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arXiv:2308.00384

Engineering unsteerable quantum states with active feedback

Samuel Morales, Yuval Gefen, Igor Gornyi, Alex Zazunov, Reinhold Egger

quant-phcond-mat.mes-hallSubmitted Aug 1, 2023• Announced Aug 2, 2023• 0 citations
v1 · Aug 1, 2023v2 · Feb 7, 2024
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Abstract

We propose active steering protocols for quantum state preparation in quantum circuits where each ancilla qubit (detector) is connected to a single system 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 ancilla 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.

Journal reference
Phys. Rev. Research 6, 013244 (2024)
DOI
10.1103/PhysRevResearch.6.013244
Comments
22 pages, 14 figures

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We propose active steering protocols for quantum state preparation in quantum circuits where each ancilla qubit (detector) is connected to a single system 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 ancilla 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
We introduce and analyze an active steering protocol designed to target multipartite entangled states. The protocol involves multiple qubits subjected to weak Bell pair measurements with active feedback, where the feedback operations are optimized to maximize the Quantum Fisher Information. Our scheme efficiently reaches a genuinely entangled one-parameter state manifold. Numerical simulations for systems with up to 22 qubits suggest that the protocol is scalable and allows high multipartite entanglement across the system.
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 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.
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 study active steering protocols for weakly measured qubits in the presence of error channels due to amplitude and phase noise. If the error rate is sufficiently small, the protocol approaches and stabilizes a predesignated pure target state with high fidelity and high purity, and thus implements autonomous state stabilization. We present numerical simulation results for one and two qubits, taking Andreev qubit circuits as an example. As a function of the error rate, a sharp threshold separates an error-correcting weak-damping regime from a strong-damping regime where the target state cannot be reached anymore. At the threshold, the purity gap closes.