Output State Fidelity Research Articles

Pauli Error Propagation-Based Gate Rescheduling for Quantum Circuit Error Mitigation

Noisy intermediate-scale quantum algorithms, which run on noisy quantum computers, should be carefully designed to boost the output state fidelity. While several compilation approaches have been proposed to minimize circuit errors, they often omit the detailed circuit structure information that does not affect the circuit depth or the gate count. In the presence of spatial variation in the error rate of the quantum gates, adjusting the circuit structure can play a major role in mitigating errors. In this article, we exploit the freedom of gate reordering based on the commutation rules to show the impact of gate error propagation paths on the output state fidelity of the quantum circuit, propose advanced predictive techniques to project the success rate of the circuit, and develop a new compilation phase postquantum circuit mapping to improve its reliability. Our proposed approaches have been validated using a variety of quantum circuits with different success metrics, which are executed on IBM quantum computers. Our results show that rescheduling quantum gates based on their error propagation paths can significantly improve the fidelity of the quantum circuit in the presence of variable gate error rates.

Effects of Quantum Noise on Quantum Approximate Optimization AlgorithmSupported by the National Key Research and Development Program of China (Grant No. 2016YFA0301700), the National Natural Science Foundation of China (Grants No. 11625419), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB24030600), and the Anhui Initiative in Quantum Information Technologies (Grant No. AHY080000).

The quantum-classical hybrid algorithm is a promising algorithm with respect to demonstrating the quantum advantage in noisy-intermediate-scale quantum (NISQ) devices. When running such algorithms, effects due to quantum noise are inevitable. In our work, we consider a well-known hybrid algorithm, the quantum approximate optimization algorithm (QAOA). We study the effects on QAOA from typical quantum noise channels, and produce several numerical results. Our research indicates that the output state fidelity, i.e., the cost function obtained from QAOA, decreases exponentially with respect to the number of gates and noise strength. Moreover, we find that when noise is not serious, the optimized parameters will not deviate from their ideal values. Our result provides evidence for the effectiveness of hybrid algorithms running on NISQ devices.

Quantum state correction using a measurement-based feedforward mechanism

One of the weaknesses of quantum optical state postselection schemes is the low success probability. Typically there is a trade-off between amplifier properties such as success probability and output state fidelity. However, here we present a state comparison amplifier for optical coherent states, which features an active measurement and feedforward mechanism to correct for errors made during the initial amplification. The simple and relatively low latency mechanism allows us to correct for a binary phase alphabet. We demonstrate a significant simultaneous improvement in the amplifier characteristic parameters: output state fidelity, correct state fraction, and success probability. This demonstrates that nondeterministic quantum amplification can be enhanced significantly by measurement and feedforward.

Protecting quantum memories using coherent parity check codes

Coherent parity check (CPC) codes are a new framework for the construction of quantum error correction codes that encode multiple qubits per logical block. CPC codes have a canonical structure involving successive rounds of bit and phase parity checks, supplemented by cross-checks to fix the code distance. In this paper, we provide a detailed introduction to CPC codes using conventional quantum circuit notation. We demonstrate the implementation of a CPC code on real hardware, by designing a [[4, 2, 2]] detection code for the IBM 5Q superconducting qubit device. Whilst the individual gate-error rates on the IBM device are too high to realise a fault tolerant quantum detection code, our results show that the syndrome information from a full encode–decode cycle of the [[4, 2, 2]] CPC code can be used to increase the output state fidelity by post-selection. Following this, we generalise CPC codes to other quantum technologies by showing that their structure allows them to be efficiently compiled using any experimentally realistic native two-qubit gate. We introduce a three-stage CPC design process for the construction of hardware-optimised quantum memories. As a proof-of-concept example, we apply our design process to an idealised linear seven-qubit ion trap. In the first stage of the process, we use exhaustive search methods to find a large set of [[7, 3, 3]] codes that saturate the quantum Hamming bound for seven qubits. We then optimise over the discovered set of codes to meet the hardware and layout demands of the ion trap device. We also discuss how the CPC design process will generalise to larger-scale codes and other qubit technologies.

