Trapped-ion Quantum Processors Research Articles

Non-Abelian topological order and anyons on a trapped-ion processor.

Non-Abelian topological order is a coveted state of matter with remarkable properties, including quasiparticles that can remember the sequence in which they are exchanged1-4. These anyonic excitations are promising building blocks of fault-tolerant quantum computers5,6. However, despite extensive efforts, non-Abelian topological order and its excitations have remained elusive, unlike the simpler quasiparticles or defects in Abelian topological order. Here we present the realization of non-Abelian topological order in the wavefunction prepared in a quantum processor and demonstrate control of its anyons. Using an adaptive circuit on Quantinuum's H2 trapped-ion quantum processor, we create the ground-state wavefunction of D4 topological order on a kagome lattice of 27 qubits, with fidelity per site exceeding 98.4 per cent. By creating and moving anyons along Borromean rings in spacetime, anyon interferometry detects an intrinsically non-Abelian braiding process. Furthermore, tunnelling non-Abelions around a torus creates all 22 ground states, as well as an excited state with a single anyon-a peculiar feature of non-Abelian topological order. This work illustrates the counterintuitive nature of non-Abelions and enables their study in quantum devices.

Quantum Deep Hedging

Quantum machine learning has the potential for a transformative impact across industry sectors and in particular in finance. In our work we look at the problem of hedging where deep reinforcement learning offers a powerful framework for real markets. We develop quantum reinforcement learning methods based on policy-search and distributional actor-critic algorithms that use quantum neural network architectures with orthogonal and compound layers for the policy and value functions. We prove that the quantum neural networks we use are trainable, and we perform extensive simulations that show that quantum models can reduce the number of trainable parameters while achieving comparable performance and that the distributional approach obtains better performance than other standard approaches, both classical and quantum. We successfully implement the proposed models on a trapped-ion quantum processor, utilizing circuits with up to 16 qubits, and observe performance that agrees well with noiseless simulation. Our quantum techniques are general and can be applied to other reinforcement learning problems beyond hedging.

Alignment between initial state and mixer improves QAOA performance for constrained optimization

Quantum alternating operator ansatz (QAOA) has a strong connection to the adiabatic algorithm, which it can approximate with sufficient depth. However, it is unclear to what extent the lessons from the adiabatic regime apply to QAOA as executed in practice with small to moderate depth. In this paper, we demonstrate that the intuition from the adiabatic algorithm applies to the task of choosing the QAOA initial state. Specifically, we observe that the best performance is obtained when the initial state of QAOA is set to be the ground state of the mixing Hamiltonian, as required by the adiabatic algorithm. We provide numerical evidence using the examples of constrained portfolio optimization problems with both low (p ≤ 3) and high (p = 100) QAOA depth. Additionally, we successfully apply QAOA with XY mixer to portfolio optimization on a trapped-ion quantum processor using 32 qubits and discuss our findings in near-term experiments.

Quantum Circuit Compiler for a Shuttling-Based Trapped-Ion Quantum Computer

The increasing capabilities of quantum computing hardware and the challenge of realizing deep quantum circuits require fully automated and efficient tools for compiling quantum circuits. To express arbitrary circuits in a sequence of native gates specific to the quantum computer architecture, it is necessary to make algorithms portable across the landscape of quantum hardware providers. In this work, we present a compiler capable of transforming and optimizing a quantum circuit targeting a shuttling-based trapped-ion quantum processor. It consists of custom algorithms set on top of the quantum circuit framework Pytket. The performance was evaluated for a wide range of quantum circuits and the results show that the gate counts can be reduced by factors up to 5.1 compared to standard Pytket and up to 2.2 compared to standard Qiskit compilation.

Robust two-qubit gates using pulsed dynamical decoupling

We present the experimental implementation of a two-qubit phase gate, using a radio frequency (RF) controlled trapped-ion quantum processor. The RF-driven gate is generated by a pulsed dynamical decoupling sequence applied to the ions’ carrier transitions only. It allows for a tunable phase shift with high-fidelity results. The conditional phase shift is measured using a Ramsey-type measurement with an inferred fringe contrast of up to . We also prepare a Bell state using this laser-free gate. The phase gate is robust against common sources of error. We investigate the effect of the excitation of the center-of-mass (COM) mode, errors in the axial trap frequency, pulse area errors and errors in sequence timing. The contrast of the phase gate is not significantly reduced up to a COM mode excitation 20 phonons, trap frequency errors of +10%, and pulse area errors of −8%. The phase shift is not significantly affected up to 10 phonons and pulse area errors of −2%. Both, contrast and phase shift are robust to timing errors up to −30% and +15%. The gate implementation is resource efficient, since only a single driving field is required per ion. Furthermore, it holds the potential for fast gate speeds (gate times on the order of 100 µs) by using two axial motional modes of a two-ion crystal through improved setups.

