The execution of quantum circuits on real systems has largely been limited to those which are simply time-ordered sequences of unitary operations followed by a projective measurement.As hardware platforms for quantum computing continue to mature in size and capability, it is imperative to enable quantum circuits beyond their conventional construction. Here we break into the realm of dynamic quantum circuits on a superconducting-based quantum system. Dynamic quantum circuits involve not only the evolution of the quantum state throughout the computation, but also periodic measurements of a subset of qubits mid-circuit and concurrent processing of the resulting classical information within timescales shorter than the execution times of the circuits. Using noisy quantum hardware, we explore one of the most fundamental quantum algorithms, quantum phase estimation, in its adaptive version, which exploits dynamic circuits, and compare the results to a non-adaptive implementation of the same algorithm. We demonstrate that the version of real-time quantum computing with dynamic circuits can offer a substantial and tangible advantage when noise and latency are sufficiently low in the system, opening the door to a new realm of available algorithms on real quantum systems.
As superconducting quantum circuits scale to larger sizes, the problem of frequency crowding proves a formidable task. Here we present a solution for this problem in fixed-frequencyqubit architectures. By systematically adjusting qubit frequencies post-fabrication, we show a nearly ten-fold improvement in the precision of setting qubit frequencies. To assess scalability, we identify the types of ‚frequency collisions‘ that will impair a transmon qubit and cross-resonance gate architecture. Using statistical modeling, we compute the probability of evading all such conditions, as a function of qubit frequency precision. We find that without post-fabrication tuning, the probability of finding a workable lattice quickly approaches 0. However with the demonstrated precisions it is possible to find collision-free lattices with favorable yield. These techniques and models are currently employed in available quantum systems and will be indispensable as systems continue to scale to larger sizes.
Cross-resonance interactions are a promising way to implement all-microwave two-qubit gates with fixed-frequency qubits. In this work, we study the dependence of the cross-resonanceinteraction rate on qubit-qubit detuning and compare with a model that includes the higher levels of a transmon system. To carry out this study we employ two transmon qubits–one fixed frequency and the other flux tunable–to allow us to vary the detuning between qubits. We find that the interaction closely follows a three-level model of the transmon, thus confirming the presence of an optimal regime for cross-resonance gates.
Nonreciprocal microwave devices play several critical roles in high-fidelity, quantum-nondemolition (QND) measurement schemes. They separate input from output, impose unidirectionalrouting of readout signals, and protect the quantum systems from unwanted noise originated by the output chain. However, state-of-the-art, cryogenic circulators and isolators are disadvantageous in scalable superconducting quantum processors because they use magnetic materials and strong magnetic fields. Here, we realize an active isolator formed by coupling two nondegenerate Josephson mixers in an interferometric scheme. Nonreciprocity is generated by applying a phase gradient between the same-frequency pumps feeding the Josephson mixers, which play the role of the magnetic field in a Faraday medium. To demonstrate the applicability of this Josephson-based isolator for quantum measurements, we incorporate it into the output line of a superconducting qubit, coupled to a fast resonator and a Purcell filter. We also utilize a wideband, superconducting directional coupler for coupling the readout signals into and out of the qubit-resonator system and a quantum-limited Josephson amplifier for boosting the readout fidelity. By using this novel quantum setup, we demonstrate fast, high-fidelity, QND measurements of the qubit while providing more than 20 dB of protection against amplified noise reflected off the Josephson amplifier.
As quantum circuits increase in size, it is critical to establish scalable multiqubit fidelity metrics. Here we investigate three-qubit randomized benchmarking (RB) with fixed-frequencytransmon qubits coupled to a common bus with pairwise microwave-activated interactions (cross-resonance). We measure, for the first time, a three-qubit error per Clifford of 0.106 for all-to-all gate connectivity and 0.207 for linear gate connectivity. Furthermore, by introducing mixed dimensionality simultaneous RB — simultaneous one- and two-qubit RB — we show that the three-qubit errors can be predicted from the one- and two-qubit errors. However, by introducing certain coherent errors to the gates we can increase the three-qubit error to 0.302, an increase that is not predicted by a proportionate increase in the one- and two-qubit errors from simultaneous RB. This demonstrates three-qubit RB as a unique multiqubit metric.
