Realistic physical implementations of quantum computers can entail tradeoffs which depart from the ideal model of quantum computation. Although these tradeoffs have allowed successful demonstration of certain quantum algorithms, a crucial question is whether they fundamentally limit the computational capacity of such machines. We study the limitations of a quantum computation model in which only ensemble averages of measurement observables are accessible. Furthermore, we stipulate that input qubits may only be prepared in highly random, ``hot'' mixed states. In general, these limitations are believed to dramatically detract from the computational power of the system. However, we construct a class of algorithms for this limited model, which, surprisingly, are polynomially equivalent to the ideal case. This class includes the well known Deutsch-Jozsa algorithm.
Localized electronic and nuclear spin qubits in the solid state constitute a promising platform for storage and manipulation of quantum information, even at room temperature. However, the development of scalable systems requires the ability to entangle distant spins, which remains a challenge today. We propose and analyze an efficient, heralded scheme that employs a parity measurement in a decoherence free subspace to enable fast and robust entanglement generation between distant spin qubits mediated by a hot mechanical oscillator. We find that high-fidelity entanglement at cryogenic and even …
A measurement-based quantum feedback protocol is developed for spin state initialization in a gate-defined double quantum dot spin qubit coupled to a superconducting resonator. The protocol improves qubit state initialization as it is able to robustly prepare the spin in shorter time and reach a higher fidelity, which can be pre-set. Being able to pre-set the fidelity aimed at is a highly desired feature enabling qubit initialization to be more deterministic. The protocol developed herein is also effective at high temperatures, which is critical for the current efforts towards scaling up the n…
The theoretical method to study strong coupling between an ensemble of quantum emitters (QEs) and surface plasmons excited by the nanoparticle cluster has been presented by using a rigorous first-principles electromagnetic Green's tensor technique. We have demonstrated that multi-qubit entanglement for two-level QEs can be produced at different frequencies simultaneously, when they locate in hot spots of metallic nanoparticle clusters. The duration of quantum beats for such an entanglement can reach two orders longer than that for the entanglement in a photonic cavity. The phenomenon originate…
Quantum computation requires many qubits that can be coherently controlled and coupled to each other. Qubits that are defined using lithographic techniques are often argued to be promising platforms for scalability, since they can be implemented using semiconductor fabrication technology. However, leading solid-state approaches function only at temperatures below 100 mK, where cooling power is extremely limited, and this severely impacts the perspective for practical quantum computation. Recent works on spins in silicon have shown steps towards a platform that can be operated at higher tempera…
Semiconductor spins are one of the few qubit realizations that remain a serious candidate for the implementation of large-scale quantum circuits. Excellent scalability is often argued for spin qubits defined by lithography and controlled via electrical signals, based on the success of conventional semiconductor integrated circuits. However, the wiring and interconnect requirements for quantum circuits are completely different from those for classical circuits, as individual DC, pulsed and in some cases microwave control signals need to be routed from external sources to every qubit. This is fu…
Solving the traveling salesman problem on $\lceil \log_2 (N-1)! \rceil$ qubits with a variational quantum Kolmogorov--Arnold network: exact-gradient CVaR training and generalization over time-dependent graphs
We develop a valley-dependent envelope function theory that can describe the effects of arbitrary configurations of interface steps and miscuts on the qubit relaxation time. For a given interface roughness, we show how our theory can be used to find the valley-dependent dipole matrix elements, the valley splitting, and the spin-valley coupling as a function of the electromagnetic fields in a Si/SiGe quantum dot spin qubit. We demonstrate that our theory can quantitatively reproduce and explain the result of experimental measurements for the spin relaxation time with only a minimal set of free …
Non-equilibrium quasiparticle excitations degrade the performance of a variety of superconducting circuits. Understanding the energy distribution of these quasiparticles will yield insight into their generation mechanisms, the limitations they impose on superconducting devices, and how to efficiently mitigate quasiparticle-induced qubit decoherence. To probe this energy distribution, we systematically correlate qubit relaxation and excitation with charge-parity switches in an offset-charge-sensitive transmon qubit, and find that quasiparticle-induced excitation events are the dominant mechanis…
