Multi-qubit Entangled States Research Articles

Fusion of deterministically generated photonic graph states.

Entanglement has evolved from an enigmatic concept of quantum physics to a key ingredient of quantum technology. It explains correlations between measurement outcomes that contradict classical physics and has been widely explored with small sets of individual qubits. Multi-partite entangled states build up in gate-based quantum-computing protocols and-from a broader perspective-were proposed as the main resource for measurement-based quantum-information processing1,2. The latter requires the ex-ante generation of a multi-qubit entangled state described by a graph3-6. Small graph states such as Bell or linear cluster states have been produced with photons7-16, but the proposed quantum-computing and quantum-networking applications require fusion of such states into larger and more powerful states in a programmable fashion17-21. Here we achieve this goal by using an optical resonator22 containing two individually addressable atoms23,24. Ring25 and tree26 graph states with up to eight qubits, with the names reflecting the entanglement topology, are efficiently fused from the photonic states emitted by the individual atoms. The fusion process itself uses a cavity-assisted gate between the two atoms. Our technique is, in principle, scalable to even larger numbers of qubits and is the decisive step towards, for instance, a memory-less quantum repeater in a future quantum internet27-29.

Resource analysis for quantum-aided Byzantine agreement with the four-qubit singlet state

In distributed computing, a Byzantine fault is a condition where a component behaves inconsistently, showing different symptoms to different components of the system. Consensus among the correct components can be reached by appropriately crafted communication protocols even in the presence of byzantine faults. Quantum-aided protocols built upon distributed entangled quantum states are worth considering, as they are more resilient than traditional ones. Based on earlier ideas, here we establish a parameter-dependent family of quantum-aided weak broadcast protocols. We compute upper bounds on the failure probability of the protocol, and define and illustrate a procedure that minimizes the quantum resource requirements. Following earlier work demonstrating the suitability of noisy intermediate scale quantum (NISQ) devices for the study of quantum networks, we experimentally create our resource quantum state on publicly available quantum computers. Our work highlights important engineering aspects of the future deployment of quantum communication protocols with multi-qubit entangled states.

Fast joint parity measurement via collective interactions induced by stimulated emission

Parity detection is essential in quantum error correction. Error syndromes coded in parity are detected routinely by sequential CNOT gates. Here, different from the standard CNOT-gate based scheme, we propose a reliable joint parity measurement (JPM) scheme inspired by stimulated emission. By controlling the collective behavior between data qubits and syndrome qubit, we realize the parity detection and experimentally implement the weight-2 and weight-4 JPM scheme in a tunable coupling superconducting circuit, which shows comparable performance to the CNOT scheme. Moreover, with the aid of the coupling tunability in quantum system, this scheme can be further utilized for specific joint entangling state preparation (JEP) with high fidelity, such as multiqubit entangled state preparation for non-adjacent qubits. This strategy, combined with the superconducting qubit system with tunable couplers, reveals tremendous potential and applications in the surface code architecture without adding extra circuit elements. Besides, the method we develop here can readily be applied in large-scale quantum computation and quantum simulation.

Phase parameters of orthogonal arrays and special maximally multi-qubit entangled states

Quantum orthogonal arrays are combinatorial designs with a remarkable class of genuinely multipartite highly entangled states. In this paper, we propose the method for constructing maximally multi-qubit entangled state through phase parameters of orthogonal arrays. Using this method, we not only determine that maximally n-qubit entangled state, but also find the [Formula: see text] orthogonal array that gives maximally [Formula: see text] entangled states. Such states play an important role in quantum theory with a high degree of multipartite entanglement.

Decoherence-free subspace and entanglement sudden death of multi-photon polarization states in fiber channels

The construction of quantum networks requires long-distance teleportation of multi-qubit entangled states. Here, we investigate the entanglement dynamics of GHZ and W states in fiber channels. In a fiber channel, the two most important phenomena that affect polarization entanglement are polarization mode dispersion (PMD) and polarization-dependent loss (PDL). We theoretically characterize how PMD and PDL vectors affect three-qubit states. In particular, upon quantifying the entanglement at the output states using concurrence and entanglement witnesses, we reveal the occurrence of entanglement sudden death and the appearance of decoherence-free subspaces in tripartite systems. Finally, we explore the evolution of GHZ and W state with an arbitrary number of photons in a fiber network and discuss the decoherence mechanism of the 4-party cluster state.

Entanglement concentration of multi-qubit entangled states: an IBM quantum experience

Entanglement concentration of multi-qubit entangled states: an IBM quantum experience

Generation of Greenberger-Horne-Zeilinger States on Two-Dimensional Superconducting-Qubit Lattices via Parallel Multiqubit-Gate Operations

A recent major technological breakthrough in superconducting circuits is the realization of more than 50 qubits arranged on two-dimensional (2D) lattices with tunable nearest-neighbor couplings. We propose a protocol to generate Greenberger-Horne-Zeilinger (GHZ) states on 2D superconducting-qubit lattices by applying multiqubit controlled-$i$swap gates in parallel. The multiqubit gate can be naturally implemented based on an effective three-body interaction, which can be synthesized with appropriate detunings and coupling strengths between qubits. We simulate the preparation process of GHZ states with realistic parameters, and show a $37$-qubit GHZ state can be generated with a controlled-$i$swap depth of $3$. Our proposal provides a more promising method of generating GHZ states on the latest 2D superconducting-qubit architectures and will stimulate the preparation of multiqubit entangled states based on multiqubit gates.

