Parity Measurements Research Articles

Monte Carlo, fitting and Machine Learning for Tau leptons

Status of \tauτ lepton decay Monte Carlo generator TAUOLA, and its main recent applications are reviewed. It is underlined, that in recent efforts on development of new hadronic currents, the multi-dimensional nature of distributions of the experimental data must be taken with a great care. Studies for H \to \tau\tau ; \tau \to hadronsH→ττ;τ→hadrons indeed demonstrate that multi-dimensional nature of distributions is important and available for evaluation of observables where \tauτ leptons are used to constrain experimental data. For that part of the presentation, use of the TAUOLA program for phenomenology of HH and ZZ decays at LHC is discussed, in particular in the context of the Higgs boson parity measurements with the use of Machine Learning techniques. Some additions, relevant for QED lepton pair emission and electroweak corrections are mentioned as well.

Nonlinear phase estimation: Parity measurement approaches the quantum Cramér-Rao bound for coherent states

Quantum-enhanced phase estimation paves the way to ultra-precision sensing and is of great realistic significance. In this paper we investigate theoretically the estimation of a second-order nonlinear phase shift using a coherent state and parity measurement. A numerical expression is derived, the resolution and the sensitivity of parity signal are contrasted to linear phase estimation protocol, and the signal visibility is analyzed. Additionally, by virtue of phase-averaging approach to eliminate any hidden resources, we make an attempt at unveiling the low-down on the fundamental sensitivity limit from the quantum Fisher information. Finally, the effects of several realistic scenarios on the resolution and the sensitivity are studied, including photon loss, imperfect detector, and those which are a combination thereof.

Qubit parity measurement by parametric driving in circuit QED.

Multiqubit parity measurements are essential to quantum error correction. Current realizations of these measurements often rely on ancilla qubits, a method that is sensitive to faulty two-qubit gates and that requires notable experimental overhead. We propose a hardware-efficient multiqubit parity measurement exploiting the bifurcation dynamics of a parametrically driven nonlinear oscillator. This approach takes advantage of the resonator's parametric oscillation threshold, which depends on the joint parity of dispersively coupled qubits, leading to high-amplitude oscillations for one parity subspace and no oscillation for the other. We present analytical and numerical results for two- and four-qubit parity measurements, with high-fidelity readout preserving the parity eigenpaces. Moreover, we discuss a possible realization that can be readily implemented with the current circuit quantum electrodynamics (QED) experimental toolbox. These results could lead to substantial simplifications in the experimental implementation of quantum error correction and notably of the surface code.

Integrated silicon qubit platform with single-spin addressability, exchange control and single-shot singlet-triplet readout

Silicon quantum dot spin qubits provide a promising platform for large-scale quantum computation because of their compatibility with conventional CMOS manufacturing and the long coherence times accessible using 28Si enriched material. A scalable error-corrected quantum processor, however, will require control of many qubits in parallel, while performing error detection across the constituent qubits. Spin resonance techniques are a convenient path to parallel two-axis control, while Pauli spin blockade can be used to realize local parity measurements for error detection. Despite this, silicon qubit implementations have so far focused on either single-spin resonance control, or control and measurement via voltage-pulse detuning in the two-spin singlet–triplet basis, but not both simultaneously. Here, we demonstrate an integrated device platform incorporating a silicon metal-oxide-semiconductor double quantum dot that is capable of single-spin addressing and control via electron spin resonance, combined with high-fidelity spin readout in the singlet-triplet basis.

Understanding non-classical correlation using optical hybrid states in noisy quantum channels

In this article we investigate the non-classical correlation in a macroscopic physical system. As a tool, we consider an optical hybrid state that is a micro–macro entangled state. Our strategy is to study the behavior of non-classical correlation in an optical hybrid state that may go through noisy channels. We study the violation of two inequalities, which are the CHSH-inequality and the (generalized) CHSH-like-inequality, as measures of non-classical correlation. First, we find that when on/off or parity measurements are used for the side of the coherent state in an optical hybrid state, the violation of the CHSH-inequality is the same as that of the (generalized) CHSH-like-inequality. Second, we see that each measurement provides a different value of violation of (generalized) CHSH-inequality when it is an optical hybrid state that goes through noisy channels. A suprising result is that the on/off measurement can provide a violation of CHSH-inequality (or (generalized) CHSH-like-inequality) for an optical hybrid state with any amount of colored noise. This implies that colored noise cannot break the non-classical correlation in an optical hybrid state.

Non-Local Parity Measurements and the Quantum Pigeonhole Effect.

