Feedback-based Quantum Algorithms for Ground State Preparation of the Fermi-Hubbard Model
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Larsen, James Berkeley↗
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State Preparation & Linear Response on Quantum Computers
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Atomic, Nuclear and Particle Physics↗
QAOA: State Preparation, Phase Separators and Mixers for constrained problems
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Baertschi, Andreas↗
Benchmarking Quantum Simulators Using Ergodic Quantum Dynamics
Here we propose and analyze a sample-efficient protocol to estimate the fidelity between an experimentally prepared state and an ideal target state, applicable to a wide class of analog quantum simulators without advanced spatiotemporal control. Our protocol relies on universal fluctuations emerging from generic Hamiltonian dynamics, which we discover in the present work. It does not require fine-tuned control over state preparation, quantum evolution, or readout capability, while achieving near optimal sample complexity: a percent-level precision is obtained with ~103 measurements, independent of system size. Furthermore, the accuracy of our fidelity estimation improves exponentially with increasing system size. We numerically demonstrate our protocol in a variety of quantum simulator platforms, including quantum gas microscopes, trapped ions, and Rydberg atom arrays. We discuss applications of our method for tasks such as multiparameter estimation of quantum states and processes.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Robust preparation of ground state phases under noisy imaginary time evolution
Nonunitary state preparation protocols such as imaginary time evolution (ITE) offer substantial advantages relative to unitary ones, including the ability to prepare certain long-range correlated states more efficiently. Here, we ask whether such protocols are also robust to noise arising due to coupling to the environment. We consider a nonunitary ITE “circuit” subjected to a variety of noise models and investigate whether the resulting steady state remains in the same phase as the target state of the ITE at finite noise strength. Taking the one-dimensional quantum Ising model as a concrete example, we find that the ground-state order and associated phase transition persist in the presence of noise, provided the noise does not explicitly break the symmetry that protects the phase transition. That is, the noise must possess the protecting symmetry in a weak (or average) form. Our analysis is facilitated by a mapping to an effective Hamiltonian picture in a doubled Hilbert space. We discuss possible implications of these findings for quantum simulation on noisy quantum hardware. Published by the American Physical Society 2025
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Constant-Depth Preparation of Matrix Product States with Adaptive Quantum Circuits
Adaptive quantum circuits, which combine local unitary gates, midcircuit measurements, and feedforward operations, have recently emerged as a promising avenue for efficient state preparation, particularly on near-term quantum devices limited to shallow-depth circuits. Matrix product states (MPS) comprise a significant class of many-body entangled states, efficiently describing the ground states of one-dimensional gapped local Hamiltonians and finding applications in a number of recent quantum algorithms. Recently, it has been shown that the Affleck-Kennedy-Lieb-Tasaki state—a paradigmatic example of an MPS—can be exactly prepared with an adaptive quantum circuit of constant depth, an impossible feat with local unitary gates alone due to its nonzero correlation length [Smith , PRX Quantum 4, 020315 (2023)]. In this work, we broaden the scope of this approach and demonstrate that a diverse class of MPS can be exactly prepared using constant-depth adaptive quantum circuits, outperforming theoretically optimal preparation with unitary circuits. We show that this class includes short- and long-ranged entangled MPS, symmetry-protected topological (SPT) and symmetry-broken states, MPS with finite Abelian, non-Abelian, and continuous symmetries, resource states for MBQC, and families of states with tunable correlation length. Moreover, we illustrate the utility of our framework for designing constant-depth sampling protocols, such as for random MPS or for generating MPS in a particular SPT phase. We present sufficient conditions for particular MPS to be preparable in constant time, with global on-site symmetry playing a pivotal role. Altogether, this work demonstrates the immense promise of adaptive quantum circuits for efficiently preparing many-body entangled states and provides explicit algorithms that outperform known protocols to prepare an essential class of states. Published by the American Physical Society 2024
Smith, Kevin C. (ORCID:0000000223971518)↗
