Quantum State Preparation Research Articles

A Century Ago the Stern–Gerlach Experiment Ruled Unequivocally in Favor of Quantum Mechanics

AbstractIn 1921, Otto Stern conceived the idea for an experiment that would decide between a classical and a quantum description of atomic behavior, as epitomized by the Bohr–Sommerfeld–Debye model of the atom. This model entailed not only the quantization of the magnitude of the orbital electronic angular momentum but also of the projection of the angular momentum on an external magnetic field – the so‐called space quantization. Stern recognized that space quantization would have observable consequences: namely, that the magnetic dipole moment due to the orbital angular momentum would be space quantized as well, taking two opposite values for atoms whose only unpaired electron has just one quantum of orbital angular momentum. When acted upon by a suitable inhomogeneous magnetic field, a beam of such atoms would be split into two beams consisting of deflected atoms with opposite projections of the orbital angular momentum on the magnetic field. In contradistinction, if atoms behaved classically, the atomic beam would only broaden along the field gradient and have maximum intensity at zero deflection, i. e., where there would be a minimum or no intensity for a beam split due to space quantization. Stern anticipated that, although simple in principle, the experiment would be difficult to carry out – and invited Walther Gerlach to team up with him. Gerlach's realism and experimental skills together with his sometimes stubborn determination to make things work proved invaluable for the success of the Stern–Gerlach experiment (SGE). After a long struggle, Gerlach finally saw, on 8 February 1922, the splitting of a beam of silver atoms in a magnetic field. The absence of the concept of electron spin confused and confounded the interpretation of the SGE, as the silver atoms were, in fact, in a 2S state, with zero orbital and spin angular momentum. However, a key quantum feature whose existence the SGE was designed to test – namely space quantization of electronic angular momentum – was robust enough to transpire independent of whether the electronic angular momentum was orbital or due to spin. The SGE entails other key aspects of quantum mechanics such as quantum measurement, state preparation, coherence, and entanglement. Confronted with the outcome of the SGE, Stern noted: “I still have objections to the idea of beauty of quantum mechanics. But she is correct.”

Protecting security of quantum neural network with sampling checks

With the development of quantum computing, the application of quantum neural networks will be more and more extensive, and its security will also face more challenges. Although quantum communication has high security, quantum neural networks may have many internal and external insecure factors in the process of information transmission, such as noise impact during the preparation of input quantum states, privacy disclosure during transmission, and external attacks on the network structure, which may cause major security incidents. Because of the possible insecurity factors of quantum neural networks, this paper proposes a quantum sampling method to detect the state of quantum neural networks at each stage, so as to judge whether there are security risks in quantum neural networks and thus ensure their security. The method also provides a safe basis for further research on the stability and reliability of quantum neural networks.

Quantum state preparation using tensor networks

Quantum state preparation is a vital routine in many quantum algorithms, including solution of linear systems of equations, Monte Carlo simulations, quantum sampling, and machine learning. However, to date, there is no established framework of encoding classical data into gate-based quantum devices. In this work, we propose a method for the encoding of vectors obtained by sampling analytical functions into quantum circuits that features polynomial runtime with respect to the number of qubits and provides accuracy, which is better than a state-of-the-art two-qubit gate fidelity. We employ hardware-efficient variational quantum circuits, which are simulated using tensor networks, and matrix product state representation of vectors. In order to tune variational gates, we utilize Riemannian optimization incorporating auto-gradient calculation. Besides, we propose a ‘cut once, measure twice’ method, which allows us to avoid barren plateaus during gates’ update, benchmarking it up to 100-qubit circuits. Remarkably, any vectors that feature low-rank structure—not limited by analytical functions—can be encoded using the presented approach. Our method can be easily implemented on modern quantum hardware, and facilitates the use of the hybrid-quantum computing architectures.

Quantum state-resolved methane scattering from Ni(111) and NiO(111) by bolometer infrared laser tagging: The effect of surface oxidation.

