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As quantum processors grow, new performance benchmarks are required to capture the full quality of the devices at scale. While quantum volume is an excellent benchmark, it focuses on the highest quality subset of the device and so is unable to indicate the average performance over a large number of connected qubits. Furthermore, it is a discrete pass/fail and so is not reflective of continuous improvements in hardware nor does it provide quantitative direction to large-scale algorithms. For example, there may be value in error mitigated Hamiltonian simulation at scale with devices unable to pass strict quantum volume tests. Here we discuss a scalable benchmark which measures the fidelity of a connecting set of two-qubit gates over $N$ qubits by measuring gate errors using simultaneous direct randomized benchmarking in disjoint layers. Our layer fidelity can be easily related to algorithmic run time, via $\gamma$ defined in Ref.\cite{berg2022probabilistic} that can be used to estimate the number of circuits required for error mitigation. The protocol is efficient and obtains all the pair rates in the layered structure. Compared to regular (isolated) RB this approach is sensitive to crosstalk. As an example we measure a $N=80~(100)$ qubit layer fidelity on a 127 qubit fixed-coupling "Eagle" processor (ibm\_sherbrooke) of 0.26(0.19) and on the 133 qubit tunable-coupling "Heron" processor (ibm\_montecarlo) of 0.61(0.26). This can easily be expressed as a layer size independent quantity, error per layered gate (EPLG), which is here $1.7\times10^{-2}(1.7\times10^{-2})$ for ibm\_sherbrooke and $6.2\times10^{-3}(1.2\times10^{-2})$ for ibm\_montecarlo., Comment: 15 pages, 8 figures (including appendices)

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 such systems, fixed-frequency transmons are attractive due to their long coherence and noise immunity. However, scaling fixed-frequency architectures proves challenging due to precise relative frequency requirements. Here we employ 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 1000-qubit levels. Moving forward, we anticipate selective laser annealing to play a central role in scaling fixed-frequency architectures., Comment: 9 pages, 8 figures, Supplementary Information

Triple quantum dots (TQDs) are promising semiconductor spin qubits because of their all-electrical control via fast, tunable exchange interactions and immunity to global magnetic fluctuations. These qubits can experience strong transverse interaction with photons in the resonant exchange (RX) regime, when exchange is simultaneously active on both qubit axes. However, most theoretical work has been based on phenomenological Fermi-Hubbard models, which may not fully capture the complexity of the qubit spin-charge states in this regime. Here we investigate exchange in Si/SiGe and GaAs TQDs using full configuration interaction (FCI) calculations which better describe practical device operation. We show that high exchange operation in general, and the RX regime in particular, can differ significantly from simple models, presenting new challenges and opportunities for spin-photon coupling. We highlight the impact of device electrostatics and effective mass on exchange and identify a new operating point (XRX) where strong spin-photon coupling is most likely to occur in Si/SiGe TQDs. Based on our numerical results, we analyze the feasibility of a remote entanglement cavity iSWAP protocol and discuss design pathways for improving fidelity. Our analysis provides insight into the requirements for TQD spin-photon transduction and demonstrates more generally the necessity of accurate modeling of exchange in spin qubits., Comment: Published version: 25 pages, 9 figures

We show that the Randomized Benchmarking (RB) protocol is a convolution amenable to Fourier space analysis. By adopting the mathematical framework of Fourier transforms of matrix-valued functions on groups established in recent work from Gowers and Hatami [Sbornik: Mathematics 208, 1784 (2017)], we provide an alternative proof of Wallman's [Quantum 2, 47 (2018)] and Proctor's [Phys. Rev. Lett. 119, 130502 (2017)] bounds on the effect of gate-dependent noise on randomized benchmarking. We show explicitly that as long as our faulty gate-set is close to the targeted representation of the Clifford group, an RB sequence is described by the exponential decay of a process that has exactly two eigenvalues close to one and the rest close to zero. This framework also allows us to construct a gauge in which the average gate-set error is a depolarizing channel parameterized by the RB decay rates, as well as a gauge which maximizes the fidelity with respect to the ideal gate-set.

Current quantum computing architectures lack the size and fidelity required for universal fault-tolerant operation, limiting the practical implementation of key quantum algorithms to all but the smallest problem sizes. In this work we propose an alternative method for general-purpose quantum computation that is ideally suited for such "prethreshold" superconducting hardware. Computations are performed in the n-dimensional single-excitation subspace (SES) of a system of n tunably coupled superconducting qubits. The approach is not scalable, but allows many operations in the unitary group SU(n) to be implemented by a single application of the Hamiltonian, bypassing the need to decompose a desired unitary into elementary gates. This feature makes large, nontrivial quantum computations possible within the available coherence time. We show how to use a programmable SES chip to perform fast amplitude amplification and phase estimation, two versatile quantum subalgorithms. We also show that an SES processor is well suited for Hamiltonian simulation, specifically simulation of the Schrodinger equation with a real but otherwise arbitrary nxn Hamiltonian matrix. We discuss the utility and practicality of such a universal quantum simulator, and propose its application to the study of realistic atomic and molecular collisions., Comment: 25 pages