Scalable Circuits for Preparing Ground States on Digital Quantum Computers: The Schwinger Model Vacuum on 100 Qubits
The vacuum of the lattice Schwinger model is prepared on up to 100 qubits of IBM’s Eagle-processor quantum computers. A new algorithm to prepare the ground state of a gapped translationally invariant system on a quantum computer is presented, which we call “scalable circuits ADAPT-VQE” (SC-ADAPT-VQE). This algorithm uses the exponential decay of correlations between distant regions of the ground state, together with ADAPT-VQE, to construct quantum circuits for state preparation that can be scaled to arbitrarily large systems. These scalable circuits can be determined with use of classical computers, avoiding the challenging task of optimizing parameterized circuits on a quantum computer. SC-ADAPT-VQE is applied to the Schwinger model, and is shown to be systematically improvable, with an accuracy that converges exponentially with circuit depth. Both the structure of the circuits and the deviations of prepared wave functions are found to become independent of the number of spatial sites, L . This allows a controlled extrapolation of the circuits, determined with use of small or modest-sized systems, to arbitrarily large L . The circuits for the Schwinger model are determined on lattices up to L = 14 (28 qubits) with the Qiskit classical simulator, and are subsequently scaled up to prepare the L = 50 (100 qubits) vacuum on IBM’s 127-superconducting-qubit quantum computers ibm_brisbane and ibm_cusco. After introduction of an improved error-mitigation technique, which we call “operator decoherence renormalization”, the chiral condensate and charge-charge correlators obtained from the quantum computers are found to be in good agreement with classical matrix product state simulations. Published by the American Physical Society 2024
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Scalable Experimental Bounds for Entangled Quantum State Fidelities
Estimating the state preparation fidelity of highly entangled states on noisy intermediate-scale quantum (NISQ) devices is important for benchmarking and application considerations. Unfortunately, exact fidelity measurements quickly become prohibitively expensive, as they scale exponentially as O(3 N for N-qubit states, using full state tomography with measurements in all Pauli bases combinations. However, Somma et al.established that the complexity could be drastically reduced when looking at fidelity lower bounds for states that exhibit symmetries, such as Dicke states and GHZ states. These bounds must still be tight enough for larger states to provide reasonable estimations on NISQ devices. For the first time and more than 15 years after the theoretical introduction, we report meaningful lower bounds for the state preparation fidelity of all Dicke states up to N=10 and all GHZ states up to N=20 on Quantinuum H1 ion-trap systems using efficient implementations of recently proposed scalable circuits for these states. Our achieved lower bounds match or exceed previously reported exact fidelities on superconducting systems for much smaller states. Furthermore, we provide evidence that for large Dicke states |$D^{N}_{N/2}\rangle$, we may resort to a GHZ-based approximate state preparation to achieve better fidelity. This work provides a path forward to benchmarking entanglement as NISQ devices improve in size and quality.
97 MATHEMATICS AND COMPUTING↗
Prepare Ground States of Highly Frustrated Magnetic Clusters on Quantum Computers
Solving challenging problems in physical, chemical, and materials sciences is one of the most promising applications of quantum utility that can be realized on current noisy hardware, considering (i) the direct map (encoding) from the quantum particles and their interactions to the qubits and their entangling gates and (ii) the rapidly improved quantum hardware and advanced error-mitigation techniques. Understanding quantum spin liquid in frustrated magnetic materials is a longstanding challenge in condensed matter physics and the nature of the ground-state phases is highly debated among researchers. Using IBM quantum computers with superconducting qubits, we implemented a variational quantum eigensolver (VQE) algorithm to prepare the ground states of two 12-site cluster approximations of these highly frustrated magnetic materials. The interaction graphs of the two corresponding Hamiltonians are (a) the six-pointed star graph (a unit cell of the kagome lattice) and (b) the cuboctahedral graph (the kagome on a sphere). These are also two instances of Quantum Max Cut problem. With the VQE based on the Hamiltonian variational ansatz acting on a valence bond solid initial trial state, we prepared the ground states and obtained the exact ground energy on simulator and high accuracy on noisy hardware. The deep ansatz necessary to reach the ground state of the cuboctahedral graph indicates that it is a hard instance of Quantum Max Cut.
