Simply put, quantum computing differs from regular computing at a binary level. A computer that does not use quantum computing uses bits which have either 1 or 0, and a quantum computer uses qubits. When unobserved qubits, can have a state of anywhere between one and zero. This is called superposition.
To understand quantum computing and its relative threat to the bitcoin network, wallet addresses need to be broken into three categories. These are as follows, firstly, there are wallets that people are using to hold funds that have sent transactions previously. Secondly, wallets that have never sent a transaction, an example of this wallet can include some of Satoshi’s wallets or brand-new addresses. Thirdly, are wallets that are dormant and have sent transactions these include various wallets to which people have lost their private keys and do not have access.
Now that we have the three types of wallets, we can break down the ways quantum computing can crack the Bitcoin network. This can be broken down into two parts, cracking ECDSA/Schnorr signatures (digital signature algorithm) and cracking SHA-256 (hashing algorithm).
If quantum computing can crack ECDSA/Schnorr signatures, this will compromise every wallet that has sent transactions. Cracking the digital signature algorithm allows the quantum computer to use the public keys to trace back through the elliptic curve and figure out private keys, this would compromise every wallet that has sent transactions. If the digital signature algorithm is broken, to avoid losing funds, active wallets must upgrade and use a quantum secure algorithm to protect themselves. This would also mean the dormant wallets would not upgrade, and they would be claimed by the quantum computer.
Therefore, it is common security practice to only use a public key once. This gives you the security that if the digital signature algorithm is ever cracked, your funds in a new wallet that has not sent a transaction would be safe.
Moving onto the case of the hashing algorithm being cracked. If sha-256 is cracked, to send funds you would also need to crack the digital signature algorithm to send the funds. This way every wallet is threatened and the only way to prevent this is for wallets to move to a quantum secure digital signature algorithm.
