Quantum communication relies on the existence of entanglement between two nodes of a network. However, due to its fragile nature, it is nearly impossible to establish entanglement at large distances through the direct transmission of qubits. Quantum repeaters have been proposed to solve this problem, which split-up the network to create small-scale entangled links and then connect them up to create the large-scale link. As researchers race to establish entanglement over larger and larger distances, it becomes essential to gauge the performance and robustness of the different protocols that have been proposed to design a quantum repeater, before deploying them in real life. Currently available noisy quantum computers are ideal for this task, as they can emulate the noisy environment in a quantum communication channel, and provide a measure for how the protocols will perform on real-life hardware. In this paper, we report the circuit-level implementation of the complete architecture of a quantum repeater, and benchmark this protocol on IBM's cloud quantum computer - IBMQ. Our experiments indicate a 26% fidelity of shared bell-pairs for a complete on-chip quantum repeater with a yield of 49%. We also compare these results with simulation data from IBM Qiskit. The results of our experiments provide a quantitative measure for the fidelity of entanglement that currently available repeaters can establish. In addition, the proposed circuit-implementation provides a robust benchmark for state-of-the-art quantum computing hardware.
Quantum communication is a secure way to transfer quantum information and to communicate with legitimate parties over distant places in a network. Although communication over a long distance has already been attained, technical problem arises due to unavoidable loss of information through the transmission channel. Quantum repeaters can extend the distance scale using entanglement swapping and purification scheme. Here we demonstrate the working of a quantum repeater by the above two processes. We use IBM's real quantum processor `ibmqx4' to create two pair of entangled qubits and design an equ…
Quantum computers have the potential to outperform classical computers in a range of computational tasks, such as prime factorisation and unstructured searching. However, real-world quantum computers are subject to noise. Quantifying noise is of vital importance, since it is often the dominant factor preventing the successful realisation of advanced quantum computations. Here we propose and demonstrate an interleaved randomised benchmarking protocol for measurement-based quantum computers that can be used to estimate the fidelity of any single-qubit measurement-based gate. We tested the protoc…
A potential quantum internet would open up the possibility of realizing numerous new applications, including provably secure communication. Since losses of photons limit long-distance, direct quantum communication and widespread quantum networks, quantum repeaters are needed. The so-called PLOB-repeaterless bound [Pirandola et al., Nat. Commun. 8, 15043 (2017)] is a fundamental limit on the quantum capacity of direct quantum communication. Here, we analytically derive the quantum-repeater gain for error-corrected, one-way quantum repeaters based on higher-dimensional qudits for two different p…
We report the observation and characterisation of a systematic error in the implementation of $U_3$ gates in the IBM quantum computers. The error appears as a consistent shift in one of the angles of the gate, whose magnitude does not correlate with IBM's cited errors calculated using Clifford randomized benchmarking. We propose a simple mitigation procedure, leading to an improvement in the observed value for the CHSH inequality, highlighting the utility of simple mitigation strategies for short-depth quantum circuits.
QPU-scale randomized benchmarking via Bell-pair injection
Moth, Switzerland（Moth）；Center for Quantum Computing and Quantum Coherence (QC2), University of Basel, Switzerland（巴塞尔大学量子计算与量子相干中心（QC2））；Moth, United Kingdom（Moth）；ICCMR, University of Plymouth, United Kingdom（普利茅斯大学ICCMR）
We propose a post-selection technique, based on quantum error detection, for quantum key distribution (QKD) systems that run over quantum repeaters with encoding. In such repeaters, quantum error correction techniques are used for entanglement distillation. By developing an analytical approach to study such quantum repeaters, we show that, in the context of QKD, it is often more efficient to use the error detection, rather than the error correction, capability of the underlying code to sift out cases where an error has been detected. We implement our technique for three-qubit repetition codes …
It is hard to achieve a theoretical quantum advantage on NISQ devices. Besides the attempts to reduce error using error mitigation and dynamical decoupling, small quantum error correction and fault-tolerant schemes that reduce the high overhead of traditional schemes have also been proposed. According to the recent advancements in fault tolerance, it is possible to minimize the number of ancillary qubits using flags. While implementing those schemes is still impossible, it is worthwhile to bridge the gap between the NISQ era and the FTQC era. Here, we introduce a benchmarking method to test fa…
Now that ever more sophisticated devices for quantum computing are being developed, we require ever more sophisticated benchmarks. This includes a need to determine how well these devices support the techniques required for quantum error correction. In this paper we introduce the \texttt{topological\_codes} module of Qiskit-Ignis, which is designed to provide the tools necessary to perform such tests. Specifically, we use the \texttt{RepetitionCode} and \texttt{GraphDecoder} classes to run tests based on the repetition code and process the results. As an example, data from a 43 qubit code runn…
