As quantum computing hardware rapidly advances, objectively evaluating the capabilities and error rates of new processors remains a critical challenge for the field. A clear and realistic understanding of current quantum performance is essential to guide research priorities and drive meaningful progress. In this work, we apply and extend a protocol-based benchmarking methodology (presented in arXiv:2505.12441) that utilizes well-defined quantumness thresholds. By evaluating performance at protocol level rather then the gate level, this approach provides a transparent and intuitive assessment of whether specific quantum processors, or isolated sub-chips within them, can demonstrate a practical quantum advantage. To illustrate the utility of this method, we compare two generations of IBM quantum computers: the older Eagle architecture and the newer Heron architecture. Our findings reveal the genuine operational strengths and limitations of these devices, demonstrating substantial performance improvements in the newer Heron generation.

We present a route-resolved comparative assessment of Rigetti's Cepheus-1-108Q and IBM Heron-r2 processors using the established 'do-nothing' state-transfer protocol. Rather than proposing a new protocol, we use this deterministic, low-complexity task as a high-resolution spatial probe. For each evaluated initial qubit, we report two complementary quantities: the largest tested radius within which every evaluated shortest route satisfies the operational success rule, and the longest successful route identified within the evaluated route family. To achieve this, we address a deceptively simple yet foundational question: “How far can you do-nothing on a quantum computer?” Operationally, this do-nothing protocol serves as a fundamental state transfer protocol: we prepare an initial quantum state, route it across the physical qubits using SWAP gates, and measure the final state fidelity against the well-established classical fidelity limit for single-qubit state transfer. While this trivial state-transfer protocol serves as the most intuitive baseline, actively preserving a quantum state across a physical lattice proves to be a non-trivial task that exposes the information to cumulative relaxation, dephasing, and environmental cross-talk. In the highlighted IBM QPU case, we identify an isotropic radius of 10 and a successful path of swap distance 27, whereas the highlighted Rigetti Cepheus case exhibits an isotropic radius of 1 but selected above-threshold routes reaching swap distance 8. These results reveal a sharp distinction between uniform spatial reliability and best-route performance. The presented quantities are empirical and conditional on the evaluated route families, finite-shot decision rule, calibration state, and execution time; they are not architecture-wide constants.

Both Superconducting and Ion-Trap are leading quantum architectures common in the current landscape of the quantum computing field, each with distinct characteristics and operational constraints. Understanding and measuring the underlying quantumness of these devices is essential for assessing their readiness for practical applications and guiding future progress and research. Building on earlier work (Meirom, Mor, Weinstein Arxiv 2505.12441), we utilize a benchmarking strategy applicable for comparing these two architectures by measuring "quantumness" directly on optimal sub-chips. Distinct from existing metrics, our approach employs rigorous binary fidelity thresholds derived from the classical limits of state transfer. This enables us to definitively establish quantum advantage of a designated sub-region. Here we apply this quality assurance methodology to platforms from both technologies. This comparison provides a protocol-based evaluation of quantumness advantage, revealing not only the strengths and weaknesses of each tested chip and its sub-chips but also offering a common language for their assessment. By abstracting away technical differences in the final result, we demonstrate a benchmarking strategy that bridges the gap between disparate quantum-circuit technologies, enabling fair performance comparisons and establishing a critical foundation for evaluating future claims of quantum advantage. This work was made possible by policies of two companies who enable independent and objective assessment on their quantum computers and sub-chips. In the name of science, we encourage other companies to emulate the independent qubit availability and the fair pricing which allow researchers to preform such assessments.

Benchmarking quantum computers often deals with the parameters of single qubits or gates and sometimes deals with algorithms run on an entire chip or a noisy simulator of a chip. Here we propose the idea of using protocols to benchmark quantum computers. The advantage of using protocols, especially the seven suggested here, over other benchmarking methods is that there is a clear cutoff (i.e., a threshold) distinguishing quantumness from classicality for each of our protocols. The protocols we suggest enable a comparison among various circuit-based quantum computers, and also between real chips and their noisy simulators. This latter method may then be used to better understand the various types of noise of the real chips. We use some of these protocols to answer an important question: ``How many effective qubits are there in this N-qubit quantum computer/simulator?'', and we then conclude which effective sub-chips can be named ``truly-quantum''.

