Macroscopic Einstein-Podolsky-Rosen pairs in superconducting circuits

Two-qubit gates are important components of quantum computing. However, unwanted interactions between qubits (so-called parasitic gates) can be particularly problematic and degrade the performance of quantum applications. In this work, we present two software methods to mitigate parasitic two-qubit gate errors. The first approach is built upon the Cartan’s KAK decomposition and keeps the original unitary decomposition for the error-free native two-qubit gate. It counteracts a parasitic two-qubit gate by only applying single-qubit rotations and therefore has no two-qubit gate overhead. We show the optimal choice of single-qubit mitigation gates. The second approach applies a numerical optimisation algorithm to re-compile a target unitary into the error-parasitic two-qubit gate plus single-qubit gates. We demonstrate these approaches on the CPhase-parasitic iSWAP-like gates. The KAK-based approach helps decrease unitary infidelity by a factor of 3 compared to the noisy implementation without error mitigation. When arbitrary single-qubit rotations are allowed, recompilation could completely mitigate the effect of parasitic errors but may require more native gates than the KAK-based approach. We also compare their average gate fidelity under realistic noise models, including relaxation and depolarising errors. Numerical results suggest that different approaches are advantageous in different error regimes, providing error mitigation guidance for near-term quantum computers.

Course 9 Solid state quantum bit circuits

Unlike classical digital computers in which a bit can represent either 1 or 0 at any time, quantum computers use a two-level system, i.e., a qubit, to implement logical operations based on quantum mechanical laws, which can represent both values at once. Owing to the superposition property of qubits, quantum computers have natural parallel processing advantages and thus have potential to exceed the computational efficiency of classical computers for particular tasks. Quantum logic gates are the generalization of classical logic gates in computational networks. It has been proved that two-qubit quantum gates together with one-qubit quantum gates are adequate for constructing networks with any possible quantum computational property. Directional couplers are the most critical elementsfor constructing the quantum gates. In recent years, photonic quantum technologies have emerged as a promising experimental platform for quantum computing. Single photons have robust noise resistance, long coherence time, high transmission speed and great compatibility with other systems. They can be easily manipulated and encoded in any of several degrees of freedom, for example, polarization, path, spatial mode or time bin. Optical waveguide technology enables the realizing of complex optical schemes comprised of many elements with desired scalability, stability and miniaturization. Femtosecond laser direct writing of waveguide has been adopted as a powerful tool for integrated quantum photonics with characteristics of rapidness, cost-effectiveness, mask-less and single-step process. In particular, it has the ability to build arbitrary three-dimensional circuits directly inside bulk materials, which is impossible to achieve with conventional lithography. In this article we review the femtosecond laser writing and quantum characterization of directional coupler and important one-qubit and two-qubit optical quantum logic gates, such as Hadamard gate, Pauli-X gate, controlled-NOT gate, and controlled-Phase gate. The qubits in these gates are usually encoded through optical paths or polarizations of photons. The key to the realization of polarization-encoded one-qubit gates is to achieve flexible wave-plate operations, which is described in detail. Controlled-NOT gate and controlled-phase gate are the most crucial two-qubit gates in the linear optics computation and sometimes they can be converted into each other by adding some one-qubit gates or special superposition states. Many different kinds of waveguide circuits have been used to implement these two-qubit gates. The outlook and challenges for the femtosecond laser writing of three-qubit gates, such as Toffoli gate and Fredkin gate, are briefly introduced.

Quantum key distribution protocol of mesh network structure based on n + 1 EPR pairs

We propose a two-qubit quantum logic gate between a superconducting atom and a propagating microwave photon. The atomic qubit is encoded on its lowest two levels and the photonic qubit is encoded on its carrier frequencies. The gate operation completes deterministically upon reflection of a photon, and various two-qubit gates (SWAP, $\sqrt{\rm SWAP}$, and Identity) are realized through {\it in situ} control of the drive field. The proposed gate is applicable to construction of a network of superconducting atoms, which enables gate operations between non-neighboring atoms.

Rapid progress in semiconductor spin qubits has enabled experimental demonstrations of a two-qubit logic gate. Understanding spin decoherence in a two-qubit logic gate is necessary for optimal qubit operation. We study spin decoherence due to 1/f charge noise for two electrons in a double quantum dot used for a two-qubit controlled-phase gate. In contrast to the usual belief, spin decoherence can be dominated by the tunneling noise from 1/f charge noise instead of the detuning noise. Tunneling noise can dominate because the effect of tunneling noise on the spin qubit is first order in the charge admixture; while the effect of the detuning noise is only second order. The different orders of contributions result in different detuning dependence of the decoherence, which provides a way to identify the noise source. We find that decoherence in a recent two-qubit experiment was dominated by the tunneling noise from 1/f charge noise. The results illustrate the importance of considering tunneling noise to design optimal operation of spin qubits.

Device-independent randomness certification using multiple copies of entangled states

We introduce two methods for quantum process and detector tomography. In the quantum process tomography method, we develop an analytical procedure for projecting the linear inversion estimation of a quantum channel onto the set of completely positive trace-preserving matrices. By integrating this method with alternate projection techniques, we achieve a three-order-of-magnitude improvement in approximating the closest quantum channel to an arbitrary Hermitian matrix compared to existing methods without compromising computational efficiency. Our second method extends this approach to quantum detector tomography, demonstrating superior efficiency compared to current techniques. Through numerical simulations, we evaluate our protocols across channels of up to four qubits in quantum process tomography and systems of up to six qubits in quantum detector tomography, showcasing superior precision and efficiency.

