Quantum Overlapping Tomography

• Published in: Physical review letters 2020-03, Vol.124 (10), p.100401-100401, Article 100401
• Main Authors: Cotler, Jordan, Wilczek, Frank
• Format: Article
• Language: English
• Subjects: Correlators; Entangled states; Qubits (quantum computing)
• ISSN: 0031-9007; 1079-7114; 1079-7114
• DOI: 10.1103/PhysRevLett.124.100401

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^{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 near-term experiments, every two-point correlator in a system of 1024 qubits could be measured and completely characterized in a few days. This corresponds to determining nearly 4.5 million correlators.