There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of quantum supremacy with fifty qubits is anticipated in just a few years. Quantum supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software development and experimentation, even via web interfaces. Therefore, the time is ripe for describing some of the recent development of superconducting devices, systems and applications. As such, the discussion of superconducting qubits and circuits is limited to devices that are proven useful for current or near future applications. Consequently, the centre of interest is the practical applications of QIP, such as computation and simulation in Physics and Chemistry.

https://iopscience.iop.org/article/10.1088/1361-6633/aa7e1a/pdf

Quantum information processing with superconducting circuits: a review

A critical question for the field of quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of state-of-the-art classical computers, achieving so-called quantum supremacy. We study the task of sampling from the output distributions of (pseudo-)random quantum circuits, a natural task for benchmarking quantum computers. Crucially, sampling this distribution classically requires a direct numerical simulation of the circuit, with computational cost exponential in the number of qubits. This requirement is typical of chaotic systems. We extend previous results in computational complexity to argue more formally that this sampling task must take exponential time in a classical computer. We study the convergence to the chaotic regime using extensive supercomputer simulations, modeling circuits with up to 42 qubits - the largest quantum circuits simulated to date for a computational task that approaches quantum supremacy. We argue that while chaotic states are extremely sensitive to errors, quantum supremacy can be achieved in the near-term with approximately fifty superconducting qubits. We introduce cross entropy as a useful benchmark of quantum circuits which approximates the circuit fidelity. We show that the cross entropy can be efficiently measured when circuit simulations are available. Beyond the classically tractable regime, the cross entropy can be extrapolated and compared with theoretical estimates of circuit fidelity to define a practical quantum supremacy test.

Characterizing Quantum Supremacy in Near-Term Devices

The field of quantum algorithms aims to find ways to speed up the solution of computational problems by using a quantum computer. A key milestone in this field will be when a universal quantum computer performs a computational task that is beyond the capability of any classical computer, an event known as quantum supremacy. This would be easier to achieve experimentally than full-scale quantum computing, but involves new theoretical challenges. Here we present the leading proposals to achieve quantum supremacy, and discuss how we can reliably compare the power of a classical computer to the power of a quantum computer. Proposals for demonstrating quantum supremacy, when a quantum computer supersedes any possible classical computer at a specific task, are reviewed.

/pdf/quantum-computational-supremacy-44xs7qgoko.pdf

Quantum computational supremacy

We introduce a simple protocol for verifiable measurement-only blind quantum computing. Alice, a client, can perform only single-qubit measurements, whereas Bob, a server, can generate and store entangled many-qubit states. Bob generates copies of a graph state, which is a universal resource state for measurement-based quantum computing, and sends Alice each qubit of them one by one. Alice adaptively measures each qubit according to her program. If Bob is honest, he generates the correct graph state, and, therefore, Alice can obtain the correct computation result. Regarding the security, whatever Bob does, Bob cannot get any information about Alice's computation because of the no-signaling principle. Furthermore, malicious Bob does not necessarily send the copies of the correct graph state, but Alice can check the correctness of Bob's state by directly verifying the stabilizers of some copies.

Verifiable Measurement-Only Blind Quantum Computing with Stabilizer Testing

Blind quantum computation is a new secure quantum computing protocol which enables Alice (who does not have sufficient quantum technology) to delegate her quantum computation to Bob (who has a full-fledged quantum computer) in such a way that Bob cannot learn anything about Alice's input, output, and algorithm. In previous protocols, Alice needs to have a device which generates quantum states, such as single-photon states. Here we propose another type of blind computing protocol where Alice does only measurements, such as the polarization measurements with a threshold detector. In several experimental setups, such as optical systems, the measurement of a state is much easier than the generation of a single-qubit state. Therefore our protocols ease Alice's burden. Furthermore, the security of our protocol is based on the no-signaling principle, which is more fundamental than quantum physics. Finally, our protocols are device independent in the sense that Alice does not need to trust her measurement device in order to guarantee the security.

Blind quantum computation protocol in which Alice only makes measurements

Deterministic quantum computation with one quantum bit (DQC1) [E. Knill and R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998)] is a model of quantum computing where the input is restricted to containing a single qubit in a pure state and has all other qubits in a completely mixed state. Only the single pure qubit is measured at the end of the computation. While it is known that DQC1 can efficiently solve several problems for which no known classical efficient algorithms exist, the question of whether DQC1 is really more powerful than classical computation remains open. In this Letter, we introduce a slightly modified version of DQC1, which we call $\mathrm{DQC}{1}_{k}$, where $k$ output qubits are measured, and show that $\mathrm{DQC}{1}_{k}$ cannot be classically efficiently simulated for any $k\ensuremath{\ge}3$ unless the polynomial hierarchy collapses at the third level.

Hardness of classically simulating the one-clean-qubit model.

Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum computation to Bob, who has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice's input, output and algorithm. A recent proof-of-principle experiment demonstrating blind quantum computation in an optical system has raised new challenges regarding the scalability of blind quantum computation in realistic noisy conditions. Here we show that fault-tolerant blind quantum computation is possible in a topologically protected manner using the Raussendorf–Harrington–Goyal scheme. The error threshold of our scheme is 4.3×10−3, which is comparable to that (7.5×10−3) of non-blind topological quantum computation. As the error per gate of the order 10−3 was already achieved in some experimental systems, our result implies that secure cloud quantum computation is within reach. Blind quantum computation is a protocol that permits an algorithm, its input and output to be kept secret from the owner of the computational resource doing the calculation. Morimae and Fujii propose a strategy for topologically protected fault-tolerant blind quantum computation that is robust to environmental noise.

/pdf/blind-topological-measurement-based-quantum-computation-2b1zsqcctm.pdf

Blind topological measurement-based quantum computation.

We propose a set of protocols for verifying quantum computing at any time after the computation itself has been performed. We provide two constructions: one requires five entangled provers and a completely classical verifier; the other requires a single prover, a verifier, who is restricted to measuring qubits in the $X$ or $Z$ basis, and one-way quantum communication from the prover to the verifier. These results demonstrate that the verification can be achieved independently from the blindness. We also show that a constant round protocol with a single prover and a completely classical verifier is not possible, unless bounded error quantum polynomial time (BQP) is contained in the third level of the polynomial hierarchy.

Tomoyuki Morimae

Papers

Verifiable Measurement-Only Blind Quantum Computing with Stabilizer Testing

Blind quantum computation protocol in which Alice only makes measurements

Hardness of classically simulating the one-clean-qubit model.

Blind topological measurement-based quantum computation.

Post hoc Verification of Quantum Computation.