Quantum State Preparation Research Articles

Quantum state preparation of topological chiral spin liquids via Floquet engineering

Quantum state preparation of topological chiral spin liquids via Floquet engineering

Versatile Fidelity Estimation with Confidence.

As quantum devices become more complex and the requirements on these devices become more demanding, it is crucial to be able to verify the performance of such devices in a scalable and reliable fashion. A cornerstone task in this challenge is quantifying how close an experimentally prepared quantum state is to the desired one. Here we present a method to construct an estimator for the quantum state fidelity that is compatible with any measurement protocol. Our method provides a confidence interval on this estimator that is guaranteed to be nearly minimax optimal for the specified measurement protocol. For a well-chosen measurement scheme, our method is competitive in the number of measurement outcomes required for estimation. We demonstrate our method using simulations and experimental data from a trapped-ion quantum computer and compare the results to state-of-the-art techniques. Our method can be easily extended to estimate the expectation value of any observable, such as entanglement witnesses.

Simulating quantum field theories on continuous-variable quantum computers

We delve into the use of photonic quantum computing to simulate quantum mechanics and extend its application towards quantum field theory. We develop and prove a method that leverages this form of continuous-variable quantum computing (CVQC) to reproduce the time evolution of quantum-mechanical states under arbitrary Hamiltonians, and we demonstrate the method's remarkable efficacy with various potentials. Our method centers on constructing an , a specially prepared quantum state that induces the desired time evolution on the target state. This is achieved by introducing a non-Gaussian operation using a measurement-based quantum computing approach, enhanced by machine learning. Furthermore, we propose a framework in which these methods can be extended to encode field theories in CVQC without discretizing the field values, thus preserving the continuous nature of the fields. This opens new avenues for quantum computing applications in quantum field theory. Published by the American Physical Society 2024

Quantum squeezing in a nonlinear mechanical oscillator

Mechanical degrees of freedom are natural candidates for continuous-variable quantum information processing and bosonic quantum simulations. However, these applications require the engineering of squeezing and nonlinearities in the quantum regime. Here we demonstrate squeezing below the zero-point fluctuations of a gigahertz-frequency mechanical resonator coupled to a superconducting qubit. This is achieved by parametrically driving the qubit, which results in an effective two-phonon drive. In addition, we show that the resonator mode inherits a nonlinearity from the off-resonant coupling with the qubit, which can be tuned by controlling the detuning. We, thus, realize a mechanical squeezed Kerr oscillator, in which we demonstrate the preparation of non-Gaussian quantum states of motion with Wigner function negativities and high quantum Fisher information. This shows that our results can also have applications in quantum metrology and sensing.

High-performance photon number resolving detectors for 850–950 nm wavelength range

Since their first demonstration in 2001 [Gol’tsman et al., Appl. Phys. Lett. 79, 705–707 (2001)], superconducting-nanowire single-photon detectors (SNSPDs) have witnessed two decades of great developments. SNSPDs are the detector of choice in most modern quantum optics experiments and are slowly finding their way into other photon-starved fields of optics. Until now, however, in nearly all experiments, SNSPDs were used as “binary” detectors, meaning that they could only distinguish between 0 and >=1 photons, and photon number information was lost. Recent research has demonstrated proof-of-principle photon-number resolution (PNR) SNSPDs counting 2–5 photons. The photon-number-resolving capability is highly demanded in various quantum-optics experiments, including Hong–Ou–Mandel interference, photonic quantum computing, quantum communication, and non-Gaussian quantum state preparation. In particular, PNR detectors at the wavelength range of 850–950 nm are of great interest due to the availability of high-quality semiconductor quantum dots (QDs) [Heindel et al., Adv. Opt. Photonics 15, 613–738 (2023)] and high-performance cesium-based quantum memories [Ma et al., J. Opt. 19, 043001 (2017)]. In this paper, we demonstrate NbTiN-based SNSPDs with >94% system detection efficiency, sub-11 ps timing jitter for one photon, and sub-7 ps for 2 photons. More importantly, our detectors resolve up to 7 photons using conventional cryogenic electric readout circuitry. Through theoretical analysis, we show that the PNR performance of demonstrated detectors can be further improved by enhancing the signal-to-noise ratio and bandwidth of our readout circuitry. Our results are promising for the future of optical quantum computing and quantum communication.