Ising formulation is important for many NP problems (Lucas, 2014). This formulation enables implementing novel quantum computing methods including Quantum Approximate Optimization Algorithm and Variational Quantum Eigensolver (VQE). Here, we investigate closely the traveling salesman problem (TSP). First, we present some non-trivial issues related to Ising model view versus a realistic salesman. Then, focusing on VQE we discuss and clarify the use of: a.– Conventional VQE and how it is relevant as a novel SAT-solver; b.– Qubit efficiency and its importance in the Noisy Intermediate Scale Quantum-era; and c.– the relevance and importance of a novel approach named Discrete Quantum Exhaustive Search (Alfassi, Meirom, and Mor, 2024), for enhancing VQE and other methods using mutually unbiased bases. The approach we present here in details can potentially be extended for analyzing approximating and solving various other NP complete problems. Our approach can also be extended beyond the Ising model and beyond the class NP, for example to the class Quantum Merlin Arthur (QMA) of problems, relevant for quantum chemistry and for general spin problems.

Practical implementations of Quantum Key Distribution (QKD) often deviate from the theoretical protocols, exposing the implementations to various attacks even when the underlying (ideal) protocol is proven secure. We present new analysis tools and methodologies for quantum cybersecurity, adapting the concepts of vulnerabilities, attack surfaces, and exploits from classical cybersecurity to QKD implementation attacks. We present three additional concepts, derived from the connection between classical and quantum cybersecurity: "Quantum Fuzzing", which is the first tool for black-box vulnerability research on QKD implementations; "Reversed-Space Attacks", which are a generic exploit method using the attack surface of imperfect receivers; and a concrete quantum-mechanical definition of "Quantum Side-Channel Attacks", meaningfully distinguishing them from other types of attacks. Using our tools, we analyze multiple existing QKD attacks and show that the "Bright Illumination" attack could have been fully constructed even with minimal knowledge of the device implementation. This work begins to bridge the gap between current analysis methods for experimental attacks on QKD implementations and the decades-long research in the field of classical cybersecurity, improving the practical security of QKD products and enhancing their usefulness in real-world systems.

Quantum computers promise a great computational advantage over classical computers, yet currently available quantum devices have only a limited amount of qubits and a high level of noise, limiting the size of problems that can be solved accurately with those devices. Variational Quantum Algorithms (VQAs) have emerged as a leading strategy to address these limitations by optimizing cost functions based on measurement results of shallow-depth circuits. However, the optimization process usually suffers from severe trainability issues as a result of the exponentially large search space, mainly local minima and barren plateaus. Here we propose a novel method that can improve variational quantum algorithms – “discretized quantum exhaustive search”. On classical computers, exhaustive search, also named brute force, solves small-size NP complete and NP hard problems. Exhaustive search and efficient partial exhaustive search help designing heuristics and exact algorithms for solving larger-size problems by finding easy subcases or good approximations. We adopt this method to the quantum domain, by relying on mutually unbiased bases for the 2^n-dimensional Hilbert space. We define a discretized quantum exhaustive search that works well for small size problems. We provide an example of an efficient partial discretized quantum exhaustive search for larger-size problems, in order to extend classical tools to the quantum computing domain, for near future and far future goals. Our method enables obtaining intuition on NP-complete and NP-hard problems as well as on Quantum Merlin Arthur (QMA)-complete and QMA-hard problems. We demonstrate our ideas in many simple cases, providing the energy landscape for various problems and presenting two types of energy curves via VQAs.

We present a complete classification of the geometry of the mutually complementary sets of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding the geometric structure of the pure product states in a given three-dimensional Hilbert subspace, which determines all the possible separable and entangled mixed states over the same subspace. In bipartite systems, we characterise the 14 possible qualitatively different geometric shapes for the set of separable states in any three-dimensional Hilbert subspace (5 classes which also appear in two-dimensional subspaces and were found and analysed by Boyer et al. (Phys Rev A 95:032308, 2017. https://doi.org/10.1103/PhysRevA.95.032308 ), and 9 novel classes which appear only in three-dimensional subspaces), describe their geometries, and provide figures illustrating them. We also generalise these results to characterise the sets of fully separable states (and hence the complementary sets of somewhat entangled states) in three-dimensional subspaces of multipartite systems. Our results show which geometrical forms quantum entanglement can and cannot take in low-dimensional subspaces.