Quantum Simulations of Interacting Systems with Broken Time-Reversal Symmetry

Many-body systems of quantum interacting particles in which time-reversal symmetry is broken give rise to a variety of rich collective behaviors and are, therefore, a major target of research in modern physics. Quantum simulators can potentially be used to explore and understand such systems, which are often beyond the computational reach of classical simulation. Of these, platforms with universal quantum control can experimentally access a wide range of physical properties. However, simultaneously achieving strong programmable interactions, strong time-reversal symmetry breaking, and high-fidelity quantum control in a scalable manner is challenging. Here, we realize quantum simulations of interacting, time-reversal-broken quantum systems in a universal trapped-ion quantum processor. Using a recently proposed, scalable scheme, we implement time-reversal-breaking synthetic gauge fields, shown for the first time in a trapped-ion chain, along with unique coupling geometries, potentially extendable to simulation of multidimensional systems. Our high-fidelity single-site resolution in control and measurement, along with highly programmable interactions, allow us to perform full state tomography of a ground state showcasing persistent current and to observe dynamics of a time-reversal-broken system with nontrivial interactions. Our results open a path toward simulation of time-reversal-broken many-body systems with a wide range of features and coupling geometries.4 MoreReceived 4 July 2022Accepted 4 April 2023DOI:https://doi.org/10.1103/PhysRevX.13.021021Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum simulationQuantum verificationPhysical SystemsTrapped ionsAtomic, Molecular & OpticalQuantum Information

Sample-efficient verification of continuously-parameterized quantum gates for small quantum processors

Most near-term quantum information processing devices will not be capable of implementing quantum error correction and the associated logical quantum gate set. Instead, quantum circuits will be implemented directly using the physical native gate set of the device. These native gates often have a parameterization (e.g., rotation angles) which provide the ability to perform a continuous range of operations. Verification of the correct operation of these gates across the allowable range of parameters is important for gaining confidence in the reliability of these devices. In this work, we demonstrate a procedure for sample-efficient verification of continuously-parameterized quantum gates for small quantum processors of up to approximately 10 qubits. This procedure involves generating random sequences of randomly-parameterized layers of gates chosen from the native gate set of the device, and then stochastically compiling an approximate inverse to this sequence such that executing the full sequence on the device should leave the system near its initial state. We show that fidelity estimates made via this technique have a lower variance than fidelity estimates made via cross-entropy benchmarking. This provides an experimentally-relevant advantage in sample efficiency when estimating the fidelity loss to some desired precision. We describe the experimental realization of this technique using continuously-parameterized quantum gate sets on a trapped-ion quantum processor from Sandia QSCOUT and a superconducting quantum processor from IBM Q, and we demonstrate the sample efficiency advantage of this technique both numerically and experimentally.

Qubit-efficient simulation of thermal states with quantum tensor networks

We present a holographic quantum simulation algorithm to variationally prepare thermal states of $d$-dimensional interacting quantum many-body systems, using only enough hardware qubits to represent a $(d\ensuremath{-}1)$-dimensional cross section. This technique implements the thermal state by approximately unraveling the quantum matrix-product density operator (qMPDO) into a stochastic mixture of quantum matrix-product states (sto-qMPS). The parameters of the quantum circuits generating the qMPS and of the probability distribution generating the stochastic mixture are determined through a variational optimization procedure. We demonstrate a small-scale proof-of-principle demonstration of this technique on Quantinuum's trapped-ion quantum processor to simulate thermal properties of correlated spin chains over a wide temperature range using only a single pair of hardware qubits. Then, through classical simulations, we explore the representational power of two versions of sto-qMPS ansatzes for larger and deeper circuits and establish empirical relationships between the circuit resources and the accuracy of the variational free energy.

Holographic dynamics simulations with a trapped-ion quantum computer

Quantum computers promise to efficiently simulate quantum dynamics, a classically intractable task central to fields ranging from chemistry to high-energy physics. Yet, quantum computational advantage has only been demonstrated for artificial tasks such as random circuit sampling, and hardware limitations and noise have limited experiments to qualitative studies of small-scale systems. Quantum processors capable of high-fidelity measurements and qubit reuse enable a recently proposed holographic technique that employs quantum tensor-network states, a class of states that efficiently compress quantum data, to simulate the evolution of infinitely long, entangled initial states using a small number of qubits. Here we benchmark this holographic technique in a trapped-ion quantum processor using 11 qubits to simulate the dynamics of an infinite entangled state. We observe the hallmarks of quantum chaos and light-cone propagation of correlations, and find excellent quantitative agreement with theoretical predictions for the infinite-size limit of the implemented model with minimal post-processing or error mitigation. These results show that quantum tensor-network methods, paired with state-of-the-art quantum processor capabilities, offer a viable route to practical quantum computational advantage on problems of direct interest to science and technology in the near term.