The pigeonhole principle upholds the idea that by ascribing to three different particles either one of two properties, we necessarily end up in a situation when at least two of the particles have the same property. In quantum physics, this principle is violated in experiments involving postselection of the particles in appropriately-chosen states. Here, we give two explicit constructions using standard gates and measurements that illustrate this fact. Intriguingly, the procedures described are manifestly non-local, which demonstrates that the correlations needed to observe the violation of this principle can be created without direct interactions between particles.

Quantum metrology beyond Heisenberg limit with entangled matter wave solitons.

Considering matter wave bright solitons from weakly coupled Bose-Einstein condensates trapped in a double-well potential, we study the formation of macroscopic non-classical states, including Schrödinger-cat superposition state and maximally path entangled N00N-state. We examine these macroscopic states by Mach-Zehnder interferometer in the context of parity measurements, which has been done to obtain Heisenberg limit accuracy for linear phase shift measurement. We reveal that the ratio of two-body scattering length to intra-well hopping parameter can be measured with the scaling beyond this limit by using nonlinear phase shift with interacting quantum solitons.

Quantum computing with Majorana fermion codes

We establish a unified framework for Majorana-based fault-tolerant quantum computation with Majorana surface codes and Majorana color codes. All logical Clifford gates are implemented with zero time overhead. This is done by introducing a protocol for Pauli product measurements with tetrons and hexons which only requires local 4-Majorana parity measurements. An analogous protocol is used in the fault-tolerant setting, where tetrons and hexons are replaced by Majorana surface code patches, and parity measurements are replaced by lattice surgery, still only requiring local few-Majorana parity measurements. To this end, we discuss twist defects in Majorana fermion surface codes and adapt the technique of twist-based lattice surgery to fermionic codes. Moreover, we propose a new family of codes that we refer to as Majorana color codes, which are obtained by concatenating Majorana surface codes with small Majorana fermion codes. Majorana surface and color codes can be used to decrease the space overhead and stabilizer weight compared to their bosonic counterparts.

Nonlinear parity readout with a microwave photodetector

Robust high-fidelity parity measurment is an important operation in many applications of quantum computing. In this work we show how in a circuit-QED architecture, one can measure parity in a single shot at very high contrast by taking advantage of the nonlinear behavior of a strongly driven microwave cavity coupled to one or multiple qubits. We work in a nonlinear dispersive regime treated in an exact dispersive transformation. We show that appropriate tuning of experimental parameters leads to very high contrast in the cavity and therefore to a high efficiency parity readout with a microwave photon counter or another amplitude detector. These tuning conditions are based on nonlinearity and are hence more robust than previously described linear tuning schemes. In the first part of the paper we show in detail how to achieve this for two qubit parity measurements and extend this to $N$ qubits in the second part of the paper. We also study the QNDness of the protocol.

Hardware-efficient bosonic quantum error-correcting codes based on symmetry operators

We establish a symmetry-operator framework for designing quantum error correcting~(QEC) codes based on fundamental properties of the underlying system dynamics. Based on this framework, we propose three hardware-efficient bosonic QEC codes that are suitable for $\chi^{(2)}$-interaction based quantum computation: the $\chi^{(2)}$ parity-check code, the $\chi^{(2)}$ embedded error-correcting code, and the $\chi^{(2)}$ binomial code, all of which detect photon-loss or photon-gain errors by means of photon-number parity measurements and then correct them via $\chi^{(2)}$ Hamiltonian evolutions and linear-optics transformations. Our symmetry-operator framework provides a systematic procedure for finding QEC codes that are not stabilizer codes. The $\chi^{(2)}$ binomial code is of special interest because, with $m\le N$ identified from channel monitoring, it can correct $m$-photon loss errors, $m$-photon gain errors, and $(m-1)$th-order dephasing errors using logical qudits that are encoded in $O(N)$ photons. In comparison, other bosonic QEC codes require $O(N^2)$ photons to correct the same degree of bosonic errors. Such improved photon-efficiency underscores the additional error-correction power that can be provided by channel monitoring. We develop quantum Hamming bounds for photon-loss errors in the code subspaces associated with the $\chi^{(2)}$ parity-check code and the $\chi^{(2)}$ embedded error-correcting code, and we prove that these codes saturate their respective bounds. Our $\chi^{(2)}$ QEC codes exhibit hardware efficiency in that they address the principal error mechanisms and exploit the available physical interactions of the underlying hardware, thus reducing the physical resources required for implementing their encoding, decoding, and error-correction operations, and their universal encoded-basis gate sets.

Magic state parity-checker with pre-distilled components

Magic states are eigenstates of non-Pauli operators. One way of suppressing errors present in magic states is to perform parity measurements in their non-Pauli eigenbasis and postselect on even parity. Here we develop new protocols based on non-Pauli parity checking, where the measurements are implemented with the aid of pre-distilled multiqubit resource states. This leads to a two step process: pre-distillation of multiqubit resource states, followed by implementation of the parity check. These protocols can prepare single-qubit magic states that enable direct injection of single-qubit axial rotations without subsequent gate-synthesis and its associated overhead. We show our protocols are more efficient than all previous comparable protocols with quadratic error reduction, including the protocols of Bravyi and Haah.