Wang, Yan↗
Quantum logic gate synthesis as a Markov decision process
Reinforcement learning has witnessed recent applications to a variety of tasks in quantum programming. The underlying assumption is that those tasks could be modeled as Markov decision processes (MDPs). Here, we investigate the feasibility of this assumption by exploring its consequences for single-qubit quantum state preparation and gate compilation. By forming discrete MDPs, we solve for the optimal policy exactly through policy iteration. We find optimal paths that correspond to the shortest possible sequence of gates to prepare a state or compile a gate, up to some target accuracy. Our method works in both the absence and presence of noise and compares favorably to other quantum compilation methods, such as the Ross–Selinger algorithm. This work provides theoretical insight into why reinforcement learning may be successfully used to find optimally short gate sequences in quantum programming.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Decomposition of high-rank factorized unitary coupled-cluster operators using ancilla and multiqubit controlled low-rank counterparts
The factorized form of the unitary coupled-cluster (UCC) approximation is one of the most promising methodologies to prepare trial states for strongly correlated systems within the variational quantum eigensolver framework. The factorized form of the UCC Ansatz can be systematically applied to a reference state to generate the desired entanglement. The difficulty associated with such an approach is the requirement of simultaneously entangling a growing number of qubits, which quickly exceeds the hardware limitations of today's quantum machines. In particular, while circuits for singles and double excitations can be performed on current hardware, higher-rank excitations require too many gate operations. In this work, we propose a set of schemes that trade off using extra qubits for a reduced gate depth to decompose high-rank UCC excitation operators into significantly lower depth circuits. These results will remain useful even when fault-tolerant machines are available to reduce the overall state-preparation circuit depth.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Classical and quantum computing of shear viscosity for ( 2 + 1 ) D SU(2) gauge theory
We perform a nonperturbative calculation of the shear viscosity for ( 2 + 1 )-dimensional SU(2) gauge theory by using the lattice Hamiltonian formulation. The retarded Green’s function of the stress-energy tensor is calculated from real time evolution via exact diagonalization of the lattice Hamiltonian with a local Hilbert space truncation, and the shear viscosity is obtained via the Kubo formula. When taking the continuum limit, we account for the renormalization group flow of the coupling but no additional operator renormalization. We find the ratio of the shear viscosity and the entropy density η s is consistent with a well-known holographic result 1 4 π at several temperatures on a 4 × 4 honeycomb lattice with the local electric representation truncated at j max = 1 2 . We also find the ratio of the spectral function and frequency ρ x y ( ω ) ω exhibits a peak structure when the frequency is small. Both the exact diagonalization method and simple matrix product state classical simulation method beyond j max = 1 2 on bigger lattices require exponentially growing resources. So we develop a quantum computing method to calculate the retarded Green’s function and analyze various systematics of the calculation including j max truncation and finite size effects, Trotter errors and the thermal state preparation efficiency. Our thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature. We test our quantum circuit on both the Quantinuum emulator and the IBM simulator for a small lattice and obtain results consistent with the classical computing ones. Published by the American Physical Society 2024
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Manipulating Growth and Propagation of Correlations in Dipolar Multilayers: From Pair Production to Bosonic Kitaev Models
Here, we study the nonequilibrium dynamics of dipoles confined in multiple stacked two-dimensional layers realizing a long-range interacting quantum spin 1/2 XXX model. We demonstrate that strong in-plane interactions can protect a manifold of collective layer dynamics. This then allows us to map the many-body spin dynamics to bosonic models. In a bilayer configuration we show how to engineer the paradigmatic two-mode squeezing Hamiltonian known from quantum optics, resulting in exponential production of entangled pairs and generation of metrologically useful entanglement from initially prepared product states. In multilayer configurations we engineer a bosonic variant of the Kitaev model displaying chiral propagation along the layer direction. Our study illustrates how the control over interactions, lattice geometry, and state preparation in interacting dipolar systems uniquely afforded by AMO platforms such as Rydberg and magnetic atoms, polar molecules, or trapped ions allows for the control over the temporal and spatial propagation of correlations for applications in quantum sensing and quantum simulation.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Inferring Quantum Network Topology Using Local Measurements
Statistical correlations that can be generated across the nodes in a quantum network depend crucially on its topology. However, this topological information might not be known a priori, or it may need to be verified. In this paper, we propose an efficient protocol for distinguishing and inferring the topology of a quantum network. We leverage entropic quantities-namely, the von Neumann entropy and the measured mutual information-as well as measurement covariance to uniquely characterize the topology. We show that the entropic quantities are sufficient to distinguish two networks that prepare GHZ states. Moreover, if qubit measurements are available, both entropic quantities and covariance can be used to infer the network topology without state-preparation assumptions. We show that the protocol can be entirely robust to noise and can be implemented via quantum variational optimization. Numerical experiments on both classical simulators and quantum hardware show that covariance is generally more reliable for accurately and efficiently inferring the topology, whereas entropy-based methods are often better at identifying the absence of entanglement in the low-shot regime.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
High-performance silicon photonic single-sideband modulators for cold-atom interferometry
The laser system is the most complex component of a light-pulse atom interferometer (LPAI), controlling frequencies and intensities of multiple laser beams to configure quantum gravity and inertial sensors. Its main functions include cold-atom generation, state preparation, state-selective detection, and generating a coherent two-photon process for the light-pulse sequence. To achieve substantial miniaturization and ruggedization, we integrate key laser system functions onto a photonic integrated circuit. Our study focuses on a high-performance silicon photonic suppressed-carrier single-sideband (SC-SSB) modulator at 1560 nanometers, capable of dynamic frequency shifting within the LPAI. By independently controlling radio frequency (RF) channels, we achieve 30-decibel carrier suppression and unprecedented 47.8-decibel sideband suppression at peak conversion efficiency of –6.846 decibels (20.7%). We investigate imbalances in both amplitudes and phases between the RF signals. Using this modulator, we demonstrate cold-atom generation, state-selective detection, and atom interferometer fringes to estimate gravitational acceleration, g ≈ 9.77 ± 0.01 meters per second squared, in a rubidium ( 87 Rb) atom system.
