TY - JOUR
T1 - Quantum Overlapping Tomography
AU - Cotler, Jordan
AU - Wilczek, Frank
N1 - Publisher Copyright:
© 2020 American Physical Society.
PY - 2020/3/13
Y1 - 2020/3/13
N2 - 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 eO(k)log2(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.
AB - 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 eO(k)log2(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.
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U2 - 10.1103/PhysRevLett.124.100401
DO - 10.1103/PhysRevLett.124.100401
M3 - Article
C2 - 32216420
AN - SCOPUS:85082529946
SN - 0031-9007
VL - 124
JO - Physical Review Letters
JF - Physical Review Letters
IS - 10
M1 - 100401
ER -