English

This study aimed at identifying Sheko cattle keepers' preferences by way of phenotypic ranking and hypothetical choice experiment in their habitat in order to define the indigenous selection criteria. The ranking experiment report was based on 15 cows and 6 to 9 bulls. Three animals of the same sex were randomly assigned in one group that resulted into five groups for cows and two to three groups for bulls. Thirty cattle keepers belonging to another community were invited to rank the groups of experimental animals according to their own preferences and give the reasons why they had chosen the animals as 1st, 2nd, and 3rd. Then they were provided with life history of each cow, including age, milk yield, parity, calving interval and heart girth measurements; while for bulls, age, milk yield of dam, sire fertility and heart girth measurements were described to determine whether she/he would consider re-ranking them. The results of farmers’ preference for traits through both methods are not consistent. In phenotypic ranking, the results indicate that, milk yield, body conformation, body size and coat color were emphasized in the selection of cow while, body size, dairy character, draught character and coat color traits were important traits for selection of bull. Information on life history provided insight in the respondents’ ranking decisions. In choice experiments, the maximum likelihood estimates of the parameters for cow selection were significant in both lowland and midland agro-ecological zones (AEZs), except for calving interval in midland. The trait mothering ability was the most preferred trait followed by milk yield in both AEZs. For bulls the estimates were significant with the exception of growth rate in midland. It was found out that by this method breeding bulls are chosen based on milk performance of mother and temperament in both AEZs. Key words: Breeding objectives, choice experiment, lowland, midland, phenotypic ranking, Sheko. &nbsp

Sagnac effect enhancement with single-mode number squeezing in the presence of photon loss

The precision of gyroscope can be improved with Sagnac effect enhancement. We show that Sagnac effect can be enhanced with single-mode number squeezing technique by calculating the quantum Fisher information (QFI) of coherent state and Fock state and obtain the minimum phase uncertainty with parity measurement in ideal case. Considering that photon losses almost cannot be avoidable in the practical application, a lossy interferometer is modeled by inserting a beam splitter theoretically to calculate the QFI in the presence of photon losses. Through theoretical analysis, the effective transmission rate (or the maximum loss rate) which can enhance Sagnac effect is obtained. For instance, if the average photon number of coherent state \(|\alpha |^{2}\) is far more than the average photon number of Fock state \(N\) and \(N = 20\), sub-shot-noise phase uncertainty can be achieved when loss rate is less than 85%, which indicates the prospect of practical application with the proposed scheme.

Three-qubit direct dispersive parity measurement with tunable coupling qubits

We consider the direct three-qubit parity measurement scheme with two measurement resonators, using circuit quantum electrodynamics to analyze its functioning for several different types of superconducting qubits. We find that for the most common, transmon-like qubit, the presence of additional qubit-state dependent coupling terms of the two resonators hinders the possibility of performing the direct parity measurement. We show how this problem can be solved by employing the Tunable Coupling Qubit (TCQ) in a particular designed configuration. In this case, we effectively engineer the original model Hamiltonian by cancelling the harmful terms. We further develop an analysis of the measurement in terms of information gains and provide some estimates of the typical parameters for optimal operation with TCQs.

Practical resources and measurements for lossy optical quantum metrology

We study the sensitivity of phase estimation in a lossy Mach-Zehnder interferometer (MZI) using two general, and practical, resources generated by a laser and a nonlinear optical medium with passive optimal elements, which are readily available in the laboratory: One is a two-mode separable coherent and squeezed vacuum state at a beam splitter and the other is a two-mode squeezed vacuum state. In view of the ultimate precision given by quantum Fisher information, we show that the two-mode squeezed vacuum state can achieve a lower bound of estimation error than the coherent and squeezed vacuum state under a photon-loss channel. We further consider practical measurement schemes, homodyne detection and photon number resolving detection (PNRD), to characterize the accuracy of phase estimation in reality and find that the coherent and squeezed vacuum state largely achieves a lower bound than the two-mode squeezed vacuum in the lossy MZI while maintaining quantum enhancement over the shot-noise limit. By comparing homodyne detection and PNRD, we demonstrate that quadrature measurement with homodyne detection is more robust against photon loss than parity measurement with PNRD. We also show that double homodyne detection can provide a better tool for phase estimation than single homodyne detection against photon loss.

Super-sensitive phase estimation with coherent boosted light using parity measurements**Project supported by the National Natural Science Foundation of China (Grant No. 11665010), the Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, China (Grant No. QSQC1414), and the Scientific Research Fund of Hunan Provincial Education Department, China (Grant No. 17B055).

