Accrediting outputs of noisy intermediate-scale quantum computing devices

Abstract

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...

Experimental accreditation of outputs of noisy quantum computers

“…In general, multicycle patterns [Fig. 6(b)] as well as patterns afflicting more than one qubit (such as those afflicting today's devices [22,37]) are detected with probability greater than 50% [24], and for these patterns we have p err < 2p inc .…”

“…This randomizes the noise to stochastic Pauli errors [4,10,24,[35][36][37]. The trap circuits are designed to detect these Pauli errors, meaning that any Pauli error alters their outputs with a probability of at least 50% [24].…”

“…To simplify the structure of the noise, a QOTP is appended to each cycle of one-qubit gates in all the circuits. This randomizes the noise into stochastic Pauli errors [4,10,24,35,36] and allows rewriting ρ (k) out as…”

“…Thus, it can detect noise (such as location-dependent noise acting on the whole register of qubits) that may arise when gates are put together to form a circuit and may be missed by the protocols for characterizing individual gates [14,[16][17][18][19][20][21][22][23]. An alternate accreditation protocol can detect even more complex noise such as temporally correlated qubit-environment couplings, albeit at the cost of looser bounds on the VD [24] (more details are in Sec. A3).…”

Verifying commuting quantum computations via fidelity estimation of weighted graph states

“…In fact, the verification of quantum computer has been actively studied as quantum characterization, verification, and validation 6 . From this importance, several efficient verification protocols have been proposed for various sub-universal quantum computing models [29][30][31][32][33]. However, there is a possibility that conjectures making classical simulations of these verifiable sub-universal models intractable will be rejected.…”