Quantum communication devices, such as quantum repeaters, quantum memories, or quantum channels, are unavoidably exposed to imperfections. However, the presence of imperfections can be tolerated, as long as we can verify such devices retain their quantum advantages. Benchmarks based on witnessing entanglement have proven useful for verifying the true quantum nature of these devices. The next challenge is to characterize how strongly a device is within the quantum domain. We present a method, based on entanglement measures and rigorous state truncation, which allows us to characterize the degre…
Quantum processors with sizes in the 10-100 qubit range are now increasingly common. However, with increased size comes increased complexity for benchmarking. The effectiveness of a given device may vary greatly between different tasks, and will not always be easy to predict from single and two qubit gate fidelities. For this reason, it is important to assess processor quality for a range of important tasks. In this work we propose and implement tests based on random quantum circuits. These are used to evaluate multiple different superconducting qubit devices, with sizes from 5 to 19 qubits, f…
Distilling precise estimates from noisy intermediate scale quantum (NISQ) data has recently attracted considerable attention. In order to augment digital qubit metrics, such as gate fidelity, we discuss analog error mitigability, i.e. the ability to accurately distill precise observable estimates, as a hybrid quantum-classical computing benchmarking task. Specifically, we characterize single qubit error rates on IBM's Poughkeepsie superconducting quantum hardware, incorporate control-mediated noise dependence into a generalized rescaling protocol, and analyze how noise characteristics influenc…
We present a framework that utilizes quantum algorithms, an architecture aware quantum noise model and an ideal simulator to benchmark quantum computers. The benchmark metrics highlight the difference between the quantum computer evolution and the simulated noisy and ideal quantum evolutions. We utilize our framework for benchmarking three IBMQ systems. The use of multiple algorithms, including continuous-time ones, as benchmarks stresses the computers in different ways highlighting their behaviour for a diverse set of circuits. The complexity of each quantum circuit affects the efficiency of …
Quantum computers will require encoding of quantum information to protect them from noise. Fault-tolerant quantum computing architectures illustrate how this might be done but have not yet shown a conclusive practical advantage. Here we demonstrate that a small but useful error detecting code improves the fidelity of the fault-tolerant gates implemented in the code space as compared to the fidelity of physically equivalent gates implemented on physical qubits. By running a randomized benchmarking protocol in the logical code space of the [4,2,2] code, we observe an order of magnitude improveme…
The performance of the quantum approximate optimization algorithm is evaluated by using three different measures: the probability of finding the ground state, the energy expectation value, and a ratio closely related to the approximation ratio. The set of problem instances studied consists of weighted MaxCut problems and 2-satisfiability problems. The Ising model representations of the latter possess unique ground states and highly-degenerate first excited states. The quantum approximate optimization algorithm is executed on quantum computer simulators and on the IBM Q Experience. Additionally…
The increasing scale of near-term quantum hardware motivates the need for efficient noise characterization methods, since qubit and gate level techniques cannot capture crosstalk and correlated noise in many qubit systems. While scalable approaches, such as cycle benchmarking, are known for special classes of quantum circuits, the characterization of noise in general circuits with non-Clifford gates has been an unreachable task. We develop an algorithm that can sample-efficiently estimate the total amount of noise induced by a layer of arbitrary non-Clifford gates, including all crosstalks, an…
With the advent of public access to small gate-based quantum processors, it becomes necessary to develop a benchmarking methodology such that independent researchers can validate the operation of these processors. We explore the usefulness of a number of simple quantum circuits as benchmarks for gate-based quantum computing devices and show that circuits performing identity operations are very simple, scalable and sensitive to gate errors and are therefore very well suited for this task. We illustrate the procedure by presenting benchmark results for the IBM Quantum Experience, a cloud-based p…
Quantum computing systems need to be benchmarked in terms of practical tasks they would be expected to do. Here, we propose 3 "application-motivated" circuit classes for benchmarking: deep (relevant for state preparation in the variational quantum eigensolver algorithm), shallow (inspired by IQP-type circuits that might be useful for near-term quantum machine learning), and square (inspired by the quantum volume benchmark). We quantify the performance of a quantum computing system in running circuits from these classes using several figures of merit, all of which require exponential classical …
Non-Clifford Benchmarking via Ensemble Feature Selection
St Kliment Ohridski University of Sofia（圣克利门特·奥赫里德斯基索菲亚大学）；Center for Quantum Technologies, St Kliment Ohridski University of Sofia（圣克利门特·奥赫里德斯基索菲亚大学量子技术中心）
Hardware efficient transpilation of quantum circuits to a quantum devices native gateset is essential for the execution of quantum algorithms on noisy quantum computers. Typical quantum devices utilize a gateset with a single two-qubit Clifford entangling gate per pair of coupled qubits, however, in some applications access to a non-Clifford two-qubit gate can result in more optimal circuit decompositions and also allows more flexibility in optimizing over noise. We demonstrate calibration of a low error non-Clifford Controlled-$\fracπ{2}$ phase (CS) gate on a cloud based IBM Quantum computing…