Parity measurement is a central tool to many quantum information processing tasks. In this Letter, we propose a method to directly measure two- and four-qubit parity with low overhead in hard- and software, while remaining robust to experimental imperfections. Our scheme relies on dispersive qubit-cavity coupling and photon counting that is sensitive only to intensity; both ingredients are widely realized in many different quantum computing modalities. For a leading technology in quantum computing, superconducting integrated circuits, we analyze the measurement contrast and the back action of the scheme and show that this measurement comes close enough to an ideal parity measurement to be applicable to quantum error correction., Comment: 5 pages + 7 pages supplementary, 4 figures + 2 figures supplementary

High-fidelity, efficient quantum nondemolition readout of quantum bits is integral to the goal of quantum computation. As superconducting circuits approach the requirements of scalable, universal fault tolerance, qubit readout must also meet the demand of simplicity to scale with growing system size. Here we propose a fast, high-fidelity, scalable measurement scheme based on the state-selective ring-up of a cavity followed by photodetection with the recently introduced Josephson photomultiplier (JPM), a current-biased Josephson junction. This scheme maps qubit state information to the binary digital output of the JPM, circumventing the need for room-temperature heterodyne detection and offering the possibility of a cryogenic interface to superconducting digital control circuitry. Numerics show that measurement contrast in excess of 95% is achievable in a measurement time of 140 ns. We discuss perspectives to scale this scheme to enable readout of multiple qubit channels with a single JPM., Comment: 14 pages, 8 figures

We propose a method for general-purpose quantum computation and simulation that is well suited for today's pre-threshold-fidelity superconducting qubits. This approach makes use of the $n$-dimensional single-excitation subspace (SES) of a system of $n$ tunably coupled qubits. It can be viewed as a nonscalable special case of the standard gate-based quantum computing model, but allows many operations in the unitary group SU($n$) to be implemented by a single application of the Hamiltonian. Our approach bypasses the need to decompose the evolution operator into elementary gates, making large, nontrivial computations possible without error correction. The method is especially well suited for universal quantum simulation, specifically simulation of the Schr\"odinger equation with a real but otherwise arbitrary $n \times n$ Hamiltonian. We argue that a 1000-qubit SES processor, which would require no known improvements in superconducting device technology and which could be built today, should be capable of achieving quantum speedup relative to a petaflop supercomputer. We speculate on the utility and practicality of such a universal quantum simulator., Comment: Superseded by arXiv:1505.04990

We describe the creation of nonclassical states of microwave radiation via ideal dichotomic single photon detection, i.e., a detector that only indicates presence or absence of photons. Ideally, such a detector has a back action in the form of the subtraction operator. Using the non-linearity of this back action, it is possible to create a large family of nonclassical states of microwave radiation, including squeezed and multi-component cat states, starting from a coherent state. We discuss the applicability of this protocol to current experimental designs of Josephson Photomultipliers (JPMs)., Comment: 7 pages, 4 figures

We describe the back action of microwave-photon detection via a Josephson photomultiplier (JPM), a superconducting qubit coupled strongly to a high-quality microwave cavity. The back action operator depends qualitatively on the duration of the measurement interval, resembling the regular photon annihilation operator at short interaction times and approaching a variant of the photon subtraction operator at long times. The optimal operating conditions of the JPM differ from those considered optimal for processing and storing of quantum information, in that a short $T_2$ of the JPM suppresses the cavity dephasing incurred during measurement. Understanding this back action opens the possibility to perform multiple JPM measurements on the same state, hence performing efficient state tomography., Comment: 16 pages, 14 figures

We introduce a protocol for the fast simulation of $n$-dimensional quantum systems on $n$-qubit quantum computers with tunable couplings. A mapping is given between the control parameters of the quantum computer and the matrix elements of $H_{\rm s}(t)$, an arbitrary, real, time-dependent $n\times n$ dimensional Hamiltonian that is simulated in the $n$-dimensional `single excitation' subspace of the quantum computer. A time-dependent energy/time rescaling minimizes the simulation time on hardware having a fixed coherence time. We demonstrate how three tunably coupled phase qubits simulate a three-channel molecular collision using this protocol, then study the simulation's fidelity as a function of total simulation time., Comment: 5 pages, 4 figures

There are well-known protocols for performing CNOT quantum logic with qubits coupled by particular high-symmetry (Ising or Heisenberg) interactions. However, many architectures being considered for quantum computation involve qubits or qubits and resonators coupled by more complicated and less symmetric interactions. Here we consider a widely applicable model of weakly but otherwise arbitrarily coupled two-level systems, and use quantum gate design techniques to derive a simple and intuitive CNOT construction. Useful variations and extensions of the solution are given for common special cases., Comment: 4 pages, Revtex

Josephson junctions have demonstrated enormous potential as qubits for scalable quantum computing architectures. Here we discuss the current approaches for making multi-qubit circuits and performing quantum information processing with them., Comment: NATO ASI book chapter, 24 pages

Many protocols for quantum computation require a quantum memory element to store qubits. We discuss the accuracy with which quantum states prepared in a Josephson junction qubit can be stored in a nanoelectromechanical resonator and then transfered back to the junction. We find that the fidelity of the memory operation depends on both the junction-resonator coupling strength and the location of the state on the Bloch sphere. Although we specifically focus on a large-area, current-biased Josesphson junction phase qubit coupled to the dilatational mode of a piezoelectric nanoelectromechanical disk resonator, many our results will apply to other qubit-oscillator models., Comment: 4 pages, Revtex