We answer an open question about Quantum Key Recycling (QKR): Is it possible to put the message entirely in the qubits without increasing the number of qubits? We show that this is indeed possible. We introduce a prepare-and-measure QKR protocol where the communication from Alice to Bob consists entirely of qubits. As usual, Bob responds with an authenticated one-bit accept/reject classical message. Compared to Quantum Key Distribution (QKD), QKR has reduced round complexity. Compared to previous qubit-wise QKR protocols, our scheme has far less classical communication. We provide a security p…
We study the statistical distribution of the ergotropy and of the efficiency of a single-qubit battery ad of a single-qubit Otto engine, respectively fuelled by random collisions. The single qubit, our working fluid, is assumed to exchange energy with two reservoirs, a non-equilibrium "hot" reservoir and a zero temperature cold reservoir. The interactions between the qubit and the reservoirs is described in terms of a collision model of open system dynamics. The qubit interacts with the non-equilibrium reservoir (a large ensemble of qudits all prepared in the same pure state) via random unitar…
Distinguishing hot from cold is the most primitive form of thermometry. Here we consider how well this task can be performed using a single qubit to distinguish between two different temperatures of a bosonic bath. In this simple setting, we find that letting the qubit equilibrate with the bath is not optimal, and depending on the interaction time it may be advantageous for the qubit to start in a state with some quantum coherence. We also briefly consider the case that the qubit is initially entangled with a second qubit that is not put into contact with the bath, and show that entanglement a…
Random samples of quantum states are an important resource for various tasks in quantum information science, and samples in accordance with a problem-specific distribution can be indispensable ingredients. Some algorithms generate random samples by a lottery that follows certain rules and yield samples from the set of distributions that the lottery can access. Other algorithms, which use random walks in the state space, can be tailored to any distribution, at the price of autocorrelations in the sample and with restrictions to low-dimensional systems in practical implementations. In this paper…
We propose and analyze a setup based on (solid-state) qubits coupled to a common multi-mode transmission line, which allows for coherent spin-spin interactions over macroscopic on-chip distances, without any ground-state cooling requirements for the data bus. Our approach allows for the realization of fast deterministic quantum gates between distant qubits, the simulation of quantum spin models with engineered (long-range) interactions, and provides a flexible architecture for the implementation of quantum approximate optimization algorithms.
Quantum error correction procedures have the potential to enable faithful operation of large-scale quantum computers. They protect information from environmental decoherence by storing it in logical qubits, built from ensembles of entangled physical qubits according to suitably tailored quantum error correcting encodings. To date, no generally accepted framework to characterise the behaviour of logical qubits as quantum memories has been developed. In this work, we show that generalisations of well-established figures of merit of physical qubits, such as relaxation times, to logical qubits fai…
By the standard second law of thermodynamics, heat spontaneously flows from a hotter body to a colder body. However, quantum systems in which quantum correlations play a prominent role can exhibit a non-classical reversal of such heat flow. We propose a quantum system consisting of a chain of qubits, each in local Gibbs states, where only adjacent qubits are allowed to thermally interact. By controlling initial quantum correlations along the chain, we then demonstrate non-classical heat reversal for the special case of a three-qubit chain on a quantum computer. We explore multiple initial cond…
We observe the continuous emission of photons into a waveguide from a superconducting qubit without the application of an external drive. To explain this observation, we build a two-bath model where the qubit couples simultaneously to a cold bath (the waveguide) and a hot bath (a secondary environment). Our results show that the thermal-photon occupation of the hot bath is up to 0.14 photons, 35 times larger than the cold waveguide, leading to nonequilibrium heat transport with a power of up to 132 zW, as estimated from the qubit emission spectrum. By adding more isolation between the sample o…
Explosive increase of interest in quantum computing has resulted in various proposals for generation of quantum bits or qubits, the basic quantum computing unit. The superconducting qubits of Josephson Junction are the most widely accepted and currently used, while the Ion-trap and a similar molecule-based qubits have been proposed more recently. In these methods, each qubit is generated individually with great effort. Here we proposed a new technique using magnetic resonance imaging (MRI)-based qubit generation, by which multiple qubits can be generated. Simultaneously this provides a complet…