We describe a novel ultrahigh vacuum state-to-state molecule/surface scattering apparatus with quantum state preparation of the incident molecular beam and angle-resolved quantum state detection of the scattered molecules. State-resolved detection is accomplished using a tunable mid-infrared laser source combined with a cryogenic bolometer detector and is applicable to any molecule with an infrared-active vibrational transition. Results on rotationally inelastic scattering of CH4 methane from a Ni(111) surface and NiO(111)/Ni(111) oxide film, obtained by the new apparatus, are presented. Molecules scattering from the oxidized surface, compared to those scattering from the bare nickel surface, are more highly excited rotationally and scatter into a broader distribution of angles. The internal alignment of molecular rotation is in addition found to be stronger in molecules scattering from the bare surface. Furthermore, the maxima of the state-resolved angular distributions shift toward and away from surface normal with increasing rotational quantum number J for the oxidized and bare surface, respectively. Finally, the rotational state populations produced in scattering from the oxidized surface are well-described by a Boltzmann distribution, while those produced in scattering from the bare surface exhibit large deviations from their best-fit Boltzmann distributions. These results point toward a marked enhancement in molecule-surface collisional energy exchange induced by oxidation of the nickel surface.

Towards quantum state preparation with materials science: An analytical review

AbstractThe field of quantum computing has undergone significant expansion and development in recent years. A quantitative and comprehensive examination of the research domain is essential to comprehend research trends and directions in the field. Henceforth, the current paper conducts a scientometric analysis of the academic literature on quantum computing retrieved from the Scopus database to understand the recent advances made by researchers in the domain. The analysis evaluates the state of the discipline's research by examining the most prominent journals and highly referenced articles. CiteSpace is leveraged to visualize the intellectual landscape of quantum state preparation by performing document co‐citation and author co‐citation analysis. The analysis reveals that trapped ions, photonic qubits, superconducting qubits, nitrogen‐vacancy centers, and nuclear spin qubits are the primary research topics in quantum computing. Furthermore, the most current research issues that require attention in the field are measurement‐based qubits, Majorana fermions, and quantum dots.

Normal-mode splitting in an optomechanical system enhanced by an optical parametric amplifier and coherent feedback

Normal-mode splitting (NMS) is an evident signature of strong coupling interactions for observing quantum phenomena, such as optomechanical squeezing and entanglement. In the previous literature, optical parametric amplifier (OPA) and coherent feedback are independently proposed to enhance the NMS. Here, we combine OPA and coherent feedback into a single optomechanical system to enhance the NMS. Controllable parameters, such as input optical power, OPA gain and phase, coherent feedback strength, are varied to observe NMS variations. In particular, we consider positive and negative feedback in terms of the amplitude reflectivity of the beam splitter for coherent feedback. The NMS appears mostly with the positive coherent feedback rather than the negative. Furthermore, the largest mode separation occurs at an OPA phase of approximately rather than zero because the effective cavity detuning changes the effective intracavity round-trip phase, and therefore changes the OPA amplification/deamplification condition. The results indicate that the interplay between OPA and coherent feedback can enhance the NMS with more controllable parameter freedoms. This scheme provides a promising way to increase the optomechanical coupling strength, thereby having potential applications in the ground state cooling of a mechanical oscillator, the preparation of optomechanical quantum states, and the sensitive detection of a weak force.

Stronger reverse uncertainty relation for multiple incompatible observables

Recently, D Mondal et al (2017)[Phys. Rev. A. 95, 052117] creatively introduce a new interesting concept of reverse uncertainty relation which indicates that one cannot only prepare quantum states with joint small uncertainty, but also with joint great uncertainty for incompatible observables. However, the uncertainty upper bound they constructed cannot express the essence of this concept well, i.e., the upper bound will go to infinity in some cases even for incompatible observables. Here, we construct a new reverse uncertainty relation and successfully fix this ‘infinity’ problem. Also, it is found that the reverse uncertainty relation and the normal uncertainty relation are the same in essential, and they both can be unified by the same theoretical framework. Moreover, taking advantage of this unified framework, one can construct a reverse uncertainty relation for multiple observables with any tightness Required. Meanwhile, the application of the new uncertainty relation in purity detection is discussed.

A Quantum States Preparation Method Based on Difference-Driven Reinforcement Learning

Due to the large state space of the two-qubit system, and the adoption of ladder reward function in the existing quantum state preparation methods, the convergence speed is slow and it is difficult to prepare the desired target quantum state with high fidelity under limited conditions. To solve the above problems, a difference-driven reinforcement learning (RL) algorithm for quantum state preparation of two-qubit system is proposed by improving the reward function and action selection strategy. Firstly, a model is constructed for the problem of preparing quantum states of a two-qubit system, with restrictions on the type of quantum gates and the time for quantum state evolution. In the preparation process, a weighted differential dynamic reward function is designed to assist the algorithm quickly obtain the maximum expected cumulative reward. Then, an adaptive [Formula: see text]-greedy action selection strategy is adopted to achieve a balance between exploration and utilization to a certain extent, thereby improving the fidelity of the final quantum state. The simulation results show that the proposed algorithm can prepare quantum state with high fidelity under limited conditions. Compared with other algorithms, it has different degrees of improvement in convergence speed and fidelity of the final quantum state.

Sunlight-pumped two-dimensional thermalized photon gas

The Liouville theorem states that the phase-space volume of an ensemble in a closed system remains constant. While gases of material particles can efficiently be cooled by sympathetic or laser cooling techniques, allowing for large phase-space compression upon suitable coupling to the environment, for light both the absence of an internal structure, as well as the nonconservation of photons upon contact with matter imposes fundamental limits for three-dimensional light-harvesting systems, such as fluorescence-based light concentrators. An advantageous physical situation can in principle be expected for dye-solution-filled microcavities with a mirror spacing in the wavelength range, where low-dimensional photon gases with nonvanishing and tunable chemical potential have been experimentally realized. Motivated by the goal to observe phase-space compression of sunlight by cooling the captured radiation to room temperature, in this work we theoretically show that in a lossless, harmonically confined system the phase-space volume scales as ${(\mathrm{\ensuremath{\Delta}}x\mathrm{\ensuremath{\Delta}}p/T)}^{d}=\mathrm{constant}$, where $\mathrm{\ensuremath{\Delta}}x$ and $\mathrm{\ensuremath{\Delta}}p$ denote the position and momentum spread and $d$ the dimensionality of the system ($d=1$ or 2). Experimentally, we realize a corresponding sunlight-pumped dye microcavity and demonstrate thermalization of scattered sunlight to a two-dimensional room temperature photon gas with nonvanishing chemical potential. Prospects of phase-space buildup of light by cooling, as can be feasible in systems with a two- or three-dimensional band gap, range from quantum state preparation in tailored potentials up to technical applications for more efficient collection of diffuse sunlight.

Simulating noisy quantum channels via quantum state preparation algorithms

In Xin et al (2017 Phys. Rev. A 96 062303) and Wei et al (2018 Sci. China Phys. Mech. Astron. 61 70311), the authors reported an algorithm to simulate, in a circuit-based quantum computer, a general quantum channel (QC). However, the application of their algorithm is limited because it entails the solution of intricate non-linear systems of equations in order to obtain the quantum circuit to be implemented for the simulation. Motivated by this issue, in this article we identify and discuss a simple way to implement the simulation of QCs on any d-level quantum system through quantum state preparation algorithms, that have received much attention in the quantum information science literature lately. We exemplify the versatility of our protocol applying it to most well known qubit QCs, to some qudit QCs, and to simulate the effect of Lorentz transformations on spin states. We also regard the application of our protocol for initial mixed states. Most of the given application examples are demonstrated using IBM’s quantum computers.

Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry

Due to intense interest in the potential applications of quantum computing, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation, for generic chemical problems where heuristic quantum state preparation might be assumed to be efficient. The availability of exponential quantum advantage then centers on whether features of the physical problem that enable efficient heuristic quantum state preparation also enable efficient solution by classical heuristics. Through numerical studies of quantum state preparation and empirical complexity analysis (including the error scaling) of classical heuristics, in both ab initio and model Hamiltonian settings, we conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for ground-state quantum chemistry through polynomial speedups, it may be prudent to assume exponential speedups are not generically available for this problem.

Decoherence-assisted quantum driving

The authors analyze a quantum state preparation procedure based oncontrolled driving of the system accompanied by repeated measurementlike interactions with an external spectator. They show that the efficiency of an imperfect realization of the procedure ismaximal if the driving proceeds along a geodesic parameter pathderived from the Provost-Vallee quantum metric.

Discrete Time Crystal Enabled by Stark Many-Body Localization.

Discrete time crystals (DTCs) have recently attracted increasing attention, but most DTC models and their properties are only revealed after disorder average. In this Letter, we propose a simple disorder-free periodically driven model that exhibits nontrivial DTC order stabilized by Stark many-body localization (MBL). We demonstrate the existence of the DTC phase by analytical analysis from perturbation theory and convincing numerical evidence from observable dynamics. The new DTC model paves a new promising way for further experiments and deepens our understanding of DTCs. Since the DTC order does not require special quantum state preparation and the strong disorder average, it can be naturally realized on the noisy intermediate-scale quantum hardware with much fewer resources and repetitions. Moreover, in addition to the robust subharmonic response, there are other novel robust beating oscillations in the Stark-MBL DTC phase that are absent in random or quasiperiodic MBL DTCs.

Optimal (controlled) quantum state preparation and improved unitary synthesis by quantum circuits with any number of ancillary qubits

As a cornerstone for many quantum linear algebraic and quantum machine learning algorithms, controlled quantum state preparation (CQSP) aims to provide the transformation of |i⟩|0n⟩→|i⟩|ψi⟩ for all i∈{0,1}k for the given n-qubit states |ψi⟩. In this paper, we construct a quantum circuit for implementing CQSP, with depth O(n+k+2n+kn+k+m) and size O(2n+k) for any given number m of ancillary qubits. These bounds, which can also be viewed as a time-space tradeoff for the transformation, are optimal for any integer parameters m,k≥0 and n≥1. When k=0, the problem becomes the canonical quantum state preparation (QSP) problem with ancillary qubits, which asks for efficient implementations of the transformation |0n⟩|0m⟩→|ψ⟩|0m⟩. This problem has many applications with many investigations, yet its circuit complexity remains open. Our construction completely solves this problem, pinning down its depth complexity to Θ(n+2n/(n+m)) and its size complexity to Θ(2n) for any m. Another fundamental problem, unitary synthesis, asks to implement a general n-qubit unitary by a quantum circuit. Previous work shows a lower bound of Ω(n+4n/(n+m)) and an upper bound of O(n2n) for m=Ω(2n/n) ancillary qubits. In this paper, we quadratically shrink this gap by presenting a quantum circuit of the depth of O(n2n/2+n1/223n/2m1/2  ).

Preparing valence-bond-solid states on noisy intermediate-scale quantum computers

Quantum state preparation is a key step in all digital quantum simulation algorithms. Here we propose methods to initialize on a gate-based quantum computer a general class of quantum spin wave functions, the so-called valence-bond-solid (VBS) states, that are important for two reasons. First, VBS states are the exact ground states of a class of interacting quantum spin models introduced by Affleck, Kennedy, Lieb, and Tasaki (AKLT). Second, the two-dimensional VBS states are universal resource states for measurement-based quantum computing. We find that schemes to prepare VBS states based on their tensor-network representations yield quantum circuits that are too deep to be within reach of noisy intermediate-scale quantum (NISQ) computers. We then apply the general nondeterministic method herein proposed to the preparation of the spin-1 and spin-$3/2$ VBS states, the ground states of the AKLT models defined in one dimension and in the honeycomb lattice, respectively. Shallow quantum circuits of depth independent of the lattice size are explicitly derived for both cases, making use of optimization schemes that outperform standard basis gate decomposition methods. The probabilistic nature of the proposed routine translates into an average number of repetitions to successfully prepare the VBS state that scales exponentially with the number of lattice sites $N$. However, two strategies to quadratically reduce this repetition overhead for any bipartite lattice are devised. Our approach should permit to use NISQ processors to explore the AKLT model and variants thereof, outperforming conventional numerical methods in the near future.

Realizing symmetry-protected topological phases in a spin-1/2 chain with next-nearest-neighbor hopping on superconducting qubits

Quantum simulation on near-term quantum hardware is a topic of intense interest. The preparation of novel quantum states of matter provides a quantitative assessment of the capabilities of near-term digital quantum computers to implement circuits with structure of relevance to quantum simulation. Here, we conduct a benchmark study by realizing symmetry-protected topological (SPT) phases of a spin-1/2 Hamiltonian with next-nearest-neighbor hopping on up to 11 qubits on a programmable superconducting quantum processor using adiabatic state preparation. Using recompilation techniques to reduce the gate count to around 50 two-qubit gates, we observe clear signatures of the two distinct SPT phases, such as excitations localized to specific edges and finite string-order parameters. We identify a parasitic phase associated with the two-qubit gate as the dominant imperfection that limits the depth of the circuits, indicating a research topic of interest for future hardware development.

VECSEL systems for quantum information processing with trapped beryllium ions

We demonstrate two systems based on vertical-external-cavity surface-emitting lasers (VECSELs) for producing ultraviolet laser light at wavelengths of 235 and 313 nm. The systems are suitable for quantum information processing with trapped beryllium ions. Each system consists of a compact, single-frequency, continuous-wave VECSEL producing high-power near-infrared light, tunable over tens of nanometers. One system generates 2.4 W at 940 nm, using a gain mirror based on GaInAs/GaAs quantum wells, which is converted to 54 mW of 235 nm light for photoionization of neutral beryllium atoms. The other system uses a gain mirror based on GaInNAs/GaAs quantum wells, enabling wavelength extension above 1200 nm with manageable strain in the GaAs lattice. This system generates 1.6 W at 1252 nm, which is converted to 41 mW of 313 nm light that is used to laser cool trapped 9Be+ ions and quantum state preparation and detection. The 313 nm system is also suitable for implementing high-fidelity quantum gates.

Assisted quantum simulation of open quantum systems

Universal quantum algorithms (UQA) implemented on fault-tolerant quantum computers are expected to achieve an exponential speedup over classical counterparts. However, the deep quantum circuits make the UQA implausible in the current era. With only the noisy intermediate-scale quantum (NISQ) devices in hand, we introduce the quantum-assisted quantum algorithm, which reduces the circuit depth of UQA via NISQ technology. Based on this framework, we present two quantum-assisted quantum algorithms for simulating open quantum systems, which utilize two parameterized quantum circuits to achieve a short-time evolution. We propose a variational quantum state preparation method, as a subroutine to prepare the ancillary state, for loading a classical vector into a quantum state with a shallow quantum circuit and logarithmic number of qubits. We demonstrate numerically our approaches for a two-level system with an amplitude damping channel and an open version of the dissipative transverse field Ising model on two sites.

Noisy-Intermediate-Scale Quantum Electromagnetic Transients Program

Quantum-empowered electromagnetic transients program (QEMTP) is a promising paradigm for tackling EMTP’s computational burdens. Nevertheless, no existing studies truly achieve a practical and scalable QEMTP operable on today’s noisy-intermediate-scale quantum (NISQ) computers. The strong reliance on noise-free and fault-tolerant quantum devices–which appears to be decades away– hinder practical applications of current QEMTP methods. This paper devises a NISQ-QEMTP methodology which for the first time transitions the QEMTP operations from ideal, noise-free quantum simulators to real, noisy quantum computers. The main contributions lie in: (1) design of shallow-depth QEMTP quantum circuits for mitigating noises on NISQ quantum devices; (2) practical QEMTP linear solvers incorporating executable quantum state preparation and measurements for nodal voltage computations; (3) a noise-resilient QEMTP algorithm leveraging quantum resources logarithmically scaled with power system dimension; (4) a quantum shifted frequency analysis (QSFA) for accelerating QEMTP by exploiting dynamic phasor simulations with larger time steps; (5) a systematical analysis on QEMTP’s performance under various noisy quantum environments. Extensive experiments systematically verify the accuracy, efficacy, universality and noise-resilience of QEMTP on both noise-free simulators and IBM real quantum computers.

Faster quantum sampling of Markov chains in nonregular graphs with fewer qubits

Sampling from the stationary distribution is one of the fundamental tasks of Markov chain-based algorithms and has important applications in machine learning, combinatorial optimization and network science. For the quantum case, qsampling from Markov chains can be constructed as preparing quantum states with amplitudes arbitrarily close to the square root of a stationary distribution instead of classical sampling from a stationary distribution. In this paper, a new qsampling algorithm for all reversible Markov chains is constructed by discrete-time quantum walks and works without any limit compared with existing results. In detail, we build a qsampling algorithm that not only accelerates non-regular graphs but also keeps the speed-up of existing quantum algorithms for regular graphs. In non-regular graphs, the invocation of the quantum fast-forward algorithm accelerates existing state-of-the-art qsampling algorithms for both discrete-time and continuous-time cases, especially on sparse graphs. Compared to existing algorithms we reduce log n, where n is the number of graph vertices. In regular graphs, our result matches other quantum algorithms, and our reliance on the gap of Markov chains achieves quadratic speedup compared with classical cases. For both cases, we reduce the number of ancilla qubits required compared to the existing results. In some widely used graphs and a series of sparse graphs where stationary distributions are difficult to reach quickly, our algorithm is the first algorithm to achieve complete quadratic acceleration (without log factor) over the classical case without any limit. To enlarge success probability amplitude amplification is introduced. We construct a new reflection on stationary state with fewer ancilla qubits and think it may have independent application.