Gate Error Research Articles

Coherent interaction of multistate quantum systems possessing the Wigner–Majorana and Morris–Shore dynamic symmetries with pulse trains

We present exact analytic formulae which describe the interaction of multistate quantum systems possessing the Wigner–Majorana and Morris–Shore dynamic symmetries with a train of pulses. The pulse train field can be viewed as repeated interactions of the quantum system with the same field and hence the overall propagator is expressed as the matrix power of the single-pulse propagator. Because of the symmetries the multistate dynamics is characterized by intrinsic two-state features, described by one or more pairs of complex-valued Cayley–Klein parameters. This facilitates the derivation of explicit formulae linking the single-step and multi-step propagators. The availability of such analytic relations opens the prospects for a variety of applications with ensembles of qubits, qutrits and generally qudits, e.g. analytic description of coherent pulse-train interactions, coherent amplification of quantum gate errors for accurate quantum gate tomography, dynamical rephasing of inhomogeneously broadened ensembles, quantum sensing of small electric or magnetic fields, etc.

Hardware Efficient Quantum Simulation of Non-Abelian Gauge Theories with Qudits on Rydberg Platforms.

Non-Abelian gauge theories underlie our understanding of fundamental forces in nature, and developing tailored quantum hardware and algorithms to simulate them is an outstanding challenge in the rapidly evolving field of quantum simulation. Here we take an approach where gauge fields, discretized in spacetime, are represented by qudits and are time evolved in Trotter steps with multiqudit quantum gates. This maps naturally and hardware efficiently to an architecture based on Rydberg tweezer arrays, where long-lived internal atomic states represent qudits, and the required quantum gates are performed as holonomic operations supported by a Rydberg blockade mechanism. We illustrate our proposal for a minimal digitization of SU(2) gauge fields, demonstrating a significant reduction in circuit depth and gate errors in comparison to a traditional qubit-based approach, which puts simulations of non-Abelian gauge theories within reach of NISQ devices.

Numerical Simulation of the Performance of Single Qubit Gates for Trapped Ions

Finite gate errors limit performance of modern quantum computers. In this work, we study single qubit gate fidelities for trapped ions. For this we have numerically solved Schrödinger equation using full Hamiltonian of the system for one, two, three and four ions. This approach allows us to analyze gate errors beyond the LambDicke approximation and to take into account not only a finite occupation of the phonon modes, but also the effects related to the ion–phonon entanglement. As a result, we show how infidelity of the global single qubit gates depend on the initial phonon mode occupations, the Lamb–Dicke parameter, Rabi frequency and the number of ions.

Cnot Gates for Fluxonium Qubits via Selective Darkening of Transitions

We analyze the cross-resonance effect for fluxonium circuits and investigate a two-qubit gate scheme based on selective darkening of a transition. In this approach, two microwave pulses at the frequency of the target qubit are applied simultaneously with a proper ratio between their amplitudes to achieve a controlled-NOT operation. We study in detail coherent gate dynamics and calculate gate error. With nonunitary effects accounted for, we demonstrate that gate error below $10^{-4}$ is possible for realistic hardware parameters. This number is facilitated by long coherence times of computational transitions and strong anharmonicity of fluxoniums, which easily prevents excitation to higher excited states during the gate microwave drive.

Fast Flux Entangling Gate for Fluxonium Circuits

We analyze a high-fidelity two-qubit gate using fast flux pulses on superconducting fluxonium qubits. The gate is realized by temporarily detuning magnetic flux through fluxonium loop away from the half flux quantum sweet spot. We simulate dynamics of two capacitively coupled fluxoniums during the flux pulses and optimize the pulse parameters to obtain a highly accurate $\sqrt{i\mathrm{swap}}$-like entangling gate. We also evaluate the effect of the flux noise and qubit relaxation on the gate fidelity. Our results demonstrate that the gate error remains below $10^{-4}$ for currently achievable magnitude of the flux noise and qubit relaxation time.

Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits.

Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron-electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. The transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

Realization of the iSWAP-like gate among the superconducting qutrits

High-dimensional quantum systems, such as qutrits (quantum three-level systems), have multiple accessible energy levels beyond the two-level qubits. Therefore, qutrits can offer a larger state space to improve the efficiency of quantum computation. Here, we demonstrate a high-fidelity iSWAP-like gate operation on a frequency-tunable superconducting qutrits system. The superconducting quantum system consists of two qutrits that are coupled via a resonator with fixed qutrit-resonator coupling strengths. Through designing the frequency pulse profile and optimizing the parameter values, the gate error can be suppressed below 1.5 × 10−3. To bear out the feasibility of the proposal, we have conducted our study with experimentally accessible parameters. As the resonator can mediate the interaction between the irrelevant qutrits, the presented approach can also be used to couple multiple qutrits together, providing a good platform for quantum information processing.

Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays

Executing quantum algorithms on error-corrected logical qubits is a critical step for scalable quantum computing, but the requisite numbers of qubits and physical error rates are demanding for current experimental hardware. Recently, the development of error correcting codes tailored to particular physical noise models has helped relax these requirements. In this work, we propose a qubit encoding and gate protocol for 171Yb neutral atom qubits that converts the dominant physical errors into erasures, that is, errors in known locations. The key idea is to encode qubits in a metastable electronic level, such that gate errors predominantly result in transitions to disjoint subspaces whose populations can be continuously monitored via fluorescence. We estimate that 98% of errors can be converted into erasures. We quantify the benefit of this approach via circuit-level simulations of the surface code, finding a threshold increase from 0.937% to 4.15%. We also observe a larger code distance near the threshold, leading to a faster decrease in the logical error rate for the same number of physical qubits, which is important for near-term implementations. Erasure conversion should benefit any error correcting code, and may also be applied to design new gates and encodings in other qubit platforms.

Blueprint for a High-Performance Fluxonium Quantum Processor

The technological development of hardware heading toward universal fault-tolerant quantum computation requires a large-scale processing unit with high performance. While fluxonium qubits are promising with high coherence and large anharmonicity, their scalability has not been systematically explored. In this work, we propose a superconducting quantum information processor based on compact high-coherence fluxoniums with suppressed crosstalk, reduced design complexity, improved operational efficiency, high-fidelity gates, and resistance to parameter fluctuations. In this architecture, the qubits are readout dispersively using individual resonators connected to a common bus and manipulated via combined on-chip RF and DC control lines, both of which can be designed to have low crosstalk. A multi-path coupling approach enables exchange interactions between the high-coherence computational states and at the same time suppresses the spurious static ZZ rate, leading to fast and high-fidelity entangling gates. We numerically investigate the cross resonance controlled-NOT and the differential AC-Stark controlled-Z operations, revealing low gate error for qubit-qubit detuning bandwidth of up to 1 GHz. Our study on frequency crowding indicates high fabrication yield for quantum processors consisting of over thousands of qubits. In addition, we estimate low resource overhead to suppress logical error rate using the XZZX surface code. These results promise a scalable quantum architecture with high performance for the pursuit of universal quantum computation.

Hamiltonian Engineering with Multicolor Drives for Fast Entangling Gates and Quantum Crosstalk Cancellation.

Quantum computers built with superconducting artificial atoms already stretch the limits of their classical counterparts. While the lowest energy states of these artificial atoms serve as the qubit basis, the higher levels are responsible for both a host of attractive gate schemes as well as generating undesired interactions. In particular, when coupling these atoms to generate entanglement, the higher levels cause shifts in the computational levels that lead to unwanted ZZ quantum crosstalk. Here, we present a novel technique to manipulate the energy levels and mitigate this crosstalk with simultaneous off-resonant drives on coupled qubits. This breaks a fundamental deadlock between qubit-qubit coupling and crosstalk. In a fixed-frequency transmon architecture with strong coupling and crosstalk cancellation, additional cross-resonance drives enable a 90ns CNOT with a gate error of (0.19±0.02)%, while a second set of off-resonant drives enables a novel CZ gate. Furthermore, we show a definitive improvement in circuit performance with crosstalk cancellation over seven qubits, demonstrating the scalability of the technique. This Letter paves the way for superconducting hardware with faster gates and greatly improved multiqubit circuit fidelities.

Gating failure can result in underestimation of cardiac function in myocardial perfusion scintigraphy

Here, we present a case with a pacemaker due to an atrioventricular (AV) block 2 Mobitz type, in whom a gating failure resulted in a relevant underestimation of cardiac function in myocardial perfusion scintigraphy. A set of quality control steps for gating errors is proposed.

