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arXiv:2111.09306 · PRX Quantum

Measurement-Driven Navigation in Many-Body Hilbert Space: Active-Decision Steering

Yaroslav Herasymenko, I. V. Gornyi, Yuval Gefen

Published Jun 21, 2023• 29 citations
arXivHTMLPDF

Abstract

The challenge of preparing a system in a designated state spans diverse facets of quantum mechanics.To complete this task of steering quantum states, one can employ quantum control through a sequence of generalized measurements, which direct the system towards the target state.In an active version of this protocol, the obtained measurement readouts are used to adjust the protocol on the go.This enables a sped-up performance relative to the passive version of the protocol, where no active adjustments are included.In this work, we consider such active measurement-driven steering as applied to the challenging case of many-body quantum systems.The target states of highest interest would be those with multipartite entanglement.Such state preparation in a measurement-based protocol is limited by the natural constraints for system-detector couplings.We develop a framework for finding such physically feasible couplings, based on parent Hamiltonian construction.For helpful decision-making strategies, we offer Hilbert-spaceorientation techniques, comparable to those used in navigation.The first one is to tie the active-decision protocol to the greedy accumulation of the cost function, such as the target state fidelity.We show the potential of a significant speedup, employing this greedy approach to a broad family of matrix product state targets.For system sizes considered here, an average value of the speedup factor f across this family settles about 20, for some targets even reaching a few thousands.We also identify a subclass of matrix product state targets, including the ground state of the Affleck-Kennedy-Lieb-Tasaki spin chain, for which the value of f increases with system size.In addition to the greedy approach, the second wayfinding technique is to map out the available measurement actions onto a quantum state machine.A decisionmaking protocol can be based on such a representation, using semiclassical heuristics.This state-machinebased approach can be applied to a more restricted set of targets, where it sometimes offers advantages over the cost-function-based method.We give an example of a W-state preparation, which is accelerated with this method by f 3.5, outperforming the greedy protocol for this target.

