A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable correct ou
tput of logical qubits under the presence of errors. However, strict requirements to encode qubits and operators render the implementation of a full fault-tolerant computation challenging even for the achievable noisy intermediate-scale quantum technology. Here, we experimentally demonstrate the existence of the threshold in a special fault-tolerant protocol. Four physical qubits are implemented using 16 optical spatial modes, in which 8 modes are used to encode two logical qubits. The experimental results clearly show that the probability of correct output in the circuit, formed with fault-tolerant gates, is higher than that in the corresponding non-encoded circuit when the error rate is below the threshold. In contrast, when the error rate is above the threshold, no advantage is observed in the fault-tolerant implementation. The developed high-accuracy optical system may provide a reliable platform to investigate error propagation in more complex circuits with fault-tolerant gates.
The concept of supersymmetry developed in particle physics has been applied to various fields of modern physics. In quantum mechanics, the supersymmetric systems refer to the systems involving two supersymmetric partner Hamiltonians, whose energy lev
els are degeneracy except one of the systems has an extra ground state possibly, and the eigenstates of the partner systems can be mapped onto each other. Recently, an interferometric scheme has been proposed to show this relationship in ultracold atoms [Phys. Rev.A 96, 043624 (2017)]. Here this approach is generalized to linear optics for observing the supersymmetric dynamics with photons. The time evolution operator is simulated approximately via Suzuki-Trotter expansion with considering the realization of the kinetic and potential terms separately. The former is realized through the diffraction nature of light and the later is implemented using phase plate. Additionally, we propose an interferometric approach which can be implemented perfectly using amplitude alternator to realize the non-unitary operator. The numerical results show that our scheme is universal and can be realized with current technologies.
The well-known counterintuitive phenomenon, where the combination of unfavorable situations can establish favorable ones, is called Parrondos paradox. Here, we study one-dimensional discrete-time quantum walks, manipulating two different coins (two-s
tate) operators representing two losing games A and B, respectively, to create the Parrondo effect in the quantum domain. We exhibit that games A and B are losing games when played individually but could produce a winning expectation when played alternatively for a particular sequence of the different periods. Moreover, we also analyze the relationships between Parrondos games and quantum entanglement in our scheme. Along with the applications of different kinds of quantum walks, our outcomes potentially encourage the development of new quantum algorithms.
Relativity theory severely restricts the ability to perform nonlocal measurements in quantum mechanics. Studying such nonlocal schemes may thus reveal insights regarding the relations between these two fundamental theories. Therefore, for the last se
veral decades, nonlocal measurements have stimulated considerable interest. However, the experimental implementation of nonlocal measurements imposes profound restrictions due to the fact that the interaction Hamiltonian cannot contain, in general, nonlocal observables such as the product of local observables belonging to different particles at spacelike-separated regions. In this work, we experimentally realize a scheme for nonlocal measurements with the aid of probabilistic quantum erasure. We apply this scheme to the tasks of performing high accuracy nonlocal measurements of the parity, as well as measurements in the Bell basis, which do not necessitate classical communication between the parties. Unlike other techniques, the nonlocal measurement outcomes are available locally (upon successful postselection). The state reconstructed via performing quantum tomography on the system after the nonlocal measurement indicates the success of the scheme in retrieving nonlocal information while erasing any local data previously acquired by the parties. This measurement scheme allows realizing any controlled-controlled-gate with any coupling strength. Hence our results are expected to have conceptual and practical applications to quantum communication and quantum computation.
Entanglement and wave function description are two of the core concepts that make quantum mechanics such a unique theory. A method to directly measure the wave function, using Weak Values, was demonstrated by Lundeen et al., Nature textbf{474}, 188(2
011). However, it is not applicable to a scenario of two disjoint systems, where nonlocal entanglement can be a crucial element since that requires obtaining the Weak Values of nonlocal observables. Here, for the first time, we propose a method to directly measure a nonlocal wave function of a bipartite system, using Modular Values. The method is experimentally implemented for a photon pair in a hyper-entangled state, i.e. entangled both in polarization and momentum degrees of freedom.
