Optimum detection for extracting maximum information from symmetric qubit sets
Jun Mizuno, Mikio Fujiwara, Makoto Akiba, Tetsuya Kawanishi, Stephen M. Barnett, Masahide Sasaki
备注：
10 pages, 11 figures, to be submitted to Phys. Rev. A Converted to REVTeX4 format, and a few other minor modifications according to the comments from PRA referree
We demonstrate a class of optimum detection strategies for extracting the maximum information from sets of equiprobable real symmetric qubit states of a single photon. These optimum strategies have been predicted by Sasaki et al. [Phys. Rev. A{\bf 59}, 3325 (1999)]. The peculiar aspect is that the detections with at least three outputs suffice for optimum extraction of information regardless of the number of signal elements. The cases of ternary (or trine), quinary, and septenary polarization signals are studied where a standard von Neumann detection (a projection onto a binary orthogonal basis) fails to access the maximum information. Our experiments demonstrate that it is possible with present technologies to attain about 96% of the theoretical limit.
Optimal labeling schemes lead to efficient experimental protocols for quantum information processing by nuclear magnetic resonance (NMR). A systematic approach of finding optimal labeling schemes for a given computation is described here. The scheme is described for both quadrupolar systems and spin-1/2 systems. Finally, one of the optimal labeling scheme has been used to experimentally implement a quantum full-adder in a 4-qubit system by NMR, using the technique of transition selective pulses.
Phase estimation is used in many quantum algorithms, particularly in order to estimate energy eigenvalues for quantum systems. When using a single qubit as the probe (used to control the unitary we wish to estimate the eigenvalue of), it is not possible to measure the phase with a minimum mean-square error. In standard methods, there would be a logarithmic (in error) number of control qubits needed in order to achieve this minimum error. Here show how to perform this measurement using only two control qubits, thereby reducing the qubit requirements of the quantum algorithm. Our method correspo…
Three-qubit mixed states are used as a channel for controlled quantum teleportation (CQT) of single-qubit states. The connection between different channel parameters to achieve maximum controlled teleportation fidelity is investigated. We show that for a given multipartite entanglement and mixedness, a class of non-maximally entangled mixed $X$ states ($X-$NMEMS) achieves optimum controlled quantum teleportation fidelity, interestingly a class of maximally entangled mixed $X$ states ($X-$MEMS) fails to do so. This demonstrates, for a given spectrum and mixedness, that $X-$MEMS are not sufficie…
Quantum convolutional neural network (QCNN) has just become as an emerging research topic as we experience the noisy intermediate-scale quantum (NISQ) era and beyond. As convolutional filters in QCNN extract intrinsic feature using quantum-based ansatz, it should use only finite number of qubits to prevent barren plateaus, and it introduces the lack of the feature information. In this paper, we propose a novel QCNN training algorithm to optimize feature extraction while using only a finite number of qubits, which is called fidelity-variation training (FV-Training).
