve as a new quantum subroutine for quantum search, quantum parallel tempering and reverse annealing optimization algorithms. We study PT in a quantum n-spin system subject to a transverse field where the energy function E(z) encodes a classical optimization problem over the set of spin configurations z. Given an initial spin configuration with low energy, PT protocol searches for other bitstrings at energies within a narrow window around the initial one. We provide an analytical solution for PT in a simple yet nontrivial model: M randomly chosen marked bit-strings are assigned energies E(z) within a narrow strip [−n−W/2,n+W/2], while the rest of the states are assigned energy 0. We find that the scaling of a typical PT runtime with n and L is the same as that in the multi-target Grover's quantum search algorithm, except for a factor that is equal to exp(n/(2B2)) for finite transverse field B≫1. Unlike the Hamiltonians used in analog quantum unstructured search algorithms known so far, the model we consider is non-integrable and population transfer is not exponentially sensitive in n to the weight of the driver Hamiltonian. We study numerically the PT subroutine as a part of quantum parallel tempering algorithm for a number of examples of binary optimization problems on fully connected graphs.
We propose a simple, robust protocol to prepare a low-energy state of an arbitrary Hamiltonian on a quantum computer or programmable quantum simulator. The protocol is inspired by the adiabatic demagnetization technique, used to cool solid-state systems to extremely low temperatures. A fraction of the qubits (or spins) is used to model a spin bath that is coupled to the system. By an adiabatic ramp down of a simulated Zeeman field acting on the bath spins, energy and entropy are extracted from the system. The bath spins are then measured and reset to the polarized state, and the process is repeated until convergence to a low-energy steady state is achieved. We demonstrate the protocol via application to the quantum Ising model. We study the protocol's performance in the presence of noise and show how the information from the measurement of the bath spins can be used to monitor the cooling process. The performance of the algorithm depends on the nature of the excitations of the system; systems with non-local (topological) excitations are more difficult to cool than those with local excitations. We explore the possible mitigation of this problem by trapping topological excitations.