47 OTHER INSTRUMENTATION↗
Adiabatic quantum imaginary time evolution
We introduce an adiabatic state preparation protocol which implements quantum imaginary time evolution under the Hamiltonian of the system. Unlike the original quantum imaginary time evolution algorithm, adiabatic quantum imaginary time evolution does not require quantum state tomography during its runtime and, unlike standard adiabatic state preparation, the final Hamiltonian is not the system Hamiltonian. Instead, the algorithm obtains the adiabatic Hamiltonian by integrating a classical differential equation that ensures that one follows the imaginary time evolution state trajectory. We introduce some heuristics that allow this protocol to be implemented on quantum architectures with limited resources. We explore the performance of this algorithm via classical simulations in a one-dimensional spin model and highlight essential features that determine its cost, performance, and implementability for longer times, and compare to the original quantum imaginary time evolution for ground-state preparation. More generally, our algorithm expands the range of states accessible to adiabatic state preparation methods beyond those that are expressed as ground states of simple explicit Hamiltonians. Published by the American Physical Society 2024
Hejazi, Kasra (ORCID:000000032349478X)↗
Long-lived Bell states in an array of optical clock qubits
The generation of long-lived entanglement in optical atomic clocks is one of the main goals of quantum metrology. Arrays of neutral atoms, where Rydberg-based interactions may generate entanglement between individually controlled and resolved atoms, constitute a promising quantum platform to achieve this. Here we leverage the programmable state preparation afforded by optical tweezers and the efficient strong confinement of a three-dimensional optical lattice to prepare an ensemble of strontium-atom pairs in their motional ground state. We engineer global single-qubit gates on the optical clock transition and two-qubit entangling gates via adiabatic Rydberg dressing, enabling the generation of Bell states with a state-preparation-and-measurement-corrected fidelity of 92.8(2.0)% (87.1(1.6)% without state-preparation-and-measurement correction). For use in quantum metrology, it is furthermore critical that the resulting entanglement be long lived; we find that the coherence of the Bell state has a lifetime of 4.2(6) s via parity correlations and simultaneous comparisons between entangled and unentangled ensembles. Such long-lived Bell states can be useful for enhancing metrological stability and bandwidth. In the future, atomic rearrangement will enable the implementation of many-qubit gates and cluster state generation, as well as explorations of the transverse field Ising model.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Three-Photon Optical Pumping for Trapped Ion Quantum Computing
In this report we describe the testing of a novel scheme for state preparation of trapped ions in a quantum computing setup. This technique optimally would allow for similar precision and speed of state preparation while allowing for individual addressability of single ions in a chain using technology already available in a trapped ion experiment. As quantum computing experiments become more complicated, mid-experiment measurements will become necessary to achieve algorithms such as quantum error correction. Any mid-experiment measurement then requires the measured qubit to be re-prepared to a known quantum state. Currently this involves the protected qubits to be moved a sizeable distance away from the qubit being re-prepared which can be costly in terms of experiment length as well as introducing errors. Theoretical calculations predict that a three-photon process would allow for state preparation without qubit movement with similar efficiencies to current state preparation methods.
97 MATHEMATICS AND COMPUTING↗