Holographic Simulation of Correlated Electrons on a Trapped-Ion Quantum Processor

A quantum tensor network method is introduced to approximately compute the properties of interacting many-electron models, reducing the quantum memory size required to simulate complex materials and molecules and shortening the computation time.

Efficient realization of quantum primitives for Shor's algorithm using PennyLane library.

Efficient realization of quantum algorithms is among main challenges on the way towards practical quantum computing. Various libraries and frameworks for quantum software engineering have been developed. Here we present a software package containing implementations of various quantum gates and well-known quantum algorithms using PennyLane library. Additoinally, we used a simplified technique for decomposition of algorithms into a set of gates which are native for trapped-ion quantum processor and realized this technique using PennyLane library. The decomposition is used to analyze resources required for an execution of Shor's algorithm on the level of native operations of trapped-ion quantum computer. Our original contribution is the derivation of coefficients needed for implementation of the decomposition. Templates within the package include all required elements from the quantum part of Shor's algorithm, specifically, efficient modular exponentiation and quantum Fourier transform that can be realized for an arbitrary number of qubits specified by a user. All the qubit operations are decomposed into elementary gates realized in PennyLane library. Templates from the developed package can be used as qubit-operations when defining a QNode.

Analytical and experimental study of center-line miscalibrations in Mølmer-Sørensen gates

A major challenge for the realization of useful universal quantum computers is achieving high fidelity two-qubit entangling gate operations. However, calibration errors can affect the quantum gate operations and limit their fidelity. To reduce such errors it is desirable to have an analytical understanding and quantitative predictions of the effects that miscalibrations of gate parameters have on the gate performance. In this work, we study a systematic perturbative expansion in miscalibrated parameters of the M\o{}lmer-S\o{}rensen entangling gate, which is widely used in trapped-ion quantum processors. Our analytical treatment particularly focuses on systematic center-line detuning miscalibrations. Via a unitary Magnus expansion, we compute the gate evolution operator, which allows us to obtain relevant key properties such as relative phases, electronic populations, quantum state purity and fidelities. These quantities, subsequently, are used to assess the performance of the gate using the fidelity of entangled states as performance metric. We verify the predictions from our model by benchmarking them against measurements in a trapped-ion quantum processor. The method and the results presented here can help design and calibrate high-fidelity gate operations of large-scale quantum computers.

Detecting Heat Leaks with Trapped Ion Qubits.

The concept of passivity has been conceived to set bounds on the evolution of microscopic systems initialized in thermal states. We experimentally demonstrate the utility of two frameworks, global passivity and passivity deformation, for the detection of coupling to a hidden environment. We employ a trapped-ion quantum processor, where system qubits undergoing unitary evolution may optionally be coupled to an unobserved environment qubit, resulting in a heat leak. Evaluating the measurement data from the system qubits only, we show that global passivity can verify the presence of a heat leak, which is not detectable by a microscopic equivalent of the second law of thermodynamics. Furthermore, we experimentally show that passivity deformation allows for even more sensitive detection of heat leaks, as compared to global passivity, and detect a heat leak with an error margin of 5.3 standard deviations, in a scenario where other tests fail.

Filtering variational quantum algorithms for combinatorial optimization

Current gate-based quantum computers have the potential to provide a computational advantage if algorithms use quantum hardware efficiently. To make combinatorial optimization more efficient, we introduce the filtering variational quantum eigensolver which utilizes filtering operators to achieve faster and more reliable convergence to the optimal solution. Additionally we explore the use of causal cones to reduce the number of qubits required on a quantum computer. Using random weighted MaxCut problems, we numerically analyze our methods and show that they perform better than the original VQE algorithm and the quantum approximate optimization algorithm. We also demonstrate the experimental feasibility of our algorithms on a Quantinuum trapped-ion quantum processor powered by Honeywell.

Quantum repetition codes as building blocks of large-period discrete time crystals

Discrete time crystals (DTCs) are nonequilibrium phases of matter with exotic observable dynamics. Among their remarkable features is their response to a periodic drive at a fraction of its frequency. Current successful experiments are however only limited to realizing DTCs with period-doubling and period-tripling observable dynamics, forming only a very small subset of DTC phases. Creating larger periodic DTCs in the lab remains a longstanding challenge, yet it is necessary for developing the technological applications of DTCs, e.g., as a quantum memory for highly-entangled qubits, or exploring interesting features beyond subharmonic dynamics, e.g., condensed matter phenomena in the time domain. By highlighting the connection between DTCs and quantum error correction, we devise a general and realistic scheme for building DTCs exhibiting any large period observable dynamics, which is observable even at sufficiently small system sizes. Our proposal uses an array of spin-1/2 chains to simulate a repetition code at the hardware level, which has essential properties to realize robust observable dynamics. It is readily implemented with existing superconducting or trapped-ion quantum processors, making new families of DTCs experimentally accessible in the immediate future.

