Abstract
Performing measurements for high-weight operators has been a practical problem in quantum computation, especially for quantum codes in the stabilizer formalism. The conventional procedure of measuring a high-weight operator requires multiple pairwise unitary operations, which can be slow and prone to errors. We provide an alternative method to passively detect the value of a high-weight operator using only two-local interactions and single-qubit continuous measurements. This approach involves joint interactions between the system and continuously-monitored ancillary qubits. The measurement outcomes from the monitor qubits reveal information about the value of the operator. This information can be retrieved by using a numerical estimator or by evaluating the time average of the signals. The interaction Hamiltonian can be effectively built using only two-local operators, based on techniques from perturbation theory. We apply this indirect detection scheme to the four-qubit Bacon-Shor code, where the two stabilizers are indirectly monitored using four ancillary qubits. Due to the fact that the four-qubit Bacon-Shor code is an error-detecting code and that the Quantum Zeno Effect can suppress errors, we also study the error suppression under the indirect measurement process. In this example, we show that various types of non-Markovian errors can be suppressed.
Highlights
In many conventional quantum algorithms, circuits are presented in discrete time—unitary operations and measurements are treated as if they happened instantly
We introduce a method to indirectly detect the value of a high-weight operator using local two-body interactions and single-qubit continuous measurements
We have presented and analyzed a method for the continuous measurement of high-weight operators, and applied this to the problem of continuous quantum error detection by the four-qubit Bacon-Shor code
Summary
In many conventional quantum algorithms, circuits are presented in discrete time—unitary operations and measurements are treated as if they happened instantly. This continuous-time jumplike error correction process can be realized as applying a sequence of weak measurements [14], and the minimum number of the required ancillary qubits is found to be n − k + 1 for an [n, k, d] code [15] Another framework proposed by Ahn, Doherty, and Landahl (ADL) [16] uses continuous measurements with feedback control to maintain the fidelity of an unknown quantum state. We introduce a method to indirectly detect the value of a high-weight operator using local two-body interactions and single-qubit continuous measurements. We focus on the measurements of the weightfour stabilizers in the error-detecting Bacon-Shor code It is well-known that the quantum Zeno effect can freeze a state in an eigenstate of an observable that is frequently measured. IV, we provide a construction of the target Hamiltonian using only two-local interactions
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