Rapid Feedback Stabilization of Quantum Systems With Application to Preparation of Multiqubit Entangled States.

For stochastic quantum systems with measurement feedback, this article proposes a rapid switching control scheme based on state space partition and realizes the rapid stabilization of an eigenstate of an observable operator. Meanwhile, we apply the proposed scheme to the preparation of typical entangled states in multiqubit systems. In view of the convergence obstacle caused by the symmetric structure of the state space, especially in the case with degenerate observable operators, we first partition the state space into a subset containing the target state and its complement to distinguish the target state from its antipodal points, and then design the corresponding control laws in these two subsets, respectively, by using different Lyapunov functions. The interaction Hamiltonians are also constructed to drive the system state to the desired subset first, and further to the target state. In particular, the control law designed in the undesired subset guarantees the strictly monotonic descent of the corresponding Lyapunov function, which makes the system trajectory switch between the two subsets at most twice and has the potential to speed up the convergence process. We also prove the stability of the closed-loop system with the proposed switching control law based on the stochastic Lyapunov stability theory. By applying the proposed switching control scheme to a three-qubit system, we achieve the preparation of a GHZ state and a W state.

Enhancing the Fidelity of Controlled Quantum Teleportation by Multi-Qubit Entangled State

Enhancing the Fidelity of Controlled Quantum Teleportation by Multi-Qubit Entangled State

Structural physical approximation of partial transposition makes possible to distinguish SLOCC inequivalent classes of three-qubit system

Detection and classification of entanglement properties of a multi-qubit system is a topic of great interest. This topic has been studied extensively and thus we found different approaches for the detection and classification of multi-qubit entangled states. We have applied partial transposition operation on one of the qubit of the three-qubit system and then studied the entanglement properties of the three-qubit system, which is under investigation. Since the partial transposition operation is not a quantum operation so we have approximated partial transposition operation in such a way so that it represent a completely positive map. The approximated partial transposition operation is also known as structural physical approximation of partial transposition (SPA-PT). We have studied in detail the application of SPA-PT on a three qubit system and provided explicitly the matrix elements of the density matrix describing SPA-PT of a three qubit system. Moreover, we propose criterion to classify all possible stochastic local operations and classical communication(SLOCC) inequivalent classes of a pure as well as mixed three qubit state through SPA-PT map, which makes our criterion experimentally realizable. We have illustrated our criterion for detection and classification of three-qubit entangled states by considering few examples.

Experimental Bayesian estimation of quantum state preparation, measurement, and gate errors in multiqubit devices

We introduce a Bayesian method for the estimation of single qubit errors in quantum devices, and use it to characterize these errors on three 27-qubit superconducting qubit devices. We self-consistently estimate up to seven parameters of each qubit's state preparation, readout, and gate errors, analyze the stability of these errors as a function of time, and demonstrate easily implemented approaches for mitigating different errors before a quantum computation experiment. On the investigated devices we find non-negligible qubit reset errors that cannot be parametrized as a diagonal mixed state, but manifest as a coherent phase of a superposition with a small contribution from the qubit's excited state. We are able to mitigate such errors by applying pre-rotations on the initialized qubits, which we demonstrate with multi-qubit entangled states. Our results demonstrate that Bayesian estimation can resolve small parameters - including those pertaining to quantum gate errors - with a high relative accuracy, at a lower measurement cost as compared with standard characterization approaches.

Multicast-based N -party remote-state preparation of arbitrary Greenberger-Horne-Zeilinger–class states

As an important resource, the multiqubit entangled state is widely concerned in quantum computing and quantum communication. Based on the multiqubit partially entangled state, we propose a quantum multicast scheme. In the proposed scheme, arbitrary $N$-qubit Greenberger-Horne-Zeilinger state could be sent to $N$ receivers via a $2N$-qubit partially entangled state. Specially, the proposed scheme is accomplished with controlled-not gates, which ensure the scheme is more efficient and easier to be implemented. In addition, we construct the quantum circuit simulations and the partially entangled channel on IBMQ to prove the feasibility of the scheme. Finally, the performance of the proposed scheme is analyzed to show that the scheme owns the higher efficiency.

Spacetime Path Integrals for Entangled States

Although the path-integral formalism is known to be equivalent to conventional quantum mechanics, it is not generally obvious how to implement path-based calculations for multi-qubit entangled states. Whether one takes the formal view of entangled states as entities in a high-dimensional Hilbert space, or the intuitive view of these states as a connection between distant spatial configurations, it may not even be obvious that a path-based calculation can be achieved using only paths in ordinary space and time. Previous work has shown how to do this for certain special states; this paper extends those results to all pure two-qubit states, where each qubit can be measured in an arbitrary basis. Certain three-qubit states are also developed, and path integrals again reproduce the usual correlations. These results should allow for a substantial amount of conventional quantum analysis to be translated over into a path-integral perspective, simplifying certain calculations, and more generally informing research in quantum foundations.

