We consider the problem of classical strong (amplitude-wise) simulation of n-qubit quantum circuits, and identify a subclass of simulators we call monotone. This subclass encompasses almost all prominent simulation techniques. We prove an unconditional (i.e. without relying on any complexitytheoretic assumptions) and explicit (n – 2)(2n–3 – 1) lower bound on the running time of simulators within this subclass. Assuming the Strong Exponential Time Hypothesis (SETH), we further remark that a universal simulator computing any amplitude to precision 2–n/2 must take at least 2n–o(n) time. We then compare strong simulators to existing SAT solvers, and identify the time-complexity below which a strong simulator would improve on state-of-the-art general SAT solving. Finally, we investigate Clifford+T quantum circuits with t T-gates. Using the sparsification lemma, we identify a time complexity lower bound of 2.2451×10–8t below which a strong simulator would improve on state-of-the-art 3-SAT solving. This also yields a conditional exponential lower bound on the growth of the stabilizer rank of magic states.

A quantum instruction set is where quantum hardware and software meet. We develop characterization and compilation techniques for non-Clifford gates to accurately evaluate its designs. Applying these techniques to our fluxonium processor, we show that replacing the iSWAP gate by its square root SQiSW leads to a significant performance boost at almost no cost. More precisely, on SQiSW we measure a gate fidelity of up to 99.72% and averaging at 99.31%, and realize Haar random two-qubit gates with an average fidelity of 96.38%. This is an average error reduction of 41% for the former and a 50% reduction for the latter compared to using iSWAP on the same processor.

A function computation problem over a directed acyclic network has been considered in the literature, where a sink node is required to compute a target function correctly with the inputs arbitrarily generated at multiple source nodes. The network links are error-free but capacity-limited, and the intermediate nodes perform network coding. The computing rate of a network code is the average number of times that the target function is computed for one use of the network, i.e., each link in the network is used at most once. In the papers [1], [2], two cut-set bounds were proposed on the computing rate. However, we in this paper show that these bounds are not valid for general network function computation problems. We analyze the reason of the invalidity and propose a general cut-set bound by using a new equivalence relation associated with the inputs of the target function. Moreover, some results in [3], [4] were proved by applying the invalid upper bound in [1]. We also justify the validity of these results.

We give an arbitrary single-qubit gate compilation scheme on superconducting processors that takes advantage of tuning the phase shift of microwave pulses to obtain a continuous gate set. This scheme is compatible with any two-qubit gate, and we only need to calibrate the $X_{\pi }$ and $X_{\pi /2}$ pulses. We report an experimental implementation on a fluxonium device in [ Phys. Rev. Lett. 130, 070601 (2023)] and obtain state-of-the-art fidelities. We give two other schemes: the first requires one $X_{\pi }$ pulse and one pulse with a variable rotation angle, and the second requires four $X_{\pi /2}$ pulses. We also find that if we can do virtual $Z$ gates, then we can also do virtual gates around any axis. Our results apply to any physical platform that natively supports virtual $Z$.

Randomized benchmarking (RB) is the gold standard for experimentally evaluating the quality of quantum operations. The current framework for RB is centered on groups and their representations but this can be problematic. For example, Clifford circuits need up to $O(n^2)$ gates and thus Clifford RB cannot scale to larger devices. Attempts to remedy this include new schemes such as linear cross-entropy benchmarking (XEB), cycle benchmarking, and nonuniform RB but they do not fall within the group-based RB framework. In this work, we formulate the universal randomized benchmarking (URB) framework, which does away with the group structure and also replaces the recovery-gate-plus-measurement component with a general “postprocessing” positive operator-valued measurement (POVM). Not only does this framework cover most of the existing benchmarking schemes but it also gives the language for and helps inspire the formulation of new schemes. We specifically consider a class of URB schemes called twirling schemes. For twirling schemes, the postprocessing POVM approximately factorizes into an intermediate channel, inverting maps, and a final measurement. This leads us to study the twirling map corresponding to the gate ensemble specified by the scheme. We prove that if this twirling map is strictly within unit distance of the Haar twirling map in induced diamond norm, the probability of measurement as a function of gate length is a single exponential decay up to small error terms. The core technical tool we use is the matrix perturbation theory of linear operators on quantum channels.

The design and architecture of a quantum instruction set are paramount to the performance of a quantum computer. This work introduces a gate scheme for qubits with XX + YY coupling that directly and efficiently realizes any two-qubit gate up to single-qubit gates. First, this scheme enables high-fidelity execution of quantum operations, especially when decoherence is the primary error source. Second, since the scheme spans the entire SU(4) group of two-qubit gates, we can use it to attain the optimal two-qubit gate count for algorithm implementation. These two advantages in synergy give rise to a quantum Complex yet Reduced Instruction Set Computer (CRISC). Though the gate scheme is compact, it supports a comprehensive array of quantum operations. This may seem paradoxical but is realizable due to the fundamental differences between quantum and classical computer architectures. Using our gate scheme, we observe marked improvements across various applications, including generic n-qubit gate synthesis, quantum volume, and qubit routing. Furthermore, the proposed scheme also realizes a gate locally equivalent to the commonly used CNOT gate with a gate time of π/2g, where g is the two-qubit coupling. The AshN scheme is also completely impervious to ZZ error, the main coherent error in transversely coupled systems, as the control parameters implementing the gates can be easily adjusted to take the ZZ term into account.