Quantum entanglement is a fascinating topic with both theoretical and technological impacts. Yet, even in the simplest scenarios, there are still various open questions involving pure state and mixed state entanglement. Here we present the simplest entangled mixed states. We consider both qubits (quantum bits) and qudits (quantum digits). We first provide our simplest yet most important result for rank-2 bi-partite states, and we then generalize our results to go beyond rank-2 and to go beyond bi-partite states.

Quantum key distribution (QKD) protocols make it possible for two parties to generate a secret shared key. One of the most important QKD protocols, BB84, was suggested by Bennett and Brassard in 1984. Various proofs of unconditional security for BB84 have been suggested, but the first security proofs were not composable. Here we improve a security proof of BB84 given by [Biham, Boyer, Boykin, Mor, and Roychowdhury, J. Cryptology, 19(4):381-439, 2006] to be composable and match the state-of-the-art results for BB84, and we extend it to prove unconditional security of several variants of the BB84 protocol. Our composable security proof for BB84 and its variants is mostly self-contained, algebraic, and relatively simple, and it gives tight finite-key bounds.

State preparation and measurement errors are commonly regarded as indistinguishable. The problem of distinguishing state preparation (SPAM) errors from measurement errors is important to the field of characterizing quantum processors. In this work, we propose a method to separately characterize SPAM errors using a novel type of algorithmic cooling protocol called measurement-based algorithmic cooling (MBAC). MBAC assumes the ability to perform (potentially imperfect) projective measurements on individual qubits, which is available on many modern quantum processors. We demonstrate that MBAC can significantly reduce state preparation error under realistic assumptions, with a small overhead that can be upper bounded by measurable quantities. Thus, MBAC can be a valuable tool not only for benchmarking near-term quantum processors, but also for improving the performance of quantum processors in an algorithmic manner.

Quantum candies (qandies) represent a type of pedagogical simple model that describes many concepts from quantum information processing (QIP) intuitively without the need to understand or make use of superpositions and without the need of using complex algebra. One of the topics in quantum cryptography that has gained research attention in recent years is quantum digital signatures (QDS), which involve protocols to securely sign classical bits using quantum methods. In this paper, we show how the “qandy model” can be used to describe three QDS protocols in order to provide an important and potentially practical example of the power of “superpositionless” quantum information processing for individuals without background knowledge in the field.

The field of quantum information is becoming more known to the general public. However, effectively demonstrating the concepts underneath quantum science and technology to the general public can be a challenging job. We investigate, extend, and greatly expand here "quantum candies" (invented by Jacobs), a pedagogical model for intuitively describing some basic concepts in quantum information, including quantum bits, complementarity, the no-cloning principle, and entanglement. Following Jacob's quantum candies description of the well-known quantum key distribution protocol BB84, we explicitly demonstrate additional quantum cryptography protocols and quantum communication protocols, using generalized quantum candies (including correlated pairs of qandies). These demonstrations are done in an approachable manner, that can be explained to high-school students, without using the hard-to-grasp concept of superpositions and its mathematics. The intuitive model we investigate has a fascinating overlap with some of the most basic features of quantum theory. Hence, it can be a valuable tool for science and engineering educators who would like to help the general public to gain more insights into quantum science and technology. For the experts, the model we present, due to not employing quantum superpositions, enables - in some sense - extending far beyond quantum theory. Most remarkably, "quantum" candies of some unique type can be defined, such that non-local boxes (of the Popescu-Rohrlich type) as well as regular (correlated) quantum candies can be generated by a single `"quantum" candies machine.