Constructing a maximally multi-qubit entangled state via expanded recurrence relation

The notion of a maximally entangled state depends on the measure used to give rise to a rich envision of multipartite state. Recently, Che et al presented a recurrence relation of multi-qubit states. According to this inspiration, we present an expanded recurrence relation of the maximally multipartite state. Using this expanded recurrence relation and Bell state, some new forms of the maximally four-, six-, eight-qubits states are presented. The construct of the maximally multipartite state through recurrence relationships is of great potential.

Efficient estimation of multipartite quantum coherence

Quantification of coherence lies at the heart of quantum information processing and fundamental physics. Exact evaluation of coherence measures generally needs a full reconstruction of the density matrix, which becomes intractable for large-scale multipartite systems. Here, we propose a systematic theoretical approach to efficiently estimating lower and upper bounds of coherence in multipartite states. Under the stabilizer formalism, the lower bound is determined by the spectrum estimation method with a small number of measurements and the upper bound is determined by a single measurement. We verify our theory with a four-qubit optical quantum system.We experimentally implement various multi-qubit entangled states, including the Greenberger-Horne-Zeilinger state, the cluster state, and the W state, and show how their coherence are efficiently inferred from measuring few observables.

Photonic band structure design using persistent homology

The machine learning technique of persistent homology classifies complex systems or datasets by computing their topological features over a range of characteristic scales. There is growing interest in applying persistent homology to characterize physical systems such as spin models and multiqubit entangled states. Here, we propose persistent homology as a tool for characterizing and optimizing band structures of periodic photonic media. Using the honeycomb photonic lattice Haldane model as an example, we show how persistent homology is able to reliably classify a variety of band structures falling outside the usual paradigms of topological band theory, including “moat band” and multi-valley dispersion relations, and thereby control the properties of quantum emitters embedded in the lattice. The method is promising for the automated design of more complex systems such as photonic crystals and Moiré superlattices.

Bidirectional controlled quantum teleportation of multi-qubit entangled states via five-qubit entangled state

Several schemes for bidirectional controlled quantum teleportation (BCQT) of arbitrary single-qubit states have been proposed by utilizing five-qubit entangled states, six-qubit entangled state and seven-qubit entangled state as the quantum channels. In this paper, a generalization to BCQT of multi-qubit entangled states is presented. By using a five-qubit entangled state as the quantum channel, we propose a scheme for BCQT of certain class of multi-qubit entangled states in which two legitimate users exchange their unknown multi-qubit entangled state to each other with the help of a supervisor. Compared with previous BCQT (3 ↔ 3) scheme [2019 Int. J. Theor. Phys. 58 3594], our proposed BCQT (m ↔ n) scheme requires less consumption of quantum and classical resources, and possesses higher intrinsic efficiency. Also, the present BCQT scheme is more general and has less operation complexity.

Construct New Form of Maximally Nine-Qubit Entangled State Via Recurrence Relation

Descrying all aspects of the quantum entanglement of multipartite quantum systems is an essential part when researching the quantum entanglement. Maximally multi-qubit entangled state is one of the research objects. Recently, attracted by a criterion for maximally entangled nine-qubit state and construct a nine-qubit maximally entangled state, we construct a new genuine maximally nine-qubit entangled state via the recurrence relation. Further, nine-qubit entangled state is found which can be seen as a new form maximally nine-qubit entangled state. There are 108 of purity equal to 1/16, 18 of purity equal to 1/8 in observation. We believe the result could provide a new idea for constructing more new maximally multi-qubit states.

Bidirectional quantum teleportation and cyclic quantum teleportation of multi-qubit entangled states via G-state

We propose a novel scheme for faithful bidirectional quantum teleportation (BQT) in which Alice can transmit an unknown N-qubit entangled state to Bob and at the same time Bob can transmit an unknown M-qubit entangled state to Alice by using a four-qubit entangled G-state as a quantum channel. We also propose a new scheme for cyclic QT of multi-qubit entangled states by using two G-states as a quantum channel. The advantage of our schemes is that it seems to be much simpler and requires reduced number of qubits in quantum channel as compared with the other proposed schemes.

Fault Tolerant Multi-Party Authenticated Quantum Conference Against Collective Noise

With the advent of new science and technology, teleconference, which allows multiple participants to communicate directly without being constrained by time and distance, is becoming extremely popular. We put forward two fault tolerant three-party authenticated quantum conference protocols based on channel-encryption against collective-dephasing noise and collective-rotation noise, respectively. Whereafter, we further extend these two protocols to the most common scenario containing n participants. Compared with existing quantum conference protocols, ours own three outstanding merits: firstly, these protocols can meet the requirements of the interactivity of quantum conference well, because the previously shared quantum key can be reused many times; secondly, we introduce an updating mechanism for withstanding the special entanglement attack effectively; and thirdly, an efficient method is presented to realize the distribution of multi-qubit entangled states under collective noise environment.