Trainable parameterized quantum encoding and application based on enhanced robustness and parallel computing

One key advantage of quantum algorithms is based on the assumption that arbitrary quantum states can be efficiently prepared. However, limited by qubits’ number and decoherence time, existing preparation methods are not friendly to the quantum state preparation of high-dimensional data. In this paper, we propose a Trainable Parameterized Quantum Encoding (TPQE) method for realizing approximate encoding of arbitrary quantum states, and the representation ability is proposed as the verification criterion for TPQE for arbitrary quantum states. To enhance the robustness of the TPQE, we take into account noise as part of the TPQE and absorb the noise into the parameters through training. Moreover, we utilize parallel computing between multiple quantum processors to achieve a speedup of TPQE. Finally, the representation ability of TPQE is validated on a publicly available dataset of breast cancer using amplitude encoding as a benchmark. Experiments demonstrate that our method shows good robustness.

Semiquantum Key Distribution Using Initial States in Only One Basis Without the Classical User Measuring

AbstractFrom the perspective of resource theory, it is interesting to achieve the same quantum task using as few quantum resources as possible. Semiquantum key distribution (SQKD), which allows a quantum user to share a confidential key with a classical user who prepares and operates qubits on only one basis, is an important example for studying this issue. To further limit the quantum resources used by users, in this paper, the first SQKD protocol is constructed, which restricts the quantum user to prepare quantum states on only one basis and removes the classical user's measurement capability. Furthermore, it is proven that the constructed protocol is secure against the restricted attack by deriving a key rate expression of the error rate in the asymptotic scenario. The work in this paper provides inspiration for achieving quantum superiority with minimal quantum resources.

Holonomic swap and controlled-swap gates of neutral atoms via selective Rydberg pumping

Holonomic quantum computing offers a promising paradigm for quantum computation due to its error resistance and the ability to perform universal quantum computations. Here, we propose a scheme for the rapid implementation of a holonomic swap gate in neutral atomic systems, based on the selective Rydberg pumping mechanism. By employing time-dependent soft control, we effectively mitigate the impact of off-resonant terms even at higher driving intensities compared to time-independent driving. This approach accelerates the synthesis of logic gates and passively reduces the decoherence effects. Furthermore, by introducing an additional atom and applying the appropriate driving field, our scheme can be directly extended to implement a three-qubit controlled-swap gate. This advancement makes it a valuable tool for quantum state preparation, quantum switches, and a variational quantum algorithm in neutral atom systems.

Quadratic acceleration of multistep probabilistic algorithms for state preparation

Quantum state preparation is a fundamental building block for various problems on a quantum computer. A nonunitary operator is typically designed to decay unwanted states contained in an initial state using ancilla qubits and a probabilistically action. In this Letter, we clarify that this probabilistic nature is a drag for quantum advantages: The probabilistic algorithms do not accelerate the computational process compared to classical ones. Combining quantum amplitude amplification (QAA) with multistep probabilistic algorithms is proposed to address this drawback, achieving quadratic acceleration and quantum advantages. We also find that the multistep probabilistic method with QAA exhibits advantages over quantum phase estimation in terms of infidelity. We also demonstrate it to confirm the quadratic acceleration, using a probabilistic imaginary-time evolution method as an example. Published by the American Physical Society 2024

Experimental Direct Quantum Fidelity Learning via a Data-Driven Approach.

Fidelity estimation is an important technique for evaluating prepared quantum states in noisy quantum devices. A recent theoretical work proposed a frugal approach called neural quantum fidelity estimation (NQFE) [X. Zhang et al., Phys. Rev. Lett. 127, 130503 (2021).PRLTAO0031-900710.1103/PhysRevLett.127.130503]. While this requires a much smaller number of measurement operators than full quantum state tomography, it uses a weight-based floating measurement strategy that predetermines the top global Pauli operators that contribute the most to the fidelity and uses discrete fidelity intervals as predictions. In this Letter, we develop a measurement-fixed NQFE based on a transformer model which requires less measurement cost and can output continuous estimates of fidelity. Here we further experimentally apply the NQFE in a realistic situation using a nuclear spin quantum processor. We prepare the ground states of local Hamiltonians and arbitrary states and investigate how to estimate their fidelity with reference states, and we compare the fidelity estimation strategy with our and the original NQFE to conventional tomography. It is shown that NQFE can estimate the fidelity with comparable accuracy to the tomography approach. In the future, NQFE will become an important tool for benchmarking quantum states ahead of the advent of well-trusted fault-tolerant quantum computers.

