Blockchain is a distributed database which is cryptographically protected against malicious modifications. While promising for a wide range of applications, current blockchain platforms rely on digital signatures, which are vulnerable to attacks by means of quantum computers. The same, albeit to a lesser extent, applies to cryptographic hash functions that are used in preparing new blocks, so parties with access to quantum computation would have unfair advantage in procuring mining rewards. Here we propose a possible solution to the quantum-era blockchain challenge and report an experimental realization of a quantum-safe blockchain platform that utilizes quantum key distribution across an urban fiber network for information-theoretically secure authentication. These results address important questions about realizability and scalability of quantum-safe blockchains for commercial and governmental applications.

No abstract

rebooted brain research p.474 MUSIC Celebrating the female pioneers of electronica p.470 SPACE Rock legend Brian May retells the race to the Moon-in 3D p.469 CONSERVATION The people and places that invented the word 'environment' p.468 Quantum computers put blockchain security at risk Bitcoin and other cryptocurrencies will founder unless they integrate quantum technologies, warn Aleksey K. Fedorov, Evgeniy O. Kiktenko and Alexander I. Lvovsky. B y 2025, up to 10% of global gross domestic product is likely to be stored on blockchains 1. A blockchain is a digital tool that uses cryptography techniques to protect information from unauthorized changes. It lies at the root of the Bitcoin cryptocurrency 2. Blockchain-related products are used everywhere from finance and manufacturing to health care, in a market worth more than US$150 billion. When information is money, data security, transparency and accountability are crucial. Quantum cryptography equipment, which uses the principle of entanglement to encode data that only the sender and receiver can access.

Quantum key distribution (QKD) is a quantum-proof key exchange scheme which is fast approaching the communication industry. An essential component in QKD is the information reconciliation step, which is used for correcting the quantum channel noise errors. The recently suggested blind reconciliation technique, based on low-density parity-check (LDPC) codes, offers remarkable prospectives for efficient information reconciliation without an a priori error rate estimation. In the present work, we suggest an improvement of the blind information reconciliation protocol allowing significant increase the efficiency of the procedure and reducing its interactivity. The proposed technique is based on introducing symmetry in operations of parties, and the consideration of results of unsuccessful belief propagation decodings.

We present algorithmic solutions aimed on post-processing for industrial quantum key distribution systems with hardware sifting. The main steps of the procedure are error correction, parameter estimation, and privacy amplification. Authentication of a classical public communication channel is also considered.

Complete characterization of states and processes that occur within quantum devices is crucial for understanding and testing their potential to outperform classical technologies for communications and computing. However, solving this task with current state-of-the-art techniques becomes unwieldy for large and complex quantum systems. Here we realize and experimentally demonstrate a method for complete characterization of a quantum harmonic oscillator based on an artificial neural network known as the restricted Boltzmann machine. We apply the method to optical homodyne tomography and show it to allow full estimation of quantum states based on a smaller amount of experimental data compared to state-of-the-art methods. We link this advantage to reduced overfitting. Although our experiment is in the optical domain, our method provides a way of exploring quantum resources in a broad class of large-scale physical systems, such as superconducting circuits, atomic and molecular ensembles, and optomechanical systems.

We theoretically study operations with a four-level superconducting circuit as a two-qubit system. Using a mapping on a two-qubit system, we show how to implement iSWAP gates and Hadamard gates through pulses on transitions between particular pairs of energy levels. Our approach allows one to prepare pure two-qubit entangled states with desired form of reduced density matrices of the same purity and, in particular, arbitrary identical reduced states of qubits. We propose using schemes for the Hadamard gate and two-qubit entangled states with identical reduced density matrices in order to verify log N inequalities for Shannon and Rényi entropies for the considered noncomposite quantum system.

We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality of qudits and their topology of connections for a scalable multi-qudit processor, where higher qudit levels are used for substituting ancillas. The suggested model is of importance for the realization of quantum algorithms and as a method of quantum error correction codes for single-qubit operations.Introduction.-Remarkable progress in realizing controllable quantum systems of an intermediate scale [1][2][3][4][5] makes it realistic to study properties of strongly correlated quantum matter [6-9] and to implement various quantum algorithms [10][11][12][13][14]. However, existing quantum computing systems lack either coherence or controllable interactions between qubits, and this limits their capabilities. A serious obstacle in realizing quantum algorithms is a large number of two-qubit gates, which requires programmable inter-qubit interactions and can cause decoherence. The situation becomes even more challenging in the case of mulit-qubit gates, such as an N -qubit Toffoli gate, which is a basic building block for quantum algorithms like Shor's algorithm [15] and for quantum error corrections schemes [16][17][18]. Its implementation requires 12N − 23 two-qubit gates with N − 2 ancilla qubits or O(N 2 ) gates without them [19], which is of high cost for near-term noisy intermediate-scale quantum devices. Therefore, the reduction of the number of operations that are required for the realization of multi-qubit gates remains a crucial problem.One of possible ways to reduce the number of required operations is to use additional degrees of freedom of quantum systems. This idea has stimulated an extended activity [20,21] in theoretical [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] and experimental studies [39][40][41][42][43][44][45][46] of quantum computing models with qudits, which are d-dimensional (d > 2) quantum systems. In particular, qudits can be used for substituting ancillas [30,[37][38][39], which allows the reduction of the required number of interactions between information carriers for the realization of multi-qubit gates. In experiments with photonic quantum circuits [39], for a system of an Ndimensional qudit connected with N − 1 qubits, the Nqubit Toffoli gate was realized with 2N − 3 qubit-qudit gates. However, it is hard to expect scalability for such