We report the first implementation of the von Neumann instantaneous measurements of nonlocal variables which becomes possible due to technological achievements in creating hyperentangled photons. Tests of reliability and of the nondemolition property
of the measurements have been performed with high precision showing the suitability of the scheme as a basic ingredient of numerous quantum information protocols. The method allows to demonstrate for the first time with strong measurements a special feature of pre- and postselected quantum systems: the failure of the product rule. It has been verified experimentally that for a particular pre- and postselected pair of particles a single measurement on particle $A$ yields with certainty $sigma_x^A=-1$, a single measurement on particle $B$ yields with certainty $sigma_y^B=-1$, and a single nonlocal measurement on particles $A$ and $B$ yields with certainty $sigma_x^A sigma_y^B=-1$.
Entanglement generation in discrete time quantum walks is deemed to be another key property beyond the transport behaviors. The latter has been widely used in investigating the localization or topology in quantum walks. However, there are few experim
ents involving the former for the challenges in full reconstruction of the final wave function. Here, we report an experiment demonstrating the enhancement of the entanglement in quantum walks using dynamic disorder. Through reconstructing the local spinor state for each site, von Neumann entropy can be obtained and used to quantify the coin-position entanglement. We find that the enhanced entanglement in the dynamically disordered quantum walks is independent of the initial state, which is different from the entanglement generation in the Hadamard quantum walks. Our results are inspirational for achieving quantum computing based on quantum walks.
We report the experimental measurement of the winding number in an unitary chiral quantum walk. Fundamentally, the spin-orbit coupling in discrete time quantum walks is implemented via birefringent crystal collinearly cut based on time-multiplexing s
cheme. Our protocol is compact and avoids extra loss, making it suitable for realizing genuine single-photon quantum walks at a large-scale. By adopting heralded single-photon as the walker and with a high time resolution technology in single-photon detection, we carry out a 50-step Hadamard discrete-time quantum walk with high fidelity up to 0.948$pm$0.007. Particularly, we can reconstruct the complete wave-function of the walker that starts the walk in a single lattice site through local tomography of each site. Through a Fourier transform, the wave-function in quasi-momentum space can be obtained. With this ability, we propose and report a method to reconstruct the eigenvectors of the system Hamiltonian in quasi-momentum space and directly read out the winding numbers in different topological phases (trivial and non-trivial) in the presence of chiral symmetry. By introducing nonequivalent time-frames, we show that the whole topological phases in periodically driven system can also be characterized by two different winding numbers. Our method can also be extended to the high winding number situation.
Quantum processes of inherent dynamical nature, such as quantum walks (QWs), defy a description in terms of an equilibrium statistical physics ensemble. Up to now, it has remained a key challenge to identify general principles behind the underlying u
nitary quantum dynamics. Here, we show and experimentally observe that split-step QWs admit a characterization in terms of a dynamical topological order parameter (DTOP). This integer-quantized DTOP measures, at a given time, the winding of the geometric phase accumulated by the wave-function during the QW. We observe distinct dynamical regimes in our experimentally realized QWs each of which can be attributed to a qualitatively different temporal behavior of the DTOP. Upon identifying an equivalent many-body problem, we reveal an intriguing connection between the nonanalytic changes of the DTOP in QWs and the occurrence of dynamical quantum phase transitions.
Standard weak measurement (SWM) has been proved to be a useful ingredient for measuring small longitudinal phase shifts. [Phys. Rev. Lett. 111, 033604 (2013)]. In this letter, we show that with specfic pre-coupling and postselection, destructive inte
rference can be observed for the two conjugated variables, i.e. time and frequency, of the meter state. Using a broad band source, this conjugated destructive interference (CDI) can be observed in a regime approximately 1 attosecond, while the related spectral shift reaches hundreds of THz. This extreme sensitivity can be used to detect tiny longitudinal phase perturbation. Combined with a frequency-domain analysis, conjugated destructive interference weak measurement (CDIWM) is proved to outperform SWM by two orders of magnitude.
