Optimized Qubit Phase Estimation in Noisy Quantum Channels (original) (raw)
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A Precise Error Bound for Quantum Phase Estimation
Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring symmetry in the error definitions, an exact formula can be found. This new approach may also have value in solving other related problems in quantum computing, where an expected error is calculated. Expressions for two special cases of the formula are also developed, in the limit as the number of qubits in the quantum computer approaches infinity and in the limit as the extra added qubits to improve reliability goes to infinity. It is found that this formula is useful in validating computer simulations of the phase estimation procedure and in avoiding the overestimation of the number of qubits required in order to achieve a given reliability. This formula thus brings improved precision in the design of quantum computers.
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Lecture Notes in Computer Science, 2020
In the near-term, the number of qubits in quantum computers will be limited to a few hundreds. Therefore, problems are often too large and complex to be run on quantum devices. By distributing quantum algorithms over different devices, larger problem instances can be run. This distributing however, often requires operations between two qubits of different devices. Using shared entangled states and classical communication, these operations between different devices can still be performed. In the ideal case of perfect fidelity, distributed quantum computing is a solution to achieving scalable quantum computers with a larger number of qubits. In this work we consider the effects on the output fidelity of a quantum algorithm when using noisy shared entangled states. We consider the quantum phase estimation algorithm and present two distribution schemes for the algorithm. We give the resource requirements for both and show that using less noisy shared entangled states results in a higher overall fidelity.
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We address the problem of estimating the phase given N copies of the phase-rotation gate u . We consider, for the first time, the optimization of the general case where the circuit consists of an arbitrary input state, followed by any arrangement of the N phase rotations interspersed with arbitrary quantum operations, and ending with a general measurement. Using the polynomial method, we show that, in all cases where the measure of quality of the estimate for depends only on the difference ÿ , the optimal scheme has a very simple fixed form. This implies that an optimal general phase estimation procedure can be found by just optimizing the amplitudes of the initial state.
Scientific Reports
Hilbert–Schmidt speed (HSS) is a special type of quantum statistical speed which is easily computable, since it does not require diagonalization of the system state. We find that, when both HSS and quantum Fisher information (QFI) are calculated with respect to the phase parameter encoded into the initial state of an n-qubit register, the zeros of the HSS dynamics are actually equal to those of the QFI dynamics. Moreover, the signs of the time-derivatives of both HSS and QFI exactly coincide. These findings, obtained via a thorough investigation of several paradigmatic open quantum systems, show that HSS and QFI exhibit the same qualitative time evolution. Therefore, HSS reveals itself as a powerful figure of merit for enhancing quantum phase estimation in an open quantum system made of n qubits. Our results also provide strong evidence for both contractivity of the HSS under memoryless dynamics and its sensitivity to system-environment information backflows to detect the non-Markov...
Quantum computing, phase estimation and applications
2008
Recently, the field of unconventional computing has witnessed a huge research effort to solve the problem of the assumed power of computers operating purely according to the laws of quantum physics. Quantum computing can be seen as a special intermediate case between digital and real analog computing. Importantly, there is a threshold theorem for error correction, as opposed to the pure analog case. Alternatively, quantum computing can be viewed as generalized probabilistic computing, where non-negative real probabilities are replaced with complex amplitudes. The main new resources are quantum mechanical phenomena such as state superposition, interference and entanglement. Superposition together with interference provide a special kind of parallelism, while entanglement, especially when spatially shared, supports unique means of communication. One of the most important theoretical result is a proof by Bernstein and Vazirani (1993) that there is an oracle relative to which there is a language that can be efficiently accepted by a quantum Turing machine, but cannot be efficiently accepted by a bounded-error probabilistic Turing machine. The problem which was considered is called Recursive Fourier Sampling and the proposed quantum algorithm gives a quasipolynomial speedup, O(n) versus O(n log n). Next, Abrams and Lloyd showed that a quantum computer can efficiently simulate manybody quantum systems having a local Hamiltonian. An additional (informal) evidence of the assumed power of a quantum computer is a bounded-error quantum polynomial time algorithm for large integer factoring. The Abrams-Lloyd algorithm is potentially the most useful quantum algorithm known so far, and if a quantum computer is ever built, it will revolutionize quantum chemical calculations. Thus there is a growing consensus regarding investments into the experimental quantum computing. In this thesis, attention is paid to small experimental testbed applications with respect to the quantum phase estimation algorithm, the core approach for finding energy eigenvalues. An iterative scheme for quantum phase estimation (IPEA) is derived from the Kitaev phase estimation, a study of robustness of the IPEA utilized as a few-qubit testbed application is performed, and an improved protocol for phase reference alignment is presented. Additionally, a short overview of quantum cryptography is given, with a particular focus on quantum steganography and authentication.
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Physics Letters A, 1998
The problem of estimating a generic phase-shift experienced by a quantum state is addressed for a generally degenerate phase shift operator. The optimal positive operator-valued measure is derived along with the optimal input state. Two relevant examples are analyzed: i) a multi-mode phase shift operator for multipath interferometry; ii) the two mode heterodyne phase detection.
Optimal phase estimation for qubit mixed states
2004
We address the problem of optimal estimation of the relative phase for two-dimensional quantum systems in mixed states. In particular, we derive the optimal measurement procedures for an arbitrary number of qubits prepared in the same mixed state.
Physical Review A, 2007
We discuss the implementation of an iterative quantum phase estimation algorithm, with a single ancillary qubit. We suggest using this algorithm as a benchmark for multi-qubit implementations. Furthermore we describe in detail the smallest possible realization, using only two qubits, and exemplify with a superconducting circuit. We discuss the robustness of the algorithm in the presence of gate errors, and show that 7 bits of precision is obtainable, even with very limited gate accuracies.