The field of information is becoming more known to the general public. However, effectively demonstrating the concepts underneath science and technology to the general public can be a challenging job. We investigate, extend, and much expand here quantum (invented by Jacobs), a pedagogical model for intuitively describing some basic concepts in information, including bits, complementarity, the no-cloning principle, and entanglement. Following Jacob's candies description of the well-known key distribution protocol BB84, we explicitly demonstrate various additional cryptography protocols using candies in an approachable manner. The model we investigate can be a valuable tool for science and engineering educators who would like to help the general public to gain more insights into science and technology: most parts of this paper, including many protocols for cryptography, are expected to be easily understandable by a layperson without any previous knowledge of mathematics, physics, or cryptography.

Finding the ground state energy of the Heisenberg Hamiltonian is an important problem in the field of condensed matter physics. In some configurations, such as the antiferromagnetic translationally-invariant case on the 2D square lattice, its exact ground state energy is still unknown. We show that finding the ground state energy of the Heisenberg model cannot be an NP-Hard problem unless P=NP. We prove this result using a reduction to a sparse set and certain theorems from computational complexity theory. The result hints at the potential tractability of the problem and encourages further research towards a positive complexity result. In addition, we prove similar results for many similarly structured Hamiltonian problems, including certain forms of the Ising, t-J, and Fermi-Hubbard models.

Quantum Cryptography uses the counter-intuitive properties of Quantum Mechanics for performing cryptographic tasks in a secure and reliable way. The Quantum Key Distribution (QKD) protocol BB84 has been proven secure against several important types of attacks: collective attacks and joint attacks. Here we analyze the security of a modified BB84 protocol, for which information is sent only in the z basis while testing is done in both the z and the x bases, against collective attacks. The proof follows the framework of a previous paper [1], but it avoids a classical information-theoretical analysis and proves a fully composable security. We show that this modified BB84 protocol is as secure against collective attacks as the original BB84 protocol, and that it requires more bits for testing.

The “Bright Illumination” attack [Lydersen et al., Nat. Photon. 4, 686–689 (2010)] is a practical attack, fully implementable against quantum key distribution systems. In contrast to almost all developments in quantum information processing (for example, Shor’s factorization algorithm, quantum teleportation, Bennett-Brassard (BB84) quantum key distribution, the “Photon-Number Splitting” attack, and many other examples), for which theory has been proposed decades before a proper implementation, the “Bright Illumination” attack preceded any sign or hint of a theoretical prediction. Here we explain how the “Reversed-Space” methodology of attacks, complementary to the notion of “quantum side-channel attacks” (which is analogous to a similar term in “classical”—namely, non-quantum—computer security), has missed the opportunity of predicting the “Bright Illumination” attack.

This is an editorial paper presenting the meaning, history, and influence of quantum teleportation.

A Bloch sphere is the geometrical representation of an arbitrary two-dimensional Hilbert space. Possible classes of entanglement and separability for the pure and mixed states on the Bloch sphere were suggested by [Boyer et al 2017 PRA 95 032 308]. Here we construct a Bloch sphere for the Hilbert space spanned by one of the ground states of Kitaev’s toric code model and one of its closest product states. We prove that this sphere contains only one separable state, thus belonging to the fourth class suggested by the said paper. We furthermore study the topological order of the pure states on its surface and conclude that, according to conventional definitions, only one state (the toric code ground state) seems to present non-trivial topological order. We conjecture that most of the states on this Bloch sphere are neither ‘trivial’ states (namely, they cannot be generated from a product state using a trivial circuit) nor topologically ordered. In addition, we show that the whole setting can be understood in terms of Grover rotations with gauge symmetry, akin to the quantum search algorithm.

The field of quantum information is becoming more known to the general public. However, effectively demonstrating the concepts underneath quantum science and technology to the general public can be a challenging job. We investigate, extend, and much expand here “quantum candies” (invented by Jacobs), a pedagogical model for intuitively describing some basic concepts in quantum information, including quantum bits, complementarity, the no-cloning principle, and entanglement. Following Jacob’s quantum candies description of the well known quantum key distribution protocol BB84, we explicitly demonstrate various additional quantum cryptography protocols using quantum candies in an approachable manner. The model we investigate can be a valuable tool for science and engineering educators who would like to help the general public to gain more insights about quantum science and technology: most parts of this paper, including many protocols for quantum cryptography, are expected to be easily understandable by a layperson without any previous knowledge of mathematics, physics, or cryptography.