We explore quantum nonlocality in one of the simplest bipartite scenarios. Several new facet-defining Bell inequalities for the {[3 3 3] [3 3 3]} scenario are obtained with their quantum violations analyzed in details. Surprisingly, all these inequalities involving only genuine ternary-outcome measurements can be violated maximally by some two-qubit entangled states, such as the maximally entangled two-qubit state. This gives further evidence that in analyzing the quantum violation of Bell inequalities, or in the application of the latter to device-independent quantum information processing tasks, the commonly-held wisdom of equating the local Hilbert space dimension of the optimal state with the number of measurement outcomes is not necessarily justifiable. In addition, when restricted to the minimal qubit subspace, it can be shown that one of these Bell inequalities requires non-projective measurements to attain maximal quantum violation, thereby giving the first example of a facet-defining Bell inequality where a genuine positive-operator-valued measure is relevant. We experimentally demonstrate the quantum violation of this and two other Bell inequalities for this scenario using energy-time entangled photon pairs. Using the obtained measurement statistics, we demonstrate how characterization of the underlying resource in the spirit of device-independence, but supplemented with auxiliary assumptions, can be achieved. In particular, we discuss how one may get around the fact that, due to finite-size effects, raw measurement statistics typically violate the non-signaling condition.

By considering a multimode treatment of the parametric downconversion of light,1 in which the incident pump also consists of a bandwidth-limited pulse, it is possible to devise experiments in which the energy (frequency) and time occurrence of the parametric photons serve as the conjugate dynamical variables of an Einstein-Podolsky-Rosen (E-P-R) or Bell's inequality experiment. The physical connection between E-P-R and Bell’s inequality and the design of Bell’s inequality experiments with dynamical variables which have continuous spectra are reviewed along with several experiments performed to date. The realizability of experiments using frequency and time is discussed with reference to fundamental measurement resolution limitations,2 as well as presently achievable experimental capabilities. This lends deeper understanding to the nature of the paradoxes and the status of these variables within quantum theory.

In this paper, we consider two related problems, unambiguous discrimination of quantum mixed states and unambiguously conveying classical messages using Einstein-Podolsky-Rosen (EPR) pairs. The main technical contributions are as follows. First, we present a general upper bound on the success probability for unambiguous discrimination among arbitrary $N$ mixed quantum states with given a priori probability, which can be directly used to the unambiguous communication setting. Second, we propose a sufficient condition to show that a new upper bound can be achievable, and construct examples to clarify the relationship between the upper bound we derive and the existing upper bounds presented by other authors. Third, in the issue of conveying classical messages using EPR pairs, we also derive an upper bound on the success probability for unambiguously decoding, where Alice wants to convey $n$ bit classical information to Bob by sending $m$ quantum bits.

We present a non-mathematical explanation of Bell's inequality. Using the inequality, we show how the results of Einstein-Podolsky-Rosen (EPR) experiments violate the principle of strong locality. This indicates, given some reasonable-sounding assumptions, that some sort of faster-than-light influence is present in nature. We discuss the implications, emphasizing the relationship between EPR and the Principle of Relativity, the distinction between causal influences and signals, and the tension between EPR and determinism.

Quantum mechanics, despite its extraordinary success in describing microscopic phenomena, continues to raise foundational questions concerning measurement, nonlocality, and the nature of physical reality. These issues are exemplified by the Einstein-Podolsky-Rosen (EPR) paradox and the Bell inequality, which contrast quantum correlations with classical notions of locality and realism. In this work, we critically examine the assumptions underlying Bell’s theorem in light of the incompatible and contextual nature of quantum observables. We show that Bell’s constraint on simultaneous definite values for incompatible observables, together with the assumption of hidden variables, is not applicable to quantum mechanics itself, which is inherently nonclassical and contextual. When measurement is modeled as a local system-environment interaction within the framework of quantum decoherence, the resulting dynamics remain entirely local and unitary in the EPR scenario. Decoherence naturally selects pointer states and suppresses interference, giving rise to the appearance of wavefunction collapse consistent with quantum predictions. Importantly, the Bell correlations obtained in this framework reproduce the standard quantum results and are independent of both system-bath and inter-bath interactions, which affect only the rate of decoherence. Our analysis suggests that, in the EPR scenario, quantum mechanics can be both local and realistic when the wavefunction is treated as an ontic description of reality within the decoherence framework, offering a potential route toward a locally realistic quantum theory aligned with Einstein’s vision. This work contributes to a more rigorous foundation for quantum mechanics, providing insights that can accelerate progress in quantum computing and nanoenergy harvesting.

Based on a quantum analysis of two capacitively coupled current-biased Josephson junctions, we propose two fundamental two-qubit quantum logic gates. Each of these gates, when supplemented by single-qubit operations, is sufficient for universal quantum computation. Numerical solutions of the time-dependent Schrödinger equation demonstrate that these operations can be performed with good fidelity.

All separable states satisfy all Bell-type inequalities, which involve as their assumption only existence of local realistic (local hidden variable) models of the correlations of spatially separated systems, observed by two or more observers making independent decisions on what to measure (free will). The recent observation by Loubenets, that some separable states do not satisfy the original Bell inequality (1964) has no consequences whatsoever for the studies of the relation of separability with local realism. The original Bell inequality was derived using an additional assumption that the local results for a certain pair of local settings reveal perfect Einstein–Podolsky–Rosen (EPR) correlations. Therefore violation of this inequality by some quantum predictions implies that either (i) the predictions do not allow a local realistic model, or (ii) the predictions do not have the required EPR correlations, or finally both (i) and (ii).