High-fidelity laser-free universal control of trapped ion qubits

Universal control of multiple qubits-the ability to entangle qubits and to perform arbitrary individual qubit operations1-is a fundamental resource for quantum computing2, simulation3 and networking4. Qubits realized in trapped atomic ions have shown the highest-fidelity two-qubit entangling operations5-7 and single-qubit rotations8 so far. Universal control of trapped ion qubits has been separately demonstrated using tightly focused laser beams9-12 or by moving ions with respect to laser beams13-15, but at lower fidelities. Laser-free entangling methods16-20 may offer improved scalability by harnessing microwave technology developed for wireless communications, but so far their performance has lagged the best reported laser-based approaches. Here we demonstrate high-fidelity laser-free universal control of two trapped-ion qubits by creating both symmetric and antisymmetric maximally entangled states with fidelities of [Formula: see text] and [Formula: see text], respectively (68 per cent confidence level), corrected for initialization error. We use a scheme based on radiofrequency magnetic field gradients combined with microwave magnetic fields that is robust against multiple sources of decoherence and usable with essentially any trapped ion species. The scheme has the potential to perform simultaneous entangling operations on multiple pairs of ions in a large-scale trapped-ion quantum processor without increasing control signal power or complexity. Combining this technology with low-power laser light delivered via trap-integrated photonics21,22 and trap-integrated photon detectors for qubit readout23,24 provides an opportunity for scalable, high-fidelity, fully chip-integrated trapped-ion quantum computing.

Susceptibility of trapped-ion qubits to low-dose radiation sources

We experimentally study the real-time susceptibility of trapped-ion quantum systems to small doses of ionizing radiation. We expose an ion-trap apparatus to a variety of α, β, and γ sources and measure the resulting changes in trapped-ion qubit lifetimes, coherence times, gate fidelities, and motional heating rates. We found no quantifiable degradation of ion trap performance in the presence of low-dose radiation sources for any of the measurements performed. This finding is encouraging for the long-term prospects of using ion-based quantum information systems in extreme environments, indicating that much larger doses may be required to induce errors in trapped-ion quantum processors.

Experimental deterministic correction of qubit loss.

The successful operation of quantum computers relies on protecting qubits from decoherence and noise, which-if uncorrected-will lead to erroneous results. Because these errors accumulate during an algorithm, correcting them is a key requirement for large-scale and fault-tolerant quantum information processors. Besides computational errors, which can be addressed by quantum error correction1-9, the carrier of the information can also be completely lost or the information can leak out of the computational space10-14. It is expected that such loss errors will occur at rates that are comparable to those of computational errors. Here we experimentally implement a full cycle of qubit loss detection and correction on a minimal instance of a topological surface code15,16 in a trapped-ion quantum processor. The key technique used for this correction is a quantum non-demolition measurement performed via an ancillary qubit, which acts as a minimally invasive probe that detects absent qubits while imparting the smallest quantum mechanically possible disturbance to the remaining qubits. Upon detecting qubit loss, a recovery procedure is triggered in real time that maps the logical information onto a new encoding on the remaining qubits. Although the current demonstration is performed in a trapped-ion quantum processor17, the protocol is applicable to other quantum computing architectures and error correcting codes, including leading two- and three-dimensional topological codes. These deterministic methods provide a complete toolbox for the correction of qubit loss that, together with techniques that mitigate computational errors, constitute the building blocks of complete and scalable quantum error correction.

Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer

The quantum walk formalism is a widely used and highly successful framework for modeling quantum systems, such as simulations of the Dirac equation, different dynamics in both the low and high energy regime, and for developing a wide range of quantum algorithms. Here we present the circuit-based implementation of a discrete-time quantum walk in position space on a five-qubit trapped-ion quantum processor. We encode the space of walker positions in particular multi-qubit states and program the system to operate with different quantum walk parameters, experimentally realizing a Dirac cellular automaton with tunable mass parameter. The quantum walk circuits and position state mapping scale favorably to a larger model and physical systems, allowing the implementation of any algorithm based on discrete-time quantum walks algorithm and the dynamics associated with the discretized version of the Dirac equation.

Probabilistic eigensolver with a trapped-ion quantum processor

Quantum simulation of complex quantum systems and their properties often requires the ability to prepare initial states in an eigenstate of the Hamiltonian to be simulated. In addition, to compute the eigenvalues of a Hamiltonian is in general a non-trivial problem. Here, we propose a hybrid quantum-classical probabilistic method to compute eigenvalues and prepare eigenstates of Hamiltonians which are simulatable with a trapped-ion quantum processor.