The rotation scheme of quantum states based on EPR pairs

In this paper, we give a further discussion of short-distance teleportation. We propose bidirectional, rotation and cyclic rotation teleportation schemes for short-distance participants, respectively. In our bidirectional transmission scheme, the quantum channel is still an EPR pair and an auxiliary qubit in the ground state [Formula: see text], and two participants can transmit an unknown single-qubit state to each other. In the rotation and cyclic rotation schemes, bidirectional transmission is performed between two adjacent participants in turn. The unknown state qubits of the participants collapse into the ground state after one bidirectional transmission, and can be used as auxiliary qubits in subsequent bidirectional transmission. After a complete state rotation, each participant has held the unknown state of the other participants, and the last one owned by the participant is still the original unknown state. Although the schemes we proposed are applicable to a small range of transmission, they have certain advantages in saving quantum resources.

Encoding Two-Qubit Logical States and Quantum Operations Using the Energy States of a Physical System

In this paper, we introduce a novel coding scheme, which allows single quantum systems to encode multi-qubit registers. This allows for more efficient use of resources and the economy in designing quantum systems. The scheme is based on the notion of encoding logical quantum states using the charge degree of freedom of the discrete energy spectrum that is formed by introducing impurities in a semiconductor material. We propose a mechanism of performing single qubit operations and controlled two-qubit operations, providing a mechanism for achieving these operations using appropriate pulses generated by Rabi oscillations. The above architecture is simulated using the Armonk single qubit quantum computer of IBM to encode two logical quantum states into the energy states of Armonk’s qubit and using custom pulses to perform one and two-qubit quantum operations.

Improved upper bounds on the stabilizer rank of magic states

In this work we improve the runtime of recent classical algorithms for strong simulation of quantum circuits composed of Clifford and T gates. The improvement is obtained by establishing a new upper bound on the stabilizer rank of m copies of the magic state |T⟩=2−1(|0⟩+eiπ/4|1⟩) in the limit of large m. In particular, we show that |T⟩⊗m can be exactly expressed as a superposition of at most O(2αm) stabilizer states, where α≤0.3963, improving on the best previously known bound α≤0.463. This furnishes, via known techniques, a classical algorithm which approximates output probabilities of an n-qubit Clifford + T circuit U with m uses of the T gate to within a given inverse polynomial relative error using a runtime poly(n,m)2αm. We also provide improved upper bounds on the stabilizer rank of symmetric product states |ψ⟩⊗m more generally; as a consequence we obtain a strong simulation algorithm for circuits consisting of Clifford gates and m instances of any (fixed) single-qubit Z-rotation gate with runtime poly(n,m)2m/2. We suggest a method to further improve the upper bounds by constructing linear codes with certain properties.

Quantum uncertainty relations of Tsallis relative $\alpha$ entropy coherence baed on MUBs

In this paper, we discuss quantum uncertainty relations of Tsallis relative $\alpha$ entropy coherence for a single qubit system based on three mutually unbiased bases. For $\alpha\in[\frac{1}{2},1)\cup(1,2]$, the upper and lower bounds of sums of coherence are obtained. However, the above results cannot be verified directly for any $\alpha\in(0,\frac{1}{2})$. Hence, we only consider the special case of $\alpha=\frac{1}{n+1}$, where $n$ is a positive integer, and we obtain the upper and lower bounds. By comparing the upper and lower bounds, we find that the upper bound is equal to the lower bound for the special $\alpha=\frac{1}{2}$, and the differences between the upper and the lower bounds will increase as $\alpha$ increases. Furthermore, we discuss the tendency of the sum of coherence, and find that it has the same tendency with respect to the different $\theta$ or $\varphi$, which is opposite to the uncertainty relations based on the R\'{e}nyi entropy and Tsallis entropy.

Quantum Private Comparison of Arbitrary Single Qubit States Based on Swap Test

In this paper, by using swap test, a quantum private comparison (QPC) protocol of arbitrary single qubit states with a semi-honest third party is proposed. The semi-honest third party (TP) is required to help two participants perform the comparison. She can record intermediate results and do some calculations in the whole process of the protocol execution, but she cannot conspire with any participants. In the process of comparison, TP cannot get two participants' private information except the comparison results. According to the security analysis, the proposed protocol can resist both outsider attacks and participant attacks. Compared with the existing QPC protocols, the proposed one does not require any entanglement swapping technology, and it can compare two participants' qubits by performing swap test, which is easier to implement with current technology. Meanwhile, the proposed protocol can compare secret integers. It encodes secret integers into the amplitude of quantum state rather than transfer them as binary representations, and the encoded quantum state is compared by performing swap test. Additionally, the proposed QPC protocol is extended to the QPC of arbitrary single qubit states by using multi-qubit swap test.

Stronger correlations than dense coding with the same quantum resources

Dense coding is the seminal example of how entanglement can boost quantum communication. By sharing an Einstein-Podolsky-Rosen (EPR) pair, dense coding allows one to transmit two bits of classical information while sending only a single qubit [1]. This doubling of the channel capacity is the largest allowed in quantum theory [2]. In this letter we show in both theory and experiment that same elementary resources, namely a shared EPR pair and qubit communication, are strictly more powerful than two classical bits in more general communication tasks. In contrast to dense coding experiments [3–8], we show that these advantages can be revealed using merely standard optical Bell state analysers [9, 10]. Our results reveal that the power of entanglement in enhancing quantum communications qualitatively goes beyond boosting channel capacities.

Path-optimized nonadiabatic geometric quantum computation on superconducting qubits

Quantum computation based on nonadiabatic geometric phases has attracted a broad range of interests, due to its fast manipulation and inherent noise resistance. However, it is limited to some special evolution paths, and the gate-times are typically longer than conventional dynamical gates, resulting in weakening of robustness and more infidelities of the implemented geometric gates. Here, we propose a path-optimized scheme for geometric quantum computation on superconducting transmon qubits, where high-fidelity and robust universal nonadiabatic geometric gates can be implemented, based on conventional experimental setups. Specifically, we find that, by selecting appropriate evolution paths, the constructed geometric gates can be superior to their corresponding dynamical ones under different local errors. Numerical simulations show that the fidelities for single-qubit geometric Phase, $\pi/8$ and Hadamard gates can be obtained as $99.93\%$, $99.95\%$ and $99.95\%$, respectively. Remarkably, the fidelity for two-qubit control-phase gate can be as high as $99.87\%$. Therefore, our scheme provides a new perspective for geometric quantum computation, making it more promising in the application of large-scale fault-tolerant quantum computation.