Measurement-based quantum diffusion models are introduced to recover pure and mixed quantum states via weak measurements, quantum score matching, and Petz recovery maps with error bounds, bridging to classical stochastic reversals.
Exact and Approximate Unitary 2-Designs: Constructions and Applications
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abstract
We develop the concept of a unitary t-design as a means of expressing operationally useful subsets of the stochastic properties of the uniform (Haar) measure on the unitary group U(2^n) on n qubits. In particular, sets of unitaries forming 2-designs have wide applicability to quantum information protocols. We devise an O(n)-size in-place circuit construction for an approximate unitary 2-design. We then show that this can be used to construct an efficient protocol for experimentally characterizing the fidelity of a quantum process on n qubits with quantum circuits of size O(n) without requiring any ancilla qubits, thereby improving upon previous approaches.
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quant-ph 2representative citing papers
Open-system quantum complexity is governed by a sub-Finslerian geometry whose curvature depends on the cost penalties for unitary and dissipative controls.
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Measurement-Based Quantum Diffusion Models
Measurement-based quantum diffusion models are introduced to recover pure and mixed quantum states via weak measurements, quantum score matching, and Petz recovery maps with error bounds, bridging to classical stochastic reversals.
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The Geometry of Quantum Complexity in Open Systems
Open-system quantum complexity is governed by a sub-Finslerian geometry whose curvature depends on the cost penalties for unitary and dissipative controls.