Monitoring Fast Superconducting Qubit Dynamics Using a Neural Network

Weak measurements of a superconducting qubit produce noisy voltage signals that are weakly correlated with the qubit state. To recover individual quantum trajectories from these noisy signals, traditional methods require slow qubit dynamics and substantial prior information in the form of calibration experiments. Monitoring rapid qubit dynamics, e.g. during quantum gates, requires more complicated methods with increased demand for prior information. Here, we experimentally demonstrate an alternative method for accurately tracking rapidly driven superconducting qubit trajectories that uses a Long-Short Term Memory (LSTM) artificial neural network with minimal prior information. Despite few training assumptions, the LSTM produces trajectories that include qubit-readout resonator correlations due to a finite detection bandwidth. In addition to revealing rotated measurement eigenstates and a reduced measurement rate in agreement with theory for a fixed drive, the trained LSTM also correctly reconstructs evolution for an unknown drive with rapid modulation. Our work enables new applications of weak measurements with faster or initially unknown qubit dynamics, such as the diagnosis of coherent errors in quantum gates.

Greedy algorithm based circuit optimization for near-term quantum simulation

Simulating quantum systems is believed to be one of the most important applications of quantum computers. On noisy intermediate-scale quantum (NISQ) devices, the high-level circuit designed by quantum algorithms for Hamiltonian simulation needs to consider hardware limitations such as gate errors and circuit depth before it can be efficiently executed. In this work, we develop a hardware-agnostic circuit optimization algorithm to reduce the overall circuit cost for Hamiltonian simulation problems. Our method employ a novel sub-circuit synthesis in intermediate representation and propose a greedy ordering scheme for gate cancellation to minimize the gate count and circuit depth. To quantify the benefits of this approach, we benchmark proposed algorithm on different Hamiltonian models. Compared with state-of-the-art generic quantum compilers and specific quantum simulation compiler, the benchmarking results of our algorithm show an average reduction in circuit depth by 16.5× (up to 64.1×) and in gate count by 7.8× (up to 23.7×). This significant improvement helps enhance the performance of Hamiltonian simulation in the NISQ era.

Partial randomized benchmarking

In randomized benchmarking of quantum logical gates, partial twirling can be used for simpler implementation, better scaling, and higher accuracy and reliability. For instance, for two-qubit gates, single-qubit twirling is easier to realize than full averaging. We analyze such simplified, partial twirling and demonstrate that, unlike for the standard randomized benchmarking, the measured decay of fidelity is a linear combination of exponentials with different decay rates (3 for two qubits and single-bit twirling). The evolution with the sequence length is governed by an iteration matrix, whose spectrum gives the decay rates. For generic two-qubit gates one slowest exponential dominates and characterizes gate errors in three channels. Its decay rate is close, but different from that in the standard randomized benchmarking, and we find the leading correction. Using relations to the local invariants of two-qubit gates we identify all exceptional gates with several slow exponentials and analyze possibilities to extract their decay rates from the measured curves.

A Taxonomy of Small Markovian Errors

Errors in quantum logic gates are usually modeled by quantum process matrices (CPTP maps). But process matrices can be opaque, and unwieldy. We show how to transform a gate's process matrix into an error generator that represents the same information more usefully. We construct a basis of simple and physically intuitive elementary error generators, classify them, and show how to represent any gate's error generator as a mixture of elementary error generators with various rates. Finally, we show how to build a large variety of reduced models for gate errors by combining elementary error generators and/or entire subsectors of generator space. We conclude with a few examples of reduced models, including one with just $9N^2$ parameters that describes almost all commonly predicted errors on an N-qubit processor.

High-performance superconducting quantum processors via laser annealing of transmon qubits.

Scaling the number of qubits while maintaining high-fidelity quantum gates remains a key challenge for quantum computing. Presently, superconducting quantum processors with >50 qubits are actively available. For these systems, fixed-frequency transmons are attractive because of their long coherence and noise immunity. However, scaling fixed-frequency architectures proves challenging because of precise relative frequency requirements. Here, we use laser annealing to selectively tune transmon qubits into desired frequency patterns. Statistics over hundreds of annealed qubits demonstrate an empirical tuning precision of 18.5 MHz, with no measurable impact on qubit coherence. We quantify gate error statistics on a tuned 65-qubit processor, with median two-qubit gate fidelity of 98.7%. Baseline tuning statistics yield a frequency-equivalent resistance precision of 4.7 MHz, sufficient for high-yield scaling beyond 103 qubit levels. Moving forward, we anticipate selective laser annealing to play a central role in scaling fixed-frequency architectures.