We present and demonstrate a general three-step method for extracting the quantum efficiency of dispersive qubit readout in circuit QED. We use active depletion of post-measurement photons and optimal integration weight functions on two quadratures to maximize the signal-to-noise ratio of the non-steady-state homodyne measurement. We derive analytically and demonstrate experimentally that the method robustly extracts the quantum efficiency for arbitrary readout conditions in the linear regime. We use the proven method to optimally bias a Josephson traveling-wave parametric amplifier and to qua…
Most works on open quantum systems generally focus on the reduced physical system by tracing out the environment degrees of freedom. Here we show that the qubit distributions with the environment are essential for a thorough analysis, and demonstrate that the way that quantum correlations are distributed in a quantum register is constrained by the way in which each subsystem gets correlated with the environment. For a two-qubit system coupled to a common dissipative environment $\mathcal{E}$, we show how to optimise interqubit correlations and entanglement via a quantification of the qubit-env…
In a recent paper [Phys. Rev. Lett. 111, 100501 (2013)], a scheme was proposed where subsequent observers can extract unambiguous information about the initial state of a qubit, with finite joint probability of success. Here, we generalize the problem for arbitrary preparation probabilities (arbitrary priors). We discuss two different schemes: one where only the joint probability of success is maximized and another where, in addition, the joint probability of failure is also minimized. We also derive the mutual information for these schemes and show that there are some parameter regions for th…
We discuss sequential unambiguous state-discrimination measurements performed on the same qubit. Alice prepares a qubit in one of two possible states. The qubit is first sent to Bob, who measures it, and then on to Charlie, who also measures it. The object in both cases is to determine which state Alice sent. In an unambiguous state discrimination measurement, we never make a mistake, i.e. misidentify the state, but the measurement may fail, in which case we gain no information about which state was sent. We find that there is a nonzero probability for both Bob and Charlie to identify the stat…
Quantum Steering vs Entanglement and Extracting Work in an Anisotropic Two-Qubit Heisenberg Model in Presence of External Magnetic Fields with DM and KSEA Interactions
When estimating an unknown single pure qubit state, the optimum fidelity is 2/3. As it is well known, the value 2/3 can be achieved in one step, by a single ideal measurement of the polarization along a random direction. I analyze the opposite strategy which is the long sequence of unsharp polarization measurements. The evolution of the qubit under the influence of repeated measurements is quite complicated in the general case. Fortunately, in a certain limit of very unsharp measurements the qubit will obey simple stochastic evolution equations known for long under the name of time-continuous …
We introduce a class of quantum channels with correlations acting on pairs of qubits, where the correlation takes the form of a shift operator onto a maximally entangled state. We optimise the output purity and show that below a certain threshold the optimum is achieved by partially entangled states whose degree of entanglement increases monotonically with the correlation parameter. Above this threshold, the optimum is achieved by the maximally entangled state characterizing the shift. Although, a full analysis can only be done for the 2-norm, both numerical and heuristic arguments indicate th…
We propose an experimental scheme to verify the quantum non-equilibrium fluctuation relations using current technology. Specifically, we show that the characteristic function of the work distribution for a non-equilibrium quench of a general quantum system can be extracted from Ramsey interferometry of a single probe qubit. Our scheme paves the way for the full characterisation of non-equilibrium processes in a variety of complex quantum systems ranging from single particles to many-body atomic systems and spin chains. We demonstrate our idea using a time-dependent quench of the motional state…
We propose a realistic circuit QED experiment to test the extraction of past-future vacuum entanglement to a pair of superconducting qubits. The qubit P interacts with the quantum field along an open transmission line for an interval T_on and then, after a time-lapse T_off, the qubit F starts interacting for a time T_on in a symmetric fashion. After that, past-future quantum correlations will have transferred to the qubits, even if the qubits do not coexist at the same time. We show that this experiment can be realized with current technology and discuss its utility as a possible implementatio…
We propose a scheme for extracting entangled charge qubits from quantum-dot chains that support zero-energy edge modes. The edge mode is composed of Majorana fermions localized at the ends of each chain. The qubit, logically encoded in double quantum dots, can be manipulated through tunneling and pairing interactions between them. The detailed form of the entangled state depends on both the parity measurement (an even or odd number) of the boundary-site electrons in each chain and the teleportation between the chains. The parity measurement is realized through the dispersive coupling of cohere…
We study the statistical distribution of the ergotropy and of the efficiency of a single-qubit battery ad of a single-qubit Otto engine, respectively fuelled by random collisions. The single qubit, our working fluid, is assumed to exchange energy with two reservoirs, a non-equilibrium "hot" reservoir and a zero temperature cold reservoir. The interactions between the qubit and the reservoirs is described in terms of a collision model of open system dynamics. The qubit interacts with the non-equilibrium reservoir (a large ensemble of qudits all prepared in the same pure state) via random unitar…
Extracting Electromagnetic Bare Mode Couplings in Large Superconducting Quantum Processors
Google Quantum AI（谷歌量子人工智能）；Purdue Quantum Science and Engineering Institute, Purdue University（普渡大学量子科学与工程研究所）；Department of Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校物理系）
NISQ (Noisy, Intermediate-Scale Quantum) computing requires error mitigation to achieve meaningful computation. Our compilation tool development focuses on the fact that the error rates of individual qubits are not equal, with a goal of maximizing the success probability of real-world subroutines such as an adder circuit. We begin by establishing a metric for choosing among possible paths and circuit alternatives for executing gates between variables placed far apart within the processor, and test our approach on two IBM 20-qubit systems named Tokyo and Poughkeepsie. We find that a single-numb…
We experimentally demonstrate in NMR a quantum interferometric multi-meter for extracting certain properties of unknown quantum states without resource to quantum tomography. It can perform direct state determinations, eigenvalue/eigenvector estimations, purity tests of a quantum system, as well as the overlap of any two unknown quantum states. Using the same device, we also demonstrate one-qubit quantum fingerprinting.