Quantum memory -- the capacity to store and faithfully recover unknown quantum states -- is essential for quantum-enhanced technology. There is thus a pressing need for operationally meaningful means to benchmark candidate memories across diverse physical platforms. Here we introduce a universal benchmark distinguished by its relevance across multiple key operational settings, exactly quantifying (1) the memory's robustness to noise, (2) the number of noiseless qubits needed for its synthesis, (3) its potential to speed up statistical sampling tasks, and (4) performance advantage in non-local …
We present experimental results on running 4-qubit unstructured search on IBM quantum processors. Our best attempt attained probability of success around 24.5%. We try several algorithms and use the most recent developments in quantum search to reduce the number of entangling gates that are currently considered the main source of errors in quantum computations. Comparing theoretical expectations of an algorithm performance with the actual data, we explore the hardware limits, showing sharp, phase-transition-like degradation of performance on quantum processors. We conclude that it is extremely…
The first generation of small noisy quantum processors have recently become available to non-specialists who are not required to understand specifics of the physical platforms and, in particular, the types and sources of noise. As such, it is useful to benchmark the performance of such computers against specific tasks that may be of interest to users, ideally keeping both the circuit depth and width as free parameters. Here we benchmark the IBM Quantum Experience using the Deterministic Quantum Computing with 1 qubit (DQC1) algorithm originally proposed by Knill and Laflamme in the context of …
Recently, a quantum algorithm for a fundamentally important task in data mining, association rules mining (ARM), called qARM for short, has been proposed. Notably, qARM achieves significant speedup over its classical counterpart for implementing the main task of ARM, i.e., finding frequent itemsets from a transaction database. In this paper, we experimentally implement qARM on both real quantum computers and a quantum computing simulator via the IBM quantum computing platform. In the first place, we design quantum circuits of qARM for a 2$\times$2 transaction database (i.e., a transaction data…
Quantum state transfer (QST) provides a method to send arbitrary quantum states from one system to another. Such a concept is crucial for transmitting quantum information into the quantum memory, quantum processor, and quantum network. The standard benchmark of QST is the average fidelity between the prepared and received states. In this work, we provide a new benchmark which reveals the non-classicality of QST based on spatio-temporal steering (STS). More specifically, we show that the local-hidden-state (LHS) model in STS can be viewed as the classical strategy of state transfer. Therefore, …
Experimental demonstration of scalable cross-entropy benchmarking to detect measurement-induced phase transitions on a superconducting quantum processor
This paper presents the benchmark score definitions of QPack, an application-oriented cross-platform benchmarking suite for quantum computers and simulators, which makes use of scalable Quantum Approximate Optimization Algorithm and Variational Quantum Eigensolver applications. Using a varied set of benchmark applications, an insight of how well a quantum computer or its simulator performs on a general NISQ-era application can be quantitatively made. This paper presents what quantum execution data can be collected and transformed into benchmark scores for application-oriented quantum benchmark…
We use a massively parallel simulator of a universal quantum computer to benchmark some of the most powerful supercomputers in the world. We find nearly ideal scaling behavior on the Sunway TaihuLight, the K computer, the IBM BlueGene/Q JUQUEEN, and the Intel Xeon based clusters JURECA and JUWELS. On the Sunway TaihuLight and the K computer, universal quantum computers with up to 48 qubits can be simulated by means of an adaptive two-byte encoding to reduce the memory requirements by a factor of eight. Additionally, we discuss an alternative approach to alleviate the memory bottleneck by decom…
Recently, several quantum benchmarking algorithms have been developed to characterize noisy quantum gates on today's quantum devices. A well-known issue in benchmarking is that not everything about quantum noise is learnable due to the existence of gauge freedom, leaving open the question of what information about noise is learnable and what is not, which has been unclear even for a single CNOT gate. Here we give a precise characterization of the learnability of Pauli noise channels attached to Clifford gates, showing that learnable information corresponds to the cycle space of the pattern tra…
Hybrid quantum-classical algorithms provide ways to use noisy intermediate-scale quantum computers for practical applications. Expanding the portfolio of such techniques, we propose a quantum circuit learning algorithm that can be used to assist the characterization of quantum devices and to train shallow circuits for generative tasks. The procedure leverages quantum hardware capabilities to its fullest extent by using native gates and their qubit connectivity. We demonstrate that our approach can learn an optimal preparation of the Greenberger-Horne-Zeilinger states, also known as "cat states…
Benchmarking methods that can be adapted to multi-qubit systems are essential for assessing the overall or "holistic" performance of nascent quantum processors. The current industry standard is Clifford randomized benchmarking (RB), which measures a single error rate that quantifies overall performance. But scaling Clifford RB to many qubits is surprisingly hard. It has only been performed on 1, 2, and 3 qubits as of this writing. This reflects a fundamental inefficiency in Clifford RB: the $n$-qubit Clifford gates at its core have to be compiled into large circuits over the 1- and 2-qubit gat…
