Optimal Coherent-State Superposition for Quantum Phase Estimation

Yusef Maleki

Su‐Yong Lee, Chang-Woo Lee, Hyunchul Nha +1 more

It was recently shown that an entangled coherent state, which is a superposition of two different coherent states, can surpass the performance of noon state in estimating an unknown phase shift. This may hint at further enhancement in phase estimation by incorporating more component states in the superposition of resource state. We here introduce a four-headed cat state (4HCS), a superposition of four different coherent states, and propose its application to quantum phase estimation. We demonstrate the enhanced performance in phase estimation by employing an entangled state via the 4HCS, which can surpass that of the two-headed cat state (2HCS), particularly in the regime of small average photon numbers. Moreover, we show that an entangled state modified from the 4HCS can further enhance the phase estimation, even in the regime of large average photon number under a photon-loss channel. Our investigation further extends to incorporate an increasingly large number of component states in the resource superposition state and clearly show its merit in phase estimation.

Dhrumil Patel, Shi Jie Samuel Tan, Yiğit Subaşı +1 more

Quantum phase estimation is one of the fundamental primitives that underpins many quantum algorithms, including Shor’s algorithm for efficiently factoring large numbers. Due to its significance as a subroutine, in this work, we consider the coherent version of the phase estimation problem, where given an arbitrary input state and black-box access to unitaries U and controlled- U , the goal is to estimate the phases of U in superposition. Most existing phase estimation algorithms involve intermediary measurements that disrupt coherence. Only a couple of algorithms, including the standard quantum phase estimation algorithm, consider this coherent setting. However, the standard algorithm only succeeds with a constant probability. To boost this success probability, one can employ the coherent median technique, resulting in an algorithm with asymptotically optimal query complexity (the total number of calls to U and controlled- U ). However, this coherent median technique requires a large number of ancilla qubits and a computationally expensive quantum sorting network. To address this, in this work, we propose an improved version of the standard algorithm called the tapered quantum phase estimation algorithm, which leverages tapering (or window) functions commonly used in classical signal processing. Our algorithm achieves the asymptotically optimal query complexity without requiring the expensive coherent median technique to boost success probability. Moreover, we find the absolutely optimal taper—not only in the asymptotic scaling but in terms of exact performance. We provide an efficiently preparable ancilla state based on an approximation of the optimal taper, which incurs at most a factor-of-two increase in the probability of error, thereby maintaining near-optimal performance in practice. In the Appendixes, we give an explicit construction of the taper state preparation circuit. Finally, we derive an error bound for coherent quantum phase estimation when the phase estimate is used as a control and subsequently uncomputed.

Ugo Marzolino

Juan Yu, Yue Qin, Jiliang Qin +2 more

Xu Yu, Xiang Zhao, Luyi Shen +3 more

Mach-Zehnder interferometer is a common device in quantum phase estimation and the photon losses in it are an important issue for achieving a high phase accuracy. Here we thoroughly discuss the precision limit of the phase in the Mach-Zehnder interferometer with a coherent state and a superposition of coherent states as input states. By providing a general analytical expression of quantum Fisher information, the phase-matching condition and optimal initial parity are given. Especially, in the photon loss scenario, the sensitivity behaviors are analyzed and specific strategies are provided to restore the phase accuracies for symmetric and asymmetric losses.