Quantum circuits with measurements and unitary feedback (MF) can prepare long-range entangled states in constant depth, but a systematic construction of the MF preparation circuit for a given target state remains underexplored. We develop such a scheme for one-dimensional states, based on the notion of pushable defects: virtual-bond operators of a matrix product state that can be pushed through the tensor at the price of a physical feedback unitary. We show that the set of pushable defects, together with their pushing relations classifies finite-depth MF-preparable states and dictates their preparation circuits. To each class of the target state $|A\rangle$ , we associate a state $|B\rangle$ from which $|A\rangle$ can be prepared using a 1-round MF circuit; in particular, $|A\rangle$ is preparable from a product state using a circuit with 1 round of MF whenever $|B\rangle$ is preparable by a finite-depth local unitary (FDLU) circuit. For a general target state, the scheme is obtained by iterating this procedure until the associated state is FDLU-preparable. For open-boundary matrix product states, the scheme is complete: it constructs a preparation circuit whenever finite-depth MF preparation with left-conditioned feedback corrections is possible. Pushable defects and pushing relations thus emerge as a unifying principle for quantum state preparation via measurements and feedback. This characterization further reveals an intrinsic connection between MF circuits and non-invertible symmetries: states with certain classes of pushing relations are related to a product state by Tambara-Yamagami duality operators, or by continuous cosine symmetry operators with fusion rules $L_α L_{α'} = L_{α+α'} + L_{α-α'}$ , together with their generalizations up to (not necessarily transversal) gates.Quantum circuits with measurements and unitary feedback (MF) can prepare long-range entangled states in constant depth, but a systematic construction of the MF preparation circuit for a given target state remains underexplored. We develop such a scheme for one-dimensional states, based on the notion of pushable defects: virtual-bond operators of a matrix product state that can be pushed through the tensor at the price of a physical feedback unitary. We show that the set of pushable defects, together with their pushing relations classifies finite-depth MF-preparable states and dictates their preparation circuits. To each class of the target state $|A\rangle$, we associate a state $|B\rangle$ from which $|A\rangle$ can be prepared using a 1-round MF circuit; in particular, $|A\rangle$ is preparable from a product state using a circuit with 1 round of MF whenever $|B\rangle$ is preparable by a finite-depth local unitary (FDLU) circuit. For a general target state, the scheme is obtained by iterating this procedure until the associated state is FDLU-preparable. For open-boundary matrix product states, the scheme is complete: it constructs a preparation circuit whenever finite-depth MF preparation with left-conditioned feedback corrections is possible. Pushable defects and pushing relations thus emerge as a unifying principle for quantum state preparation via measurements and feedback. This characterization further reveals an intrinsic connection between MF circuits and non-invertible symmetries: states with certain classes of pushing relations are related to a product state by Tambara-Yamagami duality operators, or by continuous cosine symmetry operators with fusion rules $L_α L_{α'} = L_{α+α'} + L_{α-α'}$, together with their generalizations up to (not necessarily transversal) gates.

quant-pharXiv:2608.08821Aug 11, 20260 citations

Photons made to dance together

NatureSep 23, 20140 citations

Putting Photons to work

Physics TodayMay 19, 20090 citations

Quantum Cooperative Robotics and Autonomy

Farbod Khoshnoud, Bruno Marco Quadrelli, I.I. Esat +1 more

The intersection of Quantum Technologies and Robotics Autonomy is explored in the present paper. The two areas are brought together in establishing an interdisciplinary interface that contributes to advancing the field of system autonomy, and pushes the engineering boundaries beyond the existing techniques. The present research adopts the experimental aspects of quantum entanglement and quantum cryptography, and integrates these established quantum capabilities into distributed robotic platforms, to explore the possibility of achieving increased autonomy for the control of multi-agent robotic systems engaged in cooperative tasks. Experimental quantum capabilities are realized by producing single photons (using spontaneous parametric down-conversion process), polarization of photons, detecting vertical and horizontal polarizations, and single photon detecting/counting. Specifically, such quantum aspects are implemented on network of classical agents, i.e., classical aerial and ground robots/unmanned systems. With respect to classical systems for robotic applications, leveraging quantum technology is expected to lead to guaranteed security, very fast control and communication, and unparalleled quantum capabilities such as entanglement and quantum superposition that will enable novel applications.The intersection of Quantum Technologies and Robotics Autonomy is explored in the present paper. The two areas are brought together in establishing an interdisciplinary interface that contributes to advancing the field of system autonomy, and pushes the engineering boundaries beyond the existing techniques. The present research adopts the experimental aspects of quantum entanglement and quantum cryptography, and integrates these established quantum capabilities into distributed robotic platforms, to explore the possibility of achieving increased autonomy for the control of multi-agent robotic systems engaged in cooperative tasks. Experimental quantum capabilities are realized by producing single photons (using spontaneous parametric down-conversion process), polarization of photons, detecting vertical and horizontal polarizations, and single photon detecting/counting. Specifically, such quantum aspects are implemented on network of classical agents, i.e., classical aerial and ground robots/unmanned systems. With respect to classical systems for robotic applications, leveraging quantum technology is expected to lead to guaranteed security, very fast control and communication, and unparalleled quantum capabilities such as entanglement and quantum superposition that will enable novel applications.

InstrumentationFeb 5, 20240 citations