Near-term quantum computers are limited by the decoherence of qubits to only being able to run low-depth quantum circuits with acceptable fidelity. This severely restricts what quantum algorithms can be compiled and implemented on such devices. One way to overcome these limitations is to expand the available gate set from single- and two-qubit gates to multi-qubit gates, which entangle three or more qubits in a single step. Here, we show that such multi-qubit gates can be realized by the simultaneous application of multiple two-qubit gates to a group of qubits where at least one qubit is invol…
Extending the Bloch sphere model to an N-qubit system
Universidad de Castilla-La Mancha（卡斯蒂利亚-拉曼查大学）；Universidad de La Rioja（拉里奥哈大学）；Universidad Complutense de Madrid（马德里康普顿斯大学）；Roma Tre University（罗马三大学）；QSimov
Noisy Intermediate-Scale Quantum (NISQ) algorithms require novel paradigms of error mitigation. To obtain noise-robust quantum computers, each logical qubit is equipped with hundreds or thousands of physical qubits. However, it is not possible to use memory-consuming techniques for current quantum devices having at most hundreds or at best thousands of physical qubits on their own. For specific problems, valid quantum states have a unique structure as in the case of Fock states and W-states where the Hamming weight is fixed, and the evolution takes place in a smaller subspace of the full Hilbe…
The interaction of qubits with quantized modes of electromagnetic fields has been largely addressed in the quantum optics literature under the rotating wave approximation (RWA), where rapid oscillating terms in the qubit-mode interaction picture Hamiltonian can be neglected. At the same time, it is generally accepted that provided the interaction is sufficiently strong or for long times, the RWA tends to describe physical phenomena incorrectly. In this work, we extend the investigation of the validity of the RWA to a more involved setup where two qubit-mode subsystems are brought to interactio…
Verifiable blind quantum computing allows a client with poor quantum devices to delegate universal quantum computing to a remote quantum server in such a way that the client's privacy is protected and the honesty of the server is verified. In existing protocols, the client has to send single-qubit states to the server. These states might be decohered by the channel noise. Furthermore, the client hides some "trap" qubits in the server's register so that the client can detect the server's deviation. In reality, however, these trap qubits are disturbed by imperfect operations by the server, which…
Within the quantum computing, there are two ways to encode a normalized vector $\{ α_i \}$. They are one-hot encoding and binary coding. The one-hot encoding state is denoted as $\left | ψ_O^{(N)} \right \rangle=\sum_{i=0}^{N-1} α_i \left |0 \right \rangle^{\otimes N-i-1} \left |1 \right \rangle \left |0 \right \rangle ^{\otimes i}$ and the binary encoding state is denoted as $\left | ψ_B^{(N)} \right \rangle=\sum_{i=0}^{N-1} α_i \left |b_i \right \rangle$, where $b_i$ is interpreted in binary of $i$ as the tensor product sequence of qubit states. In this paper, we present a method converting …
Classical Ensembles of Single-Qubit Quantum Variational Circuits for Classification
University of KwaZulu-Natal（夸祖鲁-纳塔尔大学）；National Institute for Theoretical and Computational Science (NITheCS)（理论与计算科学国家研究所）；Centre for Artificial Intelligence Research (CAIR)（人工智能研究中心）；Stellenbosch University（斯坦伦布什大学）
We present a protocol for encoding $N$ real numbers stored in $N$ memory registers into the amplitudes of the quantum superposition that describes the state of $\log_2N$ qubits. This task is one of the main steps in quantum machine learning algorithms applied to classical data. The protocol combines partial CNOT gate rotations with probabilistic projection onto the desired state. The number of additional ancilla qubits used during the implementation of the protocol, as well as the number of quantum gates, scale linearly with the number of qubits in the processing register and hence logarithmic…
Extremely Low-Cost Magic State Preparation toward Fault-Tolerant Quantum Computing
School of Physics, Peking University（北京大学物理学院）；Center on Frontiers of Computing Studies, School of Computer Science, Peking University（北京大学前沿交叉学科研究院计算机学院）
In this paper we experimentally test the performance of the recently proposed domain-wall encoding of discrete variables from [Chancellor Quantum Sci. Technol. 4 045004] on Ising model flux qubit quantum annealers. We compare this encoding with the traditional one-hot methods and find that they outperform the one-hot encoding for three different problems at different sizes both of the problem and of the variables. From these results we conclude that the domain-wall encoding yields superior performance against a variety of metrics furthermore, we do not find a single metric by which one hot per…
Due to the limitations of present-day quantum hardware, it is especially critical to design algorithms that make the best possible use of available resources. When simulating quantum many-body systems on a quantum computer, straightforward encodings that transform many-body Hamiltonians into qubit Hamiltonians use $N$ of the available basis states of an $N$-qubit system, whereas $2^N$ are in theory available. We explore an efficient encoding that uses the entire set of basis states, where terms in the Hamiltonian are mapped to qubit operators with a Hamiltonian that acts on the basis states in…