Quantum Gibbs state sampling algorithms generally suffer from either scaling exponentially with system size or requiring specific knowledge of spectral properties \textit{a priori}. Also, these algorithms require a large overhead of bath or scratch/ancilla qubits. We propose a method, termed the minimal effective Gibbs ansatz (MEGA), which uses a quantum computer to determine a minimal ensemble of pure states that accurately reproduce thermal averages of typical observables. This technique employs properties of correlation functions that can be split into a lesser and greater part; here, we pr…
Noise affects the coherence of qubits and thereby places a bound on the performance of quantum computers. We theoretically study a generic two-level system with fluctuating control parameters in a photonic cavity and find that basic features of the noise spectral density are imprinted in the transient transmission through the cavity. We obtain analytical expressions for generic noise and proceed to study the cases of quasistatic, white and $1/f^α$ noise in more detail. Additionally, we propose a way of extracting the spectral density for arbitrary noise in a frequency band only bounded by the …
In many superconducting devices, including qubits, quasiparticle excitations are detrimental. A normal metal ($N$) in contact with a superconductor ($S$) can trap these excitations; therefore such a trap can potentially improve the devices performances. The two materials influence each other, a phenomenon known as proximity effect which has drawn attention since the '60s. Here we study whether this mutual influence places a limitation on the possible performance improvement in superconducting qubits. We first revisit the proximity effect in uniform $NS$ bilayers; despite the long history of th…
This paper explores the role of a priori knowledge in the optimization of quantum information processing by investigating optimum unambiguous discrimination problems for both the qubit and qutrit states. In general, a priori knowledge in optimum unambiguous discrimination problems can be classed into two types: a priori knowledge of discriminated states themselves and a priori probabilities of preparing the states. It is clarified that whether a priori probabilities of preparing discriminated states are available or not, what type of discriminators one should design just depends on what kind o…
By using the quantum Fisher information (QFI), we address the process of \textit{single}-parameter estimation in the presence of bosonic as well as fermionic environments and protection of information against the noise. In particular, the quantum interferometric power (IP) of the evolved state of the system is uncovered as an important lower bound for the QFIs of initially encoded parameters. Moreover, we unveil new witnesses of non-Markovianity, that can be used to detect efficiently the memory effects and backflow of information from the environment to the system. On the other hand, we also …
We address the trade-off between information and disturbance in qubit thermometry from the perspective of quantum estimation theory. Given a quantum measurement, we quantify information via the Fisher information of the measurement and disturbance via four different figures of merit, which capture different aspects (statistical, thermodynamical, geometrical) of the trade-off. For each disturbance measure, the efficient measurements, i.e. the measurements that introduce a disturbance not greater than any other measurement extracting the same amount of information, are determined explicitly. The…
We study an optimized measurement which discriminates N mixed quantum states occurring with given prior robabilities. The measurement yields the maximum achievable confidence for each of the N conclusive outcomes, thereby keeping the overall probability of inconclusive outcomes as small as possible. It corresponds to optimum unambiguous discrimination when for each outcome the confidence is equal to unity. Necessary and sufficient optimality conditions are derived and general properties of the optimum measurement are obtained. The results are applied to the optimized maximum-confidence discrim…