Implementation of a quantum controlled-SWAP gate with photonic circuits

Quantum information science addresses how the processing and transmission of information are affected by uniquely quantum mechanical phenomena. Combination of two-qubit gates has been used to realize quantum circuits, however, scalability is becoming a critical problem. The use of three-qubit gates may simplify the structure of quantum circuits dramatically. Among them, the controlled-SWAP (Fredkin) gates are essential since they can be directly applied to important protocols, e.g., error correction, fingerprinting, and optimal cloning. Here we report a realization of the Fredkin gate for photonic qubits. We achieve a fidelity of 0.85 in the computational basis and an output state fidelity of 0.81 for a 3-photon Greenberger-Horne-Zeilinger state. The estimated process fidelity of 0.77 indicates that our Fredkin gate can be applied to various quantum tasks.

Improving ancilla states for quantum computation

We analyze the improvement in output state fidelity upon improving the construction accuracy of ancilla states. Specifically, we simulate gates and syndrome measurements on a single qubit of information encoded into the [[7,1,3]] quantum error correction code and determine the output state fidelity as a function of the accuracy with which Shor states (for syndrome measurements) and magic states (to implement T-gates) are constructed. When no syndrome measurements are applied during the gate sequence, we observe that the fidelity increases after performance of a T-gate and improving magic states construction slows the fidelity decay rate. In contrast, when syndrome measurements are applied, loss of fidelity occurs primarily after the syndrome measurements taken after a T-gate. Improving magic state construction slows the fidelity decay rate, and improving Shor state construction raises the initial fidelity but does not slow the fidelity decay rate. Along the way, we show that applying syndrome measurements after every gate does not maximize the output state fidelity. Rather, syndrome measurements should be applied sparingly.

Benchmarking a Quantum Teleportation Protocol in Superconducting Circuits Using Tomography and an Entanglement Witness

Teleportation of a quantum state may be used for distributing entanglement between distant qubits in quantum communication and for quantum computation. Here we demonstrate the implementation of a teleportation protocol, up to the single-shot measurement step, with superconducting qubits coupled to a microwave resonator. Using full quantum state tomography and evaluating an entanglement witness, we show that the protocol generates a genuine tripartite entangled state of all three qubits. Calculating the projection of the measured density matrix onto the basis states of two qubits allows us to reconstruct the teleported state. Repeating this procedure for a complete set of input states we find an average output state fidelity of 86%.

Discriminating quantum-optical beam-splitter channels with number-diagonal signal states: Applications to quantum reading and target detection

We consider the problem of distinguishing, with minimum probability of error, two optical beam-splitter channels with unequal complex-valued reflectivities using general quantum probe states entangled over M signal and M' idler mode pairs of which the signal modes are bounced off the beam splitter while the idler modes are retained losslessly. We obtain a lower bound on the output state fidelity valid for any pure input state. We define number-diagonal signal (NDS) states to be input states whose density operator in the signal modes is diagonal in the multimode number basis. For such input states, we derive series formulas for the optimal error probability, the output state fidelity, and the Chernoff-type upper bounds on the error probability. For the special cases of quantum reading of a classical digital memory and target detection (for which the reflectivities are real valued), we show that for a given input signal photon probability distribution, the fidelity is minimized by the NDS states with that distribution and that for a given average total signal energy N_s, the fidelity is minimized by any multimode Fock state with N_s total signal photons. For reading of an ideal memory, it is shown that Fock state inputs minimize the Chernoff bound. For target detection under high-loss conditions, a no-go result showing the lack of appreciable quantum advantage over coherent state transmitters is derived. A comparison of the error probability performance for quantum reading of number state and two-mode squeezed vacuum state (or EPR state) transmitters relative to coherent state transmitters is presented for various values of the reflectances. While the nonclassical states in general perform better than the coherent state, the quantitative performance gains differ depending on the values of the reflectances.

Drop-in compatible entanglement for optical-fiber networks

A growing number of quantum communication protocols require entanglement distribution among remote parties, which is best accomplished by exploiting the mature technology and extensive infrastructure of low-loss optical fiber. For this reason, a practical source of entangled photons must be drop-in compatible with optical fiber networks. Here we demonstrate such a source for the first time, in which the nonlinearity of standard single-mode fiber is utilized to yield entangled photon pairs in the 1310-nm O-band. Using an ultra-stable design, we produce polarization entanglement with 98.0% +/- 0.5% fidelity to a maximally entangled state as characterized via coincidence-basis tomography. To demonstrate the source's drop-in capability, we transmit one photon from each entangled pair through a telecommunications-grade optical amplifier set to boost classical 1550-nm (C-band) communication signals. We verify that the photon pairs experience no measurable decoherence upon passing through the active amplifier (the output state's fidelity with a maximally entangled state is 98.4% +/- 1.4%).