We consider a passive and active hybrid interferometer for phase estimation, which can reach the sub-shot-noise limit in phase sensitivity with only the cheapest coherent sources. This scheme is formed by adding an optical parametric amplifier before a Mach–Zehnder interferometer. It is shown that our hybrid protocol can obtain a better quantum Cramer–Rao bound than the pure active (e.g., SU(1,1)) interferometer, and this precision can be reached by implementing the parity measurements. Furthermore, we also draw a detailed comparison between our scheme and the scheme suggested by Caves [Phys. Rev. D 23 1693 (1981)], and it is found that the optimal phase sensitivity gain obtained in our scheme is always larger than that in Caves’ scheme.

Degeneracy-Preserving Quantum Nondemolition Measurement of Parity-Type Observables for Cat Qubits.

A central requirement for any quantum error correction scheme is the ability to perform quantum nondemolition measurements of an error syndrome, corresponding to a special symmetry property of the encoding scheme. It is in particular important that such a measurement does not introduce extra error mechanisms, not included in the error model of the correction scheme. In this Letter, we ensure such a robustness by designing an interaction with a measurement device that preserves the degeneracy of the measured observable. More precisely, we propose a scheme to perform continuous and quantum nondemolition measurement of photon-number parity in a microwave cavity. This corresponds to the error syndrome in a class of error correcting codes called the cat codes, which have recently proven to be efficient and versatile for quantum information processing. In our design, we exploit the strongly nonlinear Hamiltonian of a high-impedance Josephson circuit, coupling a high-Q cavity storage cavity mode to a low-Q readout one. By driving the readout resonator at its resonance, the phase of the reflected or transmitted signal carries directly exploitable information on parity-type observables for encoded cat qubits of the high-Q mode.

A scheme for Sagnac-effect quantum enhancement with Fock state light input**Project supported by the National Natural Science Foundation of China (Grant Nos. 61573372 and 61603413).

Sagnac effect enhancement can improve optical gyro precision. For a certain input intensity, we suggest that the other input port of beam splitter (BS) should be fed with some quantum light to break through shot noise limit (SNL) to improve Sagnac effect without increasing radiation-pressure noise (NRP). We design a Sagnac effect quantum enhancement criterion (SQEC) to judge whether some quantum light can enhance Sagnac effect and present a Sagnac effect enhancement scheme that utilizing Fock state light and parity measurement technique to extract the output phase. The results of the theoretical analysis show that the maximum sensitivity can be reached at θ = 0, and the phase precision can break through SNL and even achieve Heisenberg limit (HL). When the Fock state average photon number n is far less than coherent state, the minimum measurable angular rate is improved with times, which can deduce shot noise and increase NRP little.

Parity measurements versus dual-homodyne measurements in coherent-state Mach–Zehnder interferometry

Previous studies [J. Opt. Soc. Am. B27, A170 (2010)JOBPDE0740-322410.1364/JOSAB.27.00A170; J. Appl. Phys.114, 193102 (2013)JAPIAU0021-897910.1063/1.4829016] have asserted that a coherent-state Mach–Zehnder interferometer (MZI) with parity-based phase estimation can achieve superresolution at the shot-noise limit (SNL). We show that these studies have ignored the need for repeated measurements in order to achieve root-mean-square accuracy at the SNL. Consequently, their superresolution claims need major revision. For comparison, we present the performance of a coherent-state MZI that uses dual-homodyne detection and show that it can achieve SNL scaling in a single measurement, albeit without superresolution.

Towards a heralded eigenstate-preserving measurement of multi-qubit parity in circuit QED

Eigenstate-preserving multi-qubit parity measurements lie at the heart of stabilizer quantum error correction, which is a promising approach to mitigate the problem of decoherence in quantum computers. In this work we explore a high-fidelity, eigenstate-preserving parity readout for superconducting qubits dispersively coupled to a microwave resonator, where the parity bit is encoded in the amplitude of a coherent state of the resonator. Detecting photons emitted by the resonator via a current biased Josephson junction yields information about the parity bit. We analyze theoretically the measurement back action in the limit of a strongly coupled fast detector and show that in general such a parity measurement, while approximately quantum nondemolition is not eigenstate preserving. To remediate this shortcoming we propose a simple dynamical decoupling technique during photon detection, which greatly reduces decoherence within a given parity subspace. Furthermore, by applying a sequence of fast displacement operations interleaved with the dynamical decoupling pulses, the natural bias of this binary detector can be efficiently suppressed. Finally, we introduce the concept of a heralded parity measurement, where a detector click guarantees successful multi-qubit parity detection even for finite detection efficiency.