Extracting information from quantum devices has long been a crucial problem in the field of quantum mechanics. By performing elaborate measurements, quantum state tomography, an important and fundamental tool in quantum science and technology, can be used to determine unknown quantum states completely. In this study, we explore methods to determine multi-qubit pure quantum states uniquely and directly. Two adaptive protocols are proposed, with their respective quantum circuits. Herein, two or three observables are sufficient, while the number of measurement outcomes is either the same as or fe…
Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterises the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP),…
Harnessing spin-qubit decoherence to probe strongly-interacting quantum systems
ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科技研究所）；FZU - Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；ICREA（加泰罗尼亚高级研究院）；Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris（巴黎高等师范学校物理实验室，ENS，巴黎文理研究大学，法国国家科学研究中心，索邦大学，巴黎大学）
We use the quantumcorrelation of both logarithmic negativity andmutual information between a qubit and a relativistic boson to analyze the dynamics of Universe expansion. These dynamical quantum correlations can encode the information about underlying spacetime structure, which suggests a promising application in observational cosmology. We find that the dynamics of both logarithmic negativity and mutual information between the qubit and the boson are very similar. They decrease monotonically with the growth of the expansion volume and the expansion rate. Smaller momentum and medium-sized mass…
We provide a broad outline of the requirements that should be met by components produced for a Quantum Information Technology (QIT) industry, and we identify electromagnetically induced transparency (EIT) as potentially key enabling science toward the goal of providing widely available few-qubit quantum information processing within the next decade. As a concrete example, we build on earlier work and discuss the implementation of a two-photon controlled phase gate and a one-photon phase gate using the approximate Kerr nonlinearity provided by EIT. We rigorously the dependence of the performanc…
Automating detection of Two-Level Systems in Superconducting Qubits
Nordita, KTH Royal Institute of Technology and Stockholm University（诺尔迪塔，皇家理工学院和斯德哥尔摩大学）；Rigetti Computing（瑞格蒂计算）；Department of Physics, Institute for Materials Science, University of Connecticut（康涅狄格大学物理系材料科学研究所）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Department of Physics, School of Science, RMIT University（皇家墨尔本理工大学理学院物理系）
Gisin and Popescu [PRL, 83, 432 (1999)] have shown that more information about their direction can be obtained from a pair of anti-parallel spins compared to a pair of parallel spins, where the first member of the pair (which we call the pointer member) can point equally along any direction in the Bloch sphere. They argued that this was due to the difference in dimensionality spanned by these two alphabets of states. Here we consider similar alphabets, but with the first spin restricted to a fixed small circle of the Bloch sphere. In this case, the dimensionality spanned by the anti-parallel v…
Information metrics give lower bounds for the estimation of parameters. The Cencov-Morozova-Petz Theorem classifies the monotone quantum Fisher metrics. The optimum bound for the quantum estimation problem is offered by the metric which is obtained from the symmetric logarithmic derivative. To get a better bound, it means to go outside this family of metrics, and thus inevitably, to relax some general conditions. In the paper we defined logarithmic derivatives through a phase-space correspondence. This introduces a function which quantifies the deviation from the symmetric derivative. Using th…
In this letter we propose a general principle for how to build up a quantum neural network with high learning efficiency. Our stratagem is based on the equivalence between extracting information from input state to readout qubit and scrambling information from the readout qubit to input qubits. We characterize the quantum information scrambling by operator size growth, and by Haar random averaging over operator sizes, we propose an averaged operator size to describe the information scrambling ability for a given quantum neural network architectures, and argue this quantity is positively correl…