DOI
10.1103/prxquantum.4.020347

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The challenge of preparing a system in a designated state spans diverse facets of quantum mechanics.To complete this task of steering quantum states, one can employ quantum control through a sequence of generalized measurements, which direct the system towards the target state.In an active version of this protocol, the obtained measurement readouts are used to adjust the protocol on the go.This enables a sped-up performance relative to the passive version of the protocol, where no active adjustments are included.In this work, we consider such active measurement-driven steering as applied to the challenging case of many-body quantum systems.The target states of highest interest would be those with multipartite entanglement.Such state preparation in a measurement-based protocol is limited by the natural constraints for system-detector couplings.We develop a framework for finding such physically feasible couplings, based on parent Hamiltonian construction.For helpful decision-making strategies, we offer Hilbert-spaceorientation techniques, comparable to those used in navigation.The first one is to tie the active-decision protocol to the greedy accumulation of the cost function, such as the target state fidelity.We show the potential of a significant speedup, employing this greedy approach to a broad family of matrix product state targets.For system sizes considered here, an average value of the speedup factor f across this family settles about 20, for some targets even reaching a few thousands.We also identify a subclass of matrix product state targets, including the ground state of the Affleck-Kennedy-Lieb-Tasaki spin chain, for which the value of f increases with system size.In addition to the greedy approach, the second wayfinding technique is to map out the available measurement actions onto a quantum state machine.A decisionmaking protocol can be based on such a representation, using semiclassical heuristics.This state-machinebased approach can be applied to a more restricted set of targets, where it sometimes offers advantages over the cost-function-based method.We give an example of a W-state preparation, which is accelerated with this method by f 3.5, outperforming the greedy protocol for this target.
We set out a general protocol for steering the state of a quantum system from an arbitrary initial state towards a chosen target state by coupling it to auxiliary quantum degrees of freedom. The protocol requires multiple repetitions of an elementary step: during each step the system evolves for a fixed time while coupled to auxiliary degrees of freedom (which we term 'detector qubits') that have been prepared in a specified initial state. The detectors are discarded at the end of the step, or equivalently, their state is determined by a projective measurement with an unbiased average over all outcomes. The steering harnesses back-action of the detector qubits on the system, arising from entanglement generated during the coupled evolution. We establish principles for the design of the system-detector coupling that ensure steering of a desired form. We illustrate our general ideas using both few-body examples (including a pair of spins-1/2 steered to the singlet state) and a many-body example (a spin-1 chain steered to the Affleck-Kennedy-Lieb-Tasaki state). We study the continuous time limit in our approach and discuss similarities to (and differences from) drive-and-dissipation protocols for quantum state engineering. Our protocols are amenable to implementations using present-day technology. Obvious extensions of our analysis include engineering of other many-body phases in one and higher spatial dimensions, adiabatic manipulations of the target states, and the incorporation of active error correction steps.
We set out a general protocol for steering the state of a quantum system from an arbitrary initial state toward a chosen target state by coupling it to auxiliary quantum degrees of freedom.The protocol requires multiple repetitions of an elementary step: During each step, the system evolves for a fixed time while coupled to auxiliary degrees of freedom (which we term "detector qubits") that have been prepared in a specified initial state.The detectors are discarded at the end of the step, or equivalently, their state is determined by a projective measurement with an unbiased average over all outcomes.The steering harnesses backaction of the detector qubits on the system, arising from entanglement generated during the coupled evolution.We establish principles for the design of the system-detector coupling that ensure steering of a desired form.We illustrate our general ideas using both few-body examples (including a pair of spins-1/2 steered to the singlet state) and a many-body example (a spin-1 chain steered to the Affleck-Kennedy-Lieb-Tasaki state).We study the continuous time limit in our approach and discuss similarities to (and differences from) drive-and-dissipation protocols for quantum state engineering.Our protocols are amenable to implementations using present-day technology.Obvious extensions of our analysis include engineering of other many-body phases in one and higher spatial dimensions, adiabatic manipulations of the target states, and the incorporation of active error correction steps.
We propose active steering protocols for quantum state preparation in quantum circuits where each system qubit is connected to a single detector qubit, employing a simple coupling selected from a small set of steering operators. The decision is made such that the expected cost-function gain in one time step is maximized. We apply these protocols to several many-qubit models. Our results are underlined by three remarkable insights. First, we show that the standard fidelity does not give a useful cost function; instead, successful steering is achieved by including local fidelity terms. Second, although the steering dynamics acts on each system qubit separately, entanglement in the generated target state is introduced, and can be tuned at will, by performing Bell measurements on detector qubit pairs after every time step. This implements a weak-measurement variant of entanglement swapping. Third, numerical simulations suggest that the active steering protocol can reach arbitrarily designated target states, including passively unsteerable states such as the NNN-qubit W state.
We propose active steering protocols for quantum state preparation in quantum circuits where each system qubit is connected to a single detector qubit, employing a simple coupling selected from a small set of steering operators. The decision is made such that the expected cost-function gain in one time step is maximized. We apply these protocols to several many-qubit models. Our results are underlined by three remarkable insights. First, we show that the standard fidelity does not give a useful cost function; instead, successful steering is achieved by including local fidelity terms. Second, although the steering dynamics acts on each system qubit separately, entanglement in the generated target state is introduced, and can be tuned at will, by performing Bell measurements on detector qubit pairs after every time step. This implements a weak-measurement variant of entanglement swapping. Third, numerical simulations suggest that the active steering protocol can reach arbitrarily designated target states, including passively unsteerable states such as the N -qubit W state. Published by the American Physical Society 2024
State preparation is an essential component in quantum information science. A recently developed steering protocol utilizes a sequence of generalized measurements on a detector to steer a quantum system towards a desired state. However, it is designed as an open-loop technique that requires accurate modeling of the overall quantum system and can be prone to errors. To address this challenge, we propose a closed-loop control technique that introduces feedback to the steering protocol, providing robustness to noise and faster state convergence. We introduce two strategies for feedback: (1) a gradient-based active steering protocol that changes the detector-system coupling conditioned on the detector's readout and (2) tuning the fixed detector-system coupling via model-free reinforcement learning. We study the effectiveness of these strategies under various noise models, including both incoherent and decoherent noise, and discuss potential applications in quantum technologies.
Cooling a quantum system to its ground state is important for the characterization of nontrivial interacting systems and in the context of a variety of quantum information platforms. It can be achieved by employing measurement-based passive steering protocols, where the steering steps are predetermined and are not based on measurement readouts. However, measurements realized by coupling the system to auxiliary quantum degrees of freedom (“detectors”) are rather costly and protocols in which the number of detectors scales with system size will have limited practical applicability. Here, we identify conditions under which measurement-based cooling protocols can be taken to the ultimate dilute limit where the number of detectors is independent of system size. For two examples of frustration-free one-dimensional spin chains, we show that steering on a single link is sufficient to cool these systems into their unique ground states. We corroborate our analytical arguments with finite-size numerical simulations and discuss further applications of dilute cooling. Published by the American Physical Society 2024