We realize and characterize a quantum-limited, directional Josephson amplifier suitable for qubit readout. The device consists of two nondegenerate, three-wave-mixing amplifiers thatare coupled together in an interferometric scheme, embedded in a printed circuit board. Nonreciprocity is generated by applying a phase gradient between the same-frequency pumps feeding the device, which plays the role of the magnetic field in a Faraday medium. Directional amplification and reflection-gain elimination are induced via wave interference between multiple paths in the system. We measure and discuss the main figures of merit of the device and show that the experimental results are in good agreement with theory. An improved version of this directional amplifier is expected to eliminate the need for bulky, off-chip isolation stages that generally separate quantum systems and preamplifiers in high-fidelity, quantum-nondemolition measurement setups.
Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits.Before the full power of such machines will be available, near-term quantum devices will provide several hundred qubits and limited error correction. Still, there is a realistic prospect to run useful algorithms within the limited circuit depth of such devices. Particularly promising are optimization algorithms that follow a hybrid approach: the aim is to steer a highly entangled state on a quantum system to a target state that minimizes a cost function via variation of some gate parameters. This variational approach can be used both for classical optimization problems as well as for problems in quantum chemistry. The challenge is to converge to the target state given the limited coherence time and connectivity of the qubits. In this context, the quantum volume as a metric to compare the power of near-term quantum devices is discussed.
With focus on chemistry applications, a general description of variational algorithms is provided and the mapping from fermions to qubits is explained. Coupled-cluster and heuristic trial wave-functions are considered for efficiently finding molecular ground states. Furthermore, simple error-mitigation schemes are introduced that could improve the accuracy of determining ground-state energies. Advancing these techniques may lead to near-term demonstrations of useful quantum computation with systems containing several hundred qubits.
We demonstrate a pogo pin package for a superconducting quantum processor specifically designed with a nontrivial layout topology (e.g., a center qubit that cannot be accessed fromthe sides of the chip). Two experiments on two nominally identical superconducting quantum processors in pogo packages, which use commercially available parts and require modest machining tolerances, are performed at low temperature (10 mK) in a dilution refrigerator and both found to behave comparably to processors in standard planar packages with wirebonds where control and readout signals come in from the edges. Single- and two-qubit gate errors are also characterized via randomized benchmarking. More detailed crosstalk measurements indicate levels of crosstalk less than -40 dB at the qubit frequencies, opening the possibility of integration with extensible qubit architectures.
Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstratedin many physical systems by observing and correcting storage errors, but applications require not just storing information; we must accurately compute even with faulty operations. The theory of fault-tolerant quantum computing illuminates a way forward by providing a foundation and collection of techniques for limiting the spread of errors. Here we implement one of the smallest quantum codes in a five-qubit superconducting transmon device and demonstrate fault-tolerant state preparation. We characterize the resulting codewords through quantum process tomography and study the free evolution of the logical observables. Our results are consistent with fault-tolerant state preparation in a protected qubit subspace.
Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performancecomputing resources. Finding exact numerical solutions to these interacting fermion problems has exponential cost, while Monte Carlo methods are plagued by the fermionic sign problem. These limitations of classical computational methods have made even few-atom molecular structures problems of practical interest for medium-sized quantum computers. Yet, thus far experimental implementations have been restricted to molecules involving only Period I elements. Here, we demonstrate the experimental optimization of up to six-qubit Hamiltonian problems with over a hundred Pauli terms, determining the ground state energy for molecules of increasing size, up to BeH2. This is enabled by a hardware-efficient quantum optimizer with trial states specifically tailored to the available interactions in our quantum processor, combined with a compact encoding of fermionic Hamiltonians and a robust stochastic optimization routine. We further demonstrate the flexibility of our approach by applying the technique to a problem of quantum magnetism. Across all studied problems, we find agreement between experiment and numerical simulations with a noisy model of the device. These results help elucidate the requirements for scaling the method to larger systems, and aim at bridging the gap between problems at the forefront of high-performance computing and their implementation on quantum hardware.