High-fidelity magic-state preparation with a biased-noise architecture

Magic state distillation is a resource intensive subroutine that consumes noisy input states to produce high-fidelity resource states that are used to perform logical operations in practical quantum-computing architectures. The resource cost of magic state distillation can be reduced by improving the fidelity of the raw input states. To this end, we propose an initialization protocol that offers a quadratic improvement in the error rate of the input magic states in architectures with biased noise. This is achieved by preparing an error-detecting code which detects the dominant errors that occur during state preparation. We obtain this advantage by exploiting the native gate operations of an underlying qubit architecture that experiences biases in its noise profile. We perform simulations to analyze the performance of our protocol with the XZZX surface code. Even at modest physical parameters with a two-qubit gate error rate of $0.7\%$ and total probability of dominant errors in the gate $O(10^3)$ larger compared to that of non-dominant errors, we find that our preparation scheme delivers magic states with logical error rate $O(10^{-8})$ after a single round of the standard 15-to-1 distillation protocol; two orders of magnitude lower than using conventional state preparation. Our approach therefore promises considerable savings in overheads with near-term technology.

Flopping-Mode Electric Dipole Spin Resonance in Phosphorus Donor Qubits in Silicon

Single spin qubits based on phosphorus donors in silicon are a promising candidate for a large-scale quantum computer. Despite long coherence times, achieving uniform magnetic control remains a hurdle for scale-up due to challenges in high-frequency magnetic field control at the nanometre scale. Here, we present a proposal for a flopping-mode electric dipole spin resonance qubit based on the combined electron and nuclear spin states of a double phosphorus donor quantum dot. The key advantage of utilizing a donor-based system is that we can engineer the number of donor nuclei in each quantum dot. By creating multidonor dots with antiparallel nuclear spin states and multielectron occupation we can minimize the longitudinal magnetic field gradient, known to couple charge noise into the device and dephase the qubit. We describe the operation of the qubit and show that by minimizing the hyperfine interaction of the nuclear spins we can achieve $\ensuremath{\pi}/2\ensuremath{-}X$ gate error rates of about ${10}^{\ensuremath{-}4}$ using realistic noise models. We highlight that the low charge noise environment in these all-epitaxial phosphorus-doped silicon qubits will facilitate the realization of strong coupling of the qubit to superconducting microwave cavities, allowing for long-distance two-qubit operations.

High coherence and low cross-talk in a tileable 3D integrated superconducting circuit architecture

We report high qubit coherence as well as low cross-talk and single-qubit gate errors in a superconducting circuit architecture that promises to be tileable to two-dimensional (2D) lattices of qubits. The architecture integrates an inductively shunted cavity enclosure into a design featuring nongalvanic out-of-plane control wiring and qubits and resonators fabricated on opposing sides of a substrate. The proof-of-principle device features four uncoupled transmon qubits and exhibits average energy relaxation times T1 = 149(38) μs, pure echoed dephasing times Tϕ,e = 189(34) μs, and single-qubit gate fidelities F = 99.982(4)% as measured by simultaneous randomized benchmarking. The 3D integrated nature of the control wiring means that qubits will remain addressable as the architecture is tiled to form larger qubit lattices. Band structure simulations are used to predict that the tiled enclosure will still provide a clean electromagnetic environment to enclosed qubits at arbitrary scale.

Improving qubit coherence using closed-loop feedback

Superconducting qubits are a promising platform for building a larger-scale quantum processor capable of solving otherwise intractable problems. In order for the processor to reach practical viability, the gate errors need to be further suppressed and remain stable for extended periods of time. With recent advances in qubit control, both single- and two-qubit gate fidelities are now in many cases limited by the coherence times of the qubits. Here we experimentally employ closed-loop feedback to stabilize the frequency fluctuations of a superconducting transmon qubit, thereby increasing its coherence time by 26% and reducing the single-qubit error rate from (8.5 ± 2.1) × 10−4 to (5.9 ± 0.7) × 10−4. Importantly, the resulting high-fidelity operation remains effective even away from the qubit flux-noise insensitive point, significantly increasing the frequency bandwidth over which the qubit can be operated with high fidelity. This approach is helpful in large qubit grids, where frequency crowding and parasitic interactions between the qubits limit their performance.