We present an accreditation protocol for the outputs of noisy intermediate-scale quantum devices. By testing entire circuits rather than individual gates, our accreditation protocol can provide an upperbound on the variation distance between noisy and noiseless probability distribution of the outputs of the target circuit of interest. Our accreditation protocol requires implementing quantum circuits no larger than the target circuit, therefore it is practical in the near term and scalable in the long term. Inspired by trap-based protocols for the verification of quantum computations, our accreditation protocol assumes that single-qubit gates have bounded probability of error. We allow for arbitrary spatial and temporal correlations in the noise affecting state preparation, measurements, single-qubit and two-qubit gates. We describe how to implement our protocol on real-world devices, and we also present a novel cryptographic protocol (which we call 'mesothetic' protocol) inspired by our accreditation protocol. measure [34-38] single qubits, however recently a protocol for a fully classical verifier was devised that relies on the widely believed intractability of a computational problem for quantum computers [39]. Other protocols for classical verifiers have also been devised, but they require interaction with multiple entangled and noncommunicating provers [40][41][42][43][44]. Cryptographic protocols show that with minimal assumptions, verification of the outputs of quantum computations of arbitrary size can be done efficiently, in principle.In practice, implementing cryptographic protocols in experiments remains challenging, especially in the near term. In experiments all the operations are noisy, as in figure 1(b), and the verifier does not possess noiseless quantum devices. Thus, the verifiability of protocols requiring noiseless devices for the verifier is not guaranteed. Moreover, the concept of scalability, which is of primary interest in cryptographic protocols, is not equivalent to that of practicality, which is essential for experiments. For instance, suppose that the target circuit contains a few hundred qubits and a few hundred gates. Cryptographic protocols require implementing this circuit on a large cluster state containing thousands of qubits and entangling gates [26][27][28][29][30][31]34] or on two spatially-separated devices sharing thousands of copies of Bell states [40,41]; or appending several teleportation gadgets to the target circuit (one for each T-gate in the circuit and six for each Hadamard gate) [33]; or building Feynman-Kitaev clock states, which require entangling the system with an auxiliary qubit per gate in the target circuit [35,39,43]. These protocols are scalable, as they require a number of additional qubits, gates and measurements growing linearly with the size of the target circuit, yet they remain impractical for NISQ devices.In this paper we present an accreditation protocol that provides an upper-bound on the variation distance between noisy and noiseless probability di...

We present two verification protocols where the correctness of a "target" computation is checked by means of "trap" computations that can be efficiently simulated on a classical computer. Our protocols rely on a minimal set of noise-free operations (preparation of eight single-qubit states or measurement of four observables, both on a single plane of the Bloch sphere) and achieve linear overhead. To the best of our knowledge, our protocols are the least demanding techniques able to achieve linear overhead. They represent a step towards further reducing the quantum requirements for verification.

We provide and experimentally demonstrate an accreditation protocol that upper bounds the variation distance between noisy and noiseless probability distributions of the outputs of arbitrary quantum computations. We accredit the outputs of 24 quantum circuits executed on programmable superconducting hardware, ranging from depth-9 circuits on 10 qubits to depth-21 circuits on 4 qubits. Our protocol requires implementing the "target" quantum circuit along with a number of random Clifford circuits and subsequently postprocessing the outputs of these Clifford circuits. Importantly, the number of Clifford circuits is chosen to obtain the bound with the desired confidence and accuracy and is independent of the size and nature of the target circuit. We thus demonstrate a practical and scalable method of ascertaining the correctness of the outputs of arbitrary-sized noisy quantum computers-the ultimate arbiter of the utility of the computer itself.