Quantum Overlapping Tomography

Abstract

It is now experimentally possible to entangle thousands of qubits, and efficiently measure each qubit in parallel in a distinct basis. To fully characterize an unknown entangled state of $n$ qubits, one requires an exponential number of measurements in $n$, which is experimentally unfeasible even for modest system sizes. By leveraging (i) that single-qubit measurements can be made in parallel, and (ii) the theory of perfect hash families, we show that all $k$-qubit reduced density matrices of an $n$ qubit state can be determined with at most $e^{\mathcal{O}(k)}{\log }^2(n)$ rounds of parallel measurements. We provide concrete measurement protocols which realize this bound. As an example, we argue that with current experiments, the entanglement between every pair of qubits in a system of 1000 qubits could be measured and completely characterized in a few days. This corresponds to completely characterizing entanglement of nearly half a million pairs of qubits.

arXiv comment7 pages, 1 figure; v2: New appendix added, new measurement estimates

References in corpus (24)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Quantum Computing
• Probing many-body dynamics on a 51-atom quantum simulator
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Detecting topological order in a ground state wave function
• String-net condensation: A physical mechanism for topological phases
• Machine learning phases of matter
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• An atom-by-atom assembler of defect-free arbitrary 2d atomic arrays
• Many-body quantum state tomography with neural networks
• Learning phase transitions by confusion
• Efficient quantum state tomography
• Discovering Phase Transitions with Unsupervised Learning
• 10-qubit entanglement and parallel logic operations with a superconducting circuit
• Quantum Loop Topography for Machine Learning
• Efficient tomography of a quantum many-body system
• Quantum Entanglement in Deep Learning Architectures
• Sample-optimal tomography of quantum states
• Quantum-gas microscopes - A new tool for cold-atom quantum simulators
• Quantum state tomography via reduced density matrices
• Optimal local preparation of an arbitrary mixed state of two qubits. Closed expression for the single copy case
• Quantum Marginal Problem and its Physical Relevance
• Multipartite Quantum States and their Marginals
• Harmony for 2-Qubit Entanglement

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