Verification in quantum computations is crucial since quantum systems are extremely vulnerable to the environment. However, verifying directly the output of a quantum computation is difficult since we know that efficiently simulating a large-scale quantum computation on a classical computer is usually thought to be impossible. To overcome this difficulty, we propose a self-testing system for quantum computations, which can be used to verify if a quantum computation is performed correctly by itself. Our basic idea is using some extra ancilla qubits to test the output of the computation. We design two kinds of permutation circuits into the original quantum circuit: one is applied on the ancilla qubits whose output indicates the testing information, the other is applied on all qubits (including ancilla qubits) which is aiming to uniformly permute the positions of all qubits. We show that both permutation circuits are easy to achieve. By this way, we prove that any quantum computation has an efficient self-testing system. In the end, we also discuss the relation between our self-testing system and interactive proof systems, and show that the two systems are equivalent if the verifier is allowed to have some quantum capacity.
Verification in quantum computations is crucial since quantum systems are extremely vulnerable to the environment. However, verifying directly the output of a quantum computation is difficult since we know that efficiently simulating a large-scale quantum computation on a classical computer is usually thought to be impossible. To overcome this difficulty, we propose a self-testing system for quantum computations, which can be used to verify if a quantum computation is performed correctly by itself. Our basic idea is using some extra ancilla qubits to test the output of the computation. We design two kinds of permutation circuits into the original quantum circuit: one is applied on the ancilla qubits whose output indicates the testing information, the other is applied on all qubits (including ancilla qubits) which is aiming to uniformly permute the positions of all qubits. We show that both permutation circuits are easy to achieve. By this way, we prove that any quantum computation has an efficient self-testing system. In the end, we also discuss the relation between our self-testing system and interactive proof systems, and show that the two systems are equivalent if the verifier is allowed to have some quantum capacity.
We prove that a quantum circuit together with measurement apparatuses and EPR sources can be fully verified without any reference to some other trusted set of quantum devices. Our main assumption is that the physical system we are working with consists of several identifiable sub-systems, on which we can apply some given gates locally. To achieve our goal we define the notions of simulation and equivalence. The concept of simulation refers to producing the correct probabilities when measuring physical systems. To enable the efficient testing of the composition of quantum operations, we introduce the notion of equivalence. Unlike simulation, which refers to measured quantities (i.e., probabilities of outcomes), equivalence relates mathematical objects like states, subspaces or gates. Using these two concepts, we prove that if a system satisfies some simulation conditions, then it is equivalent to the one it is purposed to implement. In addition, with our formalism, we can show that these statements are robust, and the degree of robustness can be made explicit (unlike the robustness results of [DMMS00]). In particular, we also prove the robustness of the EPR Test [MY98]. Finally, we design a test for any quantum circuit whose complexity is linear in the number of gates and qubits, and polynomial in the required precision.
Formal verification of quantum circuits is a crucial step towards building reliable quantum computers. However, the exponential scaling of quantum states makes traditional formal verification methods impractical for anything beyond small circuits. This paper proposes a novel approach leveraging self-referential quantum circuits for verification. The core idea is to create a verification circuit that recursively simulates and verifies the behavior of the original circuit. This self-referential process allows for a more efficient exploration of the state space, mitigating the exponential growth problem. We define the key components of this system, including the self-referential circuit architecture and the underlying mathematical framework. The paper outlines the potential for this approach to overcome limitations of existing techniques and represents a significant advancement in the field of quantum verification. The primary mathematical challenge addressed is the efficient simulation of quantum circuits within a self-referential structure.
Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations, and plays an important role in device-independent quantum information processing as well as quantum complexity theory. Prior works on self-testing require the assumption that the system's state is shared among multiple parties that only perform local measurements and cannot communicate. Here, we replace the setting of multiple non-communicating parties, which is difficult to enforce in practice, by a single computationally bounded party. Specifically, we construct a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a change of basis applied to both the device's state and measurements. This means that under computational assumptions, the verifier is able to certify the presence of entanglement, a property usually closely associated with two separated subsystems, inside a single quantum device. To achieve this, we build on techniques first introduced by Brakerski et al. (2018) and Mahadev (2018) which allow a classical verifier to constrain the actions of a quantum device assuming the device does not break post-quantum cryptography.
Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations, and plays an important role in device-independent quantum information processing as well as quantum complexity theory. Prior works on self-testing require the assumption that the system’s state is shared among multiple parties that only perform local measurements and cannot communicate. Here, we replace the setting of multiple non-communicating parties, which is difficult to enforce in practice, by a single computationally bounded party. Specifically, we construct a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a change of basis applied to both the device’s state and measurements. This means that under computational assumptions, the verifier is able to certify the presence of entanglement, a property usually closely associated with two separated subsystems, inside a single quantum device. To achieve this, we build on techniques first introduced by Brakerski et al. (2018) and Mahadev (2018) which allow a classical verifier to constrain the actions of a quantum device assuming the device does not break post-quantum cryptography.
Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations, and plays an important role in device-independent quantum information processing as well as quantum complexity theory. Prior works on self-testing require the assumption that the system’s state is shared among multiple parties that only perform local measurements and cannot communicate. Here, we replace the setting of multiple non-communicating parties, which is difficult to enforce in practice, by a single computationally bounded party. Specifically, we construct a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a change of basis applied to both the device’s state and measurements. This means that under computational assumptions, the verifier is able to certify the presence of entanglement, a property usually closely associated with two separated subsystems, inside a single quantum device. To achieve this, we build on techniques first introduced by Brakerski et al. (2018) and Mahadev (2018) which allow a classical verifier to constrain the actions of a quantum device assuming the device does not break post-quantum cryptography.
In order to guarantee the output of a quantum computation, we usually assume that the component devices are trusted. However, when the total computation process is large, it is not easy to guarantee the whole system when we have scaling effects, unexpected noise, or unaccounted for correlations between several subsystems. If we do not trust the measurement basis or the prepared entangled state, we do need to be worried about such uncertainties. To this end, we propose a self-guaranteed protocol for verification of quantum computation under the scheme of measurement-based quantum computation where no prior-trusted devices (measurement basis or entangled state) are needed. The approach we present enables the implementation of verifiable quantum computation using the measurement-based model in the context of a particular instance of delegated quantum computation where the server prepares the initial computational resource and sends it to the client, who drives the computation by single-qubit measurements. Applying self-testing procedures, we are able to verify the initial resource as well as the operation of the quantum devices and hence the computation itself. The overhead of our protocol scales with the size of the initial resource state to the power of 4 times the natural logarithm of the initial state's size.