A novel approach for quantum financial simulation and quantum state preparation

A novel approach for quantum financial simulation and quantum state preparation

Circuit complexity of quantum access models for encoding classical data

How to efficiently encode classical data is a fundamental task in quantum computing. While many existing works treat classical data encoding as a black box in oracle-based quantum algorithms, their explicit constructions are crucial for the efficiency of practical algorithm implementations. Here, we unveil the mystery of the classical data encoding black box and study the Clifford + T complexity in constructing several typical quantum access models. For general matrices (even including sparse ones), we prove that sparse-access input models and block-encoding both require nearly linear circuit complexities relative to the matrix dimension. We also give construction protocols achieving near-optimal gate complexities. On the other hand, the construction becomes efficient with respect to the data qubit when the matrix is a linear combination of polynomial terms of efficiently implementable unitaries. As a typical example, we propose improved block-encoding when these unitaries are Pauli strings. Our protocols are built upon improved quantum state preparation and a select oracle for Pauli strings, which hold independent values. Our access model constructions provide considerable flexibility, allowing for tunable ancillary qubit numbers and offering corresponding space-time trade-offs.

Efficient quantum state preparation with Walsh series

Efficient quantum state preparation with Walsh series

Quantum state preparation via engineered ancilla resetting

In this theoretical investigation, we examine the effectiveness of a protocol incorporating periodic quantum resetting for preparing ground states of frustration-free parent Hamiltonians. This protocol uses a steering Hamiltonian that enables local coupling between the system and ancillary degrees of freedom. At periodic intervals, the ancillary system is reset to its initial state. For infinitesimally short reset times, the dynamics can be approximated by a Lindbladian whose steady state is the target state. For finite reset times, however, the spin chain and the ancilla become entangled between reset operations. To evaluate the protocol, we employ Matrix Product State simulations and quantum trajectory techniques, focusing on the preparation of the spin-1 Affleck-Kennedy-Lieb-Tasaki state. Our analysis considers convergence time, fidelity, and energy evolution under different reset intervals. Our numerical results show that ancilla system entanglement is essential for faster convergence. In particular, there exists an optimal reset time at which the protocol performs best. Using a simple approximation, we provide insights into how to optimally choose the mapping operators applied to the system during the reset procedure. Furthermore, the protocol shows remarkable resilience to small deviations in reset time and dephasing noise. Our study suggests that stroboscopic maps using quantum resetting may offer advantages over alternative methods, such as quantum reservoir engineering and quantum state steering protocols, which rely on Markovian dynamics.

Sparse Quantum State Preparation for Strongly Correlated Systems.

Quantum computing allows, in principle, the encoding of the exponentially scaling many-electron wave function onto a linearly scaling qubit register, offering a promising solution to overcome the limitations of traditional quantum chemistry methods. An essential requirement for ground state quantum algorithms to be practical is the initialization of the qubits to a high-quality approximation of the sought-after ground state. Quantum state preparation enables the generation of approximate eigenstates derived from classical computations but is frequently treated as an oracle in quantum information. In this study, we investigate the quantum state preparation of prototypical strongly correlated systems' ground state, up to 28 qubits, using the Hyperion-1 GPU-accelerated state-vector emulator. Various variational and nonvariational methods are compared in terms of their circuit depth and classical complexity. Our results indicate that the recently developed Overlap-ADAPT-VQE algorithm offers the most advantageous performance for near-term applications.

Engineering unsteerable quantum states with active feedback

We propose active steering protocols for quantum state preparation in quantum circuits where each system qubit is connected to a single detector qubit, employing a simple coupling selected from a small set of steering operators. The decision is made such that the expected cost-function gain in one time step is maximized. We apply these protocols to several many-qubit models. Our results are underlined by three remarkable insights. First, we show that the standard fidelity does not give a useful cost function; instead, successful steering is achieved by including local fidelity terms. Second, although the steering dynamics acts on each system qubit separately, entanglement in the generated target state is introduced, and can be tuned at will, by performing Bell measurements on detector qubit pairs after every time step. This implements a weak-measurement variant of entanglement swapping. Third, numerical simulations suggest that the active steering protocol can reach arbitrarily designated target states, including passively unsteerable states such as the N-qubit W state. Published by the American Physical Society 2024

Shortcuts to Adiabaticity in Krylov Space

Shortcuts to adiabaticity provide fast protocols for quantum state preparation in which the use of auxiliary counterdiabatic controls circumvents the requirement of slow driving in adiabatic strategies. While their development is well established in simple systems, their engineering and implementation are challenging in many-body quantum systems with many degrees of freedom. We show that the equation for the counterdiabatic term—equivalently, the adiabatic gauge potential—is solved by introducing a Krylov basis. The Krylov basis spans the minimal operator subspace in which the dynamics unfolds and provides an efficient way to construct the counterdiabatic term. We apply our strategy to paradigmatic single- and many-particle models. The properties of the counterdiabatic term are reflected in the Lanczos coefficients obtained in the course of the construction of the Krylov basis by an algorithmic method. We examine how the expansion in the Krylov basis incorporates many-body interactions in the counterdiabatic term. Published by the American Physical Society 2024

Practical quantum protocols for blind millionaires’ problem based on rotation encryption and swap test

Millionaires’ problem, as the most fundamental problem in secure multiparty computation (SMC), has attracted much attention in recent years. Blind millionaires’ problem, an extension of millionaires’ problem, enables to determine the size relationship of the secrets sum. In this paper, two practical quantum protocols based on rotation encryption and swap test are proposed, which can essentially solve the blind millionaires’ problem. To verify the correctness and feasibility, the proposed protocols are simulated on IBM Quantum Platform by designing the corresponding quantum circuits. Compared with the existing quantum solutions for the blind millionaires’ problem, the proposed protocols demonstrate improved performance in terms of feasibility and security, as they utilize Bell states, single-particle measurements, rotation operations and swap tests without necessitating the preparation of d-dimensional quantum states, the shift operation of d-dimensional quantum states, quantum Fourier transform, or the measurement of computational basis and Fourier basis. Security analysis demonstrates that the private data of each participant and the secrets sum remain confidential and undisclosed.

Spacetime-Efficient Low-Depth Quantum State Preparation with Applications

We propose a novel deterministic method for preparing arbitrary quantum states. When our protocol is compiled into CNOT and arbitrary single-qubit gates, it prepares an N-dimensional state in depth O(log⁡(N)) and spacetime allocation (a metric that accounts for the fact that oftentimes some ancilla qubits need not be active for the entire circuit) O(N), which are both optimal. When compiled into the {H,S,T,CNOT} gate set, we show that it requires asymptotically fewer quantum resources than previous methods. Specifically, it prepares an arbitrary state up to error ϵ with optimal depth of O(log⁡(N)+log⁡(1/ϵ)) and spacetime allocation O(Nlog⁡(log⁡(N)/ϵ)), improving over O(log⁡(N)log⁡(log⁡(N)/ϵ)) and O(Nlog⁡(N/ϵ)), respectively. We illustrate how the reduced spacetime allocation of our protocol enables rapid preparation of many disjoint states with only constant-factor ancilla overhead – O(N) ancilla qubits are reused efficiently to prepare a product state of wN-dimensional states in depth O(w+log⁡(N)) rather than O(wlog⁡(N)), achieving effectively constant depth per state. We highlight several applications where this ability would be useful, including quantum machine learning, Hamiltonian simulation, and solving linear systems of equations. We provide quantum circuit descriptions of our protocol, detailed pseudocode, and gate-level implementation examples using Braket.

Quantum state preparation of normal distributions using matrix product states

State preparation is a necessary component of many quantum algorithms. In this work, we combine a method for efficiently representing smooth differentiable probability distributions using matrix product states with recently discovered techniques for initializing quantum states to approximate matrix product states. Using this, we generate quantum states encoding a class of normal probability distributions in a trapped ion quantum computer for up to 20 qubits. We provide an in depth analysis of the different sources of error which contribute to the overall fidelity of this state preparation procedure. Our work provides a study in quantum hardware for scalable distribution loading, which is the basis of